Global-Scale Modelling of the Land-Surface Water Balance

ACTA

UNIVERSITATIS

UPSALIENSIS

UPPSALA

2007

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 377

Global-Scale Modelling of theLand-Surface Water Balance

Development and Analysis of WASMOD-M

ELIN WIDÉN-NILSSON

ISSN 1651-6214ISBN 978-91-554-7051-7urn:nbn:se:uu:diva-8352

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Till Daniel

“We must devote more attention not only to the technical issues of hydrology raised by the model builders but also to encouraging and

preparing more young hydrologists to build a career in this direction. He who controls the future of global-scale models controls the direc-

tion of hydrology”

Peter S. Eagleson, 1986, The Emergence of Global-Scale Hydrology, Wa-ter resources research, 22(9): 6S-14S

”’It’s a little anxious,’ he said to himself, ‘to be a Very Small Animal Entirely Surrounded by Water’”

Piglet in Winnie-the-Pooh, A.A. Milne , 1926

List of papers

I Xu, C-Y., E. Widén, S. Halldin. 2005. Modelling hydrological conse-quences of climate change – progress and challenges. Advances in Atmospheric Sciences 22(6):789-797. © The Editorial office of Advances in Atmospheric Sciences (China) and Springer

II Widén-Nilsson, E., S. Halldin, C-Y. Xu. 2007. Global water-balance modelling with WASMOD-M: Parameter estimation and region-alisation. Journal of Hydrology. 340(1-2):105-118. doi:10.1016/j.jhydrol.2007.04.002 © Elsevier

III Widén-Nilsson E., L. Gong, S. Halldin, C-Y. Xu. 2007. Model perform-ance and parameter behavior for varying time aggregations and evaluation criteria in the WASMOD-M global water-balance model. Submitted to Water Resources Research in November 2007.

IV Gong L., E. Widén-Nilsson, S. Halldin, C-Y. Xu. 2007. Large-scale runoff routing with an aggregated time-delay-histogram method. Manuscript.

The Editorial Office of Advances in Atmospheric Sciences gave permission to reprint paper I and Elsevier (paper II) include publication in thesis in the authors retained rights.

In paper I, I drafted the section about global water balance modelling and contributed with references for the other sections. In paper II I made the data preparation, model codes, simulations, analysis and I was responsible for the writing. In paper III the second author made the first version of the simula-tion code and some of the data preparation, while I developed the code, made the simulations, and was responsible for the analysis. The writing was shared with the third author. The practical work of paper IV was performed by the first author, in discussions with me and the other co-authors.

Contents

Introduction...................................................................................................11

Global and continental runoff .......................................................................13 Global and continental runoff estimates...................................................13 Models that calculate global runoffs ........................................................16

Land-surface models and dynamic global vegetation models .............16 Two LSMs with hydrological focus ....................................................17 Routing models....................................................................................17 Global water balance models...............................................................19

Uncertainties of GCMs and LSMs and the effect in studies of hydrological impact of climate change ....................................................23

Methods ........................................................................................................25 Global data for WASMOD-M..................................................................25

Simulation time periods, model windup times and initial values ........27 WASMOD-M...........................................................................................28 Model parameter tuning of WASMOD-M in gauged areas .....................30

Criteria .................................................................................................31 Inter-station areas.................................................................................33

Regionalisation of WASMOD-M’s parameter values to ungauged areas34 Evaluation and validation of WASMOD-M ............................................34 Routing of daily runoff produced by WASMOD.....................................35

Site and data description......................................................................35 Resolutions ..........................................................................................35 Daily, distributed WASMOD ..............................................................36 Linear reservoir routing .......................................................................37 Time-delay-histogram routing .............................................................37 Velocity calibration .............................................................................38 Benchmark...........................................................................................39

Results...........................................................................................................40 Tuning and criteria ...................................................................................40 Parameter-value behaviour.......................................................................41 Time aggregation......................................................................................42 Regionalisation.........................................................................................43 Routing.....................................................................................................43

Validation .................................................................................................44 Within-year runoff patterns .................................................................44 Global and continental water balances ................................................45 Split-sample validation ........................................................................45 Comparison with other models ............................................................46

Discussion .....................................................................................................48 Data problems ..........................................................................................48

Geographical boundaries and positions ...............................................48 Inconsistent runoff and climate data and differing time periods .........48 Unknown and unavailable anthropogenic runoff influences. ..............49

Parameter behaviour.................................................................................50 Time aggregation and criteria relationships .............................................51 Validation .................................................................................................52

Within-year dynamics and split-sample validation .............................52 Comparison with other models and estimates .....................................53

Routing.....................................................................................................54

Conclusions...................................................................................................55 Possibilities for future work .....................................................................56

Acknowledgements.......................................................................................58

Sammanfattning på svenska (Summary in Swedish) ....................................62

References.....................................................................................................66

11

Introduction

Water is essential for life on earth. Humans need water for drinking, cooking and hygiene and indirectly for irrigation of crops, watering cattle, for indus-try and power plant usage. We also benefit from well-functioning ecological systems and excessive water withdrawal from rivers can cause collapses of some ecosystems. Today 1.1 billion people lack access to sufficient drinking water (WHO/UNICEF, 2000). This number and the extent of water scarce areas will increase with population growth and climate change (Vörösmarty et al., 2000a; Alcamo and Henrichs, 2002; Arnell, 2003). In addition to the predicted indirect human influence on the global hydrological cycle by emis-sions of greenhouse gasses, humans are known to directly influence by irri-gation, dams etc. (Vörösmarty et al., 2004; Gordon et al., 2005; Oki and Kanae, 2006, Haddeland et al., 2007). These global problems call for global models (Eagleson, 1986; Shuttleworth, 1988). The future is uncertain but projection of future water resources can be made and models are a useful tool for this. But can these models be trusted? What are their abilities to simulate current and future water resources? Do the models describe the reality in a realistic way, or are they too simplistic or overparameterised? Current models and data estimates differ around 30% in their estimates of the global runoff and up to 70% for individual continents (GRDC, 2004; paper II). Different time periods, varying methods of extrapolating data to ungauged areas and varying definitions on which runoff parts to include are some causes of these differences.

This thesis focuses on global water balance models. These models calcu-late runoff in all rivers around the world from climatic input such as precipi-tation and temperature. Calculations of evaporation and runoff are performed independently for individual grid cells, often sized 0.5° latitude × 0.5° longi-tude, and routed along flow networks to the river outlets. Thus, the models focus on renewable water resources. Many global models only calculate the amount, not the quality, of the runoff.

Environmental models are a representation of the reality, but they can never include all processes and they cannot be verified to be true since natu-ral systems never are closed (Oreskes et al., 1994). Oreskes et al. (1994) also argue against the usage of “validation”, but being such a commonly used word it is still used in this thesis, together with the more vague “evaluation”. Model simplifications is one source of model uncertainty, while others are measurement errors in input and validation data, miss-match between meas-

12

ured and model entities (the incommensurability problem), parameter errors and model structural errors. One effect of the uncertainties is equifinality, introduced to hydrological modelling community by Beven (1993), meaning that several parameter value combinations can produce equally good model results. Equifinality is an indication of an overparameterised model. It is also connected to the fact that a single representation of the system can not be found given the limitations of data (Beven, 2006). New processes are in-cluded in models to improve the results, but additional processes introduce additional parameters and these new parameters can often not be supported by the available data (Beven, 2006; 2007). The modelling done in this thesis was usually made with a wide range of parameter values to select sets that performed reasonably well, to take the equifinality into account.

The overall goal of the thesis was to calculate the global runoff variations in time and space. When the models get better in describing the current situations, they will also be more reliable tools to asses the effects on the global runoff of climate change, population growth, water withdrawal etc. The uncertainties in the global water balance models have thus been a focus of this work. The main tool has been the new, simple, global water balance model WASMOD-M. Compared to the catchment modelling community, there are few global water balance models, and the hypothesis was that a simple model would be useful to efficiently study model uncertainty. The construction of a new model could also be motivated by the advantages of model ensembles for future predictions. WASMOD-M will be able to con-tribute to analysis of present and future water resources. The overall objec-tive was approached in a series of steps to: � Review existing models (paper I; II) and their usage in climate studies

(paper I) as well as to review model and data-based estimates of the global water runoff (paper II) and compile published model errors (paper III).

� Develop a simple global water balance model, WASMOD-M (paper II; III).

� Develop a simple regionalisation methodology to extrapolate parameter values to ungauged areas and given the regionalisation, report global wa-ter balance estimates, with clear information on which parts that are in-cluded and not (paper II).

� Evaluate the performance and parameter values of WASMOD-M. Can one, or a very small number of parameter-value sets, be used to produce acceptable global and continental water balances (paper II)? Is the model, despite its simplicity, overparameterised (paper III)?

� Study the influence of different model evaluation measures, of both run-off and snow, and time aggregations on model tuning (paper III).

� Develop a river routing algorithm that is independent of the spatial resolu-tion (paper IV).

13

Global and continental runoff

Global and continental runoff estimates Estimates of the total global and continental runoffs can be based on gauge runoff data, precipitation minus evaporation (reanalysis) data, modelled run-off or remote sensing water estimates. Data and model-based runoff esti-mates are compiled in paper II and the complications in comparing these measurements are also discussed. One problem is that different continent boundaries are used. Oceania, e.g., is defined by different sources as includ-ing or excluding parts of Australia, New Zealand, Papua New Guinea and various small islands (e.g., Nijssen et al., 2001a). In addition to the border to Oceania, the borders of Asia with Europe often differ, e.g., by the assign-ment of Turkey (Nijssen et al., 2001a; Döll et al., 2003). The inclusion of whole Russia in Europe in the runoff estimate by FAO (2003) doubles the continents runoff although any influence on the higher Asian runoff in com-parsion with other estimates cannot be seen. Arctic areas (especially Antarc-tica and Greenland) are commonly excluded in modelling studies but in-cluded in data-based runoff estimates.

Runoff from rivers to oceans (exorheic) makes up the major part of the global runoff. Other contributions come from groundwater flow to oceans, river flow to inland basins (endorheic) and groundwater flow to inland ba-sins. Korzun et al. (1978) estimate the amount of river flow which evapo-rates and comes from percolation into rivers. It is not always clear which of these components are included in various global and continental runoff esti-mates (Table 1). Global runoff also varies with time (Probst and Tarty, 1987; Shiklomanov, 1997; Labat, 2006) and not all estimates include information about the time period for the calculation (Table 1). It was shown in paper II that the low runoff estimates of the LSMs (land-surface models) in the com-pilation by Oki et al. (2001) to a large degree is caused by the climate during their short simulation period. Regional and global trends in runoff and their possible relations to different forcings related to climatic warming are ana-lysed and debated (Labat et al., 2004; 2005; Legates et al., 2005; Milly et al., 2005; Shiklomanov et al., 2006; Gedney et al., 2006a; 2006b; Peel and McMahon, 2006; Piao et al., 2007).

14

The difference between the largest and smallest global runoff estimates in Table 1 exceeds the highest continental runoff estimate. Even if there is a general tendency that global runoff estimates based only on measurements are higher than modelled ones (Table 1), there are at least three reasons why the difference should be even larger (paper II). Runoff to internal basins (around 1000 km3yr-1) is commonly excluded in compilations of runoff measurements. There should also be a difference between those measure-ment compilations that include groundwater runoff into oceans and those that do not. Some of the measurement compilations include evaporation from rivers and dams, which is not included in any model with the exception of WGHM (Döll et al., 2003).

Apart from runoff from different continents, in km3yr-1 or mm, runoff can instead be presented as their ocean outlet (e.g., Fekete et al., 2002) or by latitude bands. In the latter case it is important to differentiate sums over the interior runoff generating cells and flow accumulated outlet cells. The first is smoothed and the latter peaked, especially at the outlet of the Amazon river. Baumgartner and Reichel (1975) present sums over interior runoff generat-ing cells, but Dai and Trenberth (2002) compare these with the summation over outlet cells.

Recent additions to the global water estimates come by remote sensing technologies. Levels of larger water bodies measured by satellite altimetry can be related to river flows through observed rating curves (Calmant and Seyler, 2006). The errors are in the order of decimetres or centimetres and the main disadvantage of the method is the low temporal resolution for many sites (Calmant and Seyler, 2006). The area of surface water extent is also measured and combined with altimetry measurements (Alsdorf and Letten-maier, 2003). River discharge can be calculated with reasonable accuracy without ground measurements from a combination of several space-based measures (Bjerklie et al., 2003). A more recent approach is measuring the temporal and spatial changes in Earth’s gravity by mass fluxes close to the earth surface and the GRACE (Gravity Recovery and Climate Experiment) satellite was lauched 2002 (Güntner et al., 2007a). The seasonal changes in total water storage can be tracked for continents and large river basins, but the division into separate compartments, such as snow, ice, lakes, soil mois-ture and groundwater is complicated (Güntner et al., 2007a). Simulations with simpler and more advanced LSMs/hydrological models and WGHM have been used to compare the GRACE data and to separate the different storage compartments (e.g., Andersen and Hinderer, 2005; Rodell et al., 2004; Ramillien et al., 2006; Schmidt et al., 2006; Swenson and Milly, 2006). The GRACE publications focus on changes in water storage and no global runoff estimate has yet been published to the author’s knowledge, but evaporation estimates, calculated with the usage of measured precipitation and simulated runoff, are reported for some basins (Rodell, et al., 2004; Ramillien et al., 2006).

15

Tabl

e 1.

Glo

bal a

nd c

ontin

enta

l run

off e

stim

ates

in k

m3/

year

(man

y da

ta m

ay n

ot b

e di

rect

ly c

ompa

rabl

e be

caus

e of

diff

eren

t con

tinen

tal

boun

dari

es a

nd a

vera

ging

per

iods

). K

78: K

orzu

n et

al.

(197

8), T

able

157

, tim

e pe

riod

not

spec

ified

; L79

: L'vo

vich

(197

9), T

able

20,

tim

e pe

riod

not

spec

ified

; BR7

5: B

aum

gart

ner a

nd R

eich

el (1

975)

, Tab

le X

XXV,

tim

e pe

riod

not s

peci

fied;

S97

: Shi

klom

anov

(199

7), T

able

4.2

, tim

e pe

riod

1921

-198

5; G

RDC

04: G

RDC

(200

4), t

ime

perio

d “a

ppro

xim

atel

y” 1

961-

1990

; F02

: Fek

ete

et a

l. (2

002)

, Tab

le 3

, mod

el W

BM

and

data

, alm

ost e

qual

to F

eket

e et

al.

(199

9b),

time

peri

od n

ot sp

ecifi

ed; F

99bm

: Fek

ete

et a

l. (1

999b

), m

odel

WBM

, tim

e pe

riod

not

spec

i-fie

d; O

01: O

ki e

t al.

(200

1), T

able

2, l

and-

sufa

ce m

odel

s and

TRI

P ro

utin

g m

odel

, tim

e pe

riod

198

7-19

88; D

03: D

öll e

t al.

(200

3), T

able

1,

mod

el W

GH

M, t

ime

peri

od 1

961-

1990

; G04

: Ger

ten

et a

l. (2

004)

, Tab

le 2

, mod

el L

PJ, t

ime

peri

od 1

961-

1990

, WN

07: p

aper

II, W

ASM

OD

-M

, tim

e pe

riod

196

1-19

90

Con

tinen

t A

reaa

Dat

a-ba

sed

estim

ates

C

ombi

ned

estim

ates

M

odel

est

imat

es

(1

06 km

2 ) K

78

L79

BR

75S9

7G

RD

C04

F0

2F9

9bm

O

01D

03G

04W

N07

Euro

pe

10.1

2,

970

3,11

02,

564

2,90

03,

083

2,77

22,

822

2,19

12,

763

-3,

669

Asi

a 44

.0

14,1

00

13,1

9012

,467

13,5

0813

,848

13,0

9111

,425

9,

385

11,2

34-

13,6

11A

fric

a 30

.1

4,60

0 4,

225

3,40

94,

040

3,69

04,

517

5,56

7 3,

616

3,52

9-

3,73

8N

orth

Am

eric

a 22

.4

8,18

0 5,

960

5,84

07,

770

6,29

45,

892

5,39

6 3,

824

5,54

0-

7,00

9So

uth

Am

eric

a 17

.9

12,2

00

10,3

8011

,039

12,0

3011

,897

11,7

1511

,240

8,

789

11,3

82-

9,44

8O

cean

ia

8.7

2,51

0 1,

965

2,39

42,

400

1,72

21,

320

1,30

8 1,

680

2,23

9-

1,12

9G

loba

l (ex

cept

A

ntar

ctic

a)

133 N

44,5

60

N

38,8

30 X37

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42,6

48 Xb

40,5

33 X39

,307 N

37,7

58

N

29,4

85 Nc

36,6

87 N40

,143 N

c38

,605 N

N: e

ndor

heic

bas

ins i

nclu

ded

X: e

xorh

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basi

ns o

nly

a Grid

-cel

l are

a an

d co

ntin

enta

l bou

ndar

ies

from

Fek

ete

et a

l. (1

999b

), en

dorh

eic

basi

ns in

clud

ed. T

hese

are

as a

re o

nly

valid

for

the

W e

stim

ate

(F02

and

F9

9bm

is c

alcu

late

d fo

r 1,6

% fe

wer

grid

cel

ls).

Oce

ania

is d

efin

ed a

s A

ustra

lia, N

ew Z

eela

nd, P

apua

New

Gui

nea

and

som

e sm

all I

slan

ds. W

sim

ulat

ion

is on

ly m

ade

for a

min

or p

art o

f Gre

enla

nd, w

hich

is in

clud

ed in

the

Nor

th A

mer

ica

valu

es.

b It is

ass

umed

,that

this

est

imat

e ex

clud

es e

ndor

heic

bas

ins (

not c

lear

ly st

ated

in th

e or

igin

al p

ublic

atio

n)

c It is

ass

umed

that

thes

e es

timat

es in

clud

e en

dorh

eic

basi

ns (n

ot c

lear

ly st

ated

in th

e or

igin

al p

ublic

atio

n)

16

Models that calculate global runoffs Global water balance models have runoff as its main simulated variable, but several other types of models simulate global runoff as an important by-product (paper I; II). These are the general circulation models (GCMs) used to simulate climate change with their land-surface models (LSMs), dynamic global vegetation models (DGVMs) and routing models. DGVMs and rout-ing models can also be coupled to GCMs, both off-line and online, while the DGVMs and LSMs can be applied stand-alone as well. Routing models need runoff as input from either of these models.

Land-surface models and dynamic global vegetation models The hydrological description of GCMs with the LSMs started with the sim-ple bucket model by Manabe (1969) where runoff only occur when the soil water content is at field capacity. The soil is thus described as a bucket and runoff occurs when the bucket is filled. The bucket approach together with the evaporation formulation caused too dry summers and the LSM algo-rithms developed from 1980’s and onward (Ducharne et al., 1998; Pitman, 2003). The next generation of LSMs were often called soil-vegetation-transfer schemes (SVATs) (Koster and Suarez, 1994). SVATs are one-dimensional, describing the exchanges of water and heat in a vertical column between soil, vegetation and atmosphere, where the soil is divided into sev-eral layers. The terrestrial biosphere/biophysical models SiB and BATS (Dickinson, 1987; Sellers et al., 1986) are early SVATs. LSM is a wide con-cept and also the hydrological model Sacramento Soil Accounting model and the global water balance model WGHM have been classified as LSMs (Sheffield et al., 2003; Ramillien et al., 2006), but usually only energy-balance-based LSMs are considered (Overgaard et al., 2006). An overview of many current LSMs is given by Dirmeyer et al. (2006). The LSMs are continuously developed to include more and more processes like photosyn-thesis and other plant processes together with the explicit simulation of car-bon such that some now have turned into DGVMs (Pitman, 2003). The DGVMs are very detailed models that simulate the carbon cycle and evapo-ration changes without changes in climate forcing (Gerten et al., 2004). These models simulate, e.g., photosynthesis, plant and soil respiration, plant growth and competition between plants, fires and carbon and nutrient cy-cling (Kucharik et al., 2000; Krinner et al., 2005). DGVMs are not only de-veloped from the biophysical models, but also from biogeochemical, bio-geographical and vegetation dynamic models (Cramer et al., 2001; Sitch et al., 2003). Another notation of the DGVMs is ecosystem models, to which also the biogeochemical models are counted (Prentice et al., 2000). A com-

17

plex Earth System model is formed when an atmospheric GCM is coupled with an ocean general circulation model, a DGVM, a marine biogeochemis-try model and an ice model (Mikolajewicz et al., 2007). A DGVM of special interest is LPJ (Sitch et al., 2003) since its hydrological simulations have been compared to three water balance models by Gerten (2004).

Two LSMs with hydrological focus are the VIC model (Liang et al., 1994; Nijssen et al., 1997; Wood et al., 1992) and global model by Hanasaki (2007a; 2007b). The VIC model requires special attention as it has been applied globally (Nijssen et al., 2001a, 2001b), been used by many and been compared to several global runoff models. It can operate in full energy and water balance mode as well as a simpler water balance mode only (O'Don-nell et al., 2000). It can be classified both as macro-scale hydrological model, SVAT and LSM. The model, which exist in several versions, can be applied both locally and globally and either lumped or distributed with sev-eral resolutions (Demaria et al., 2007). The within-cell and between-cell routing is described by Lohmann et al. (1996) and Nijssen et al. (1997). The VIC model can be run both with and without calibration (Nijssen et al., 2001a; 2001b). The first model version had 4 parameters (Wood et al., 1992) while Demaria et al. (2007) studied a selection of 10 streamflow parameters in VIC 4.0.4 and found overparameterisation in the baseflow formulation. Other model tests include the evaluation of a global regionalisation proce-dure (Nijssen et al., 2001a), model intercompariosn in the PILPS project (e.g., Wood et al., 1998), and comparison with independent datasets such as snow (Nijssen et al., 2001b; Hillard et al., 2003; Pan et al., 2003; Sheffield et al., 2003). The recent model by Hanasaki (2007a; 2007b) also includes the energy balance but focuses on the water balance with separate modules for water withdrawal and dam operation.

Routing models Flows in rivers are delayed by lakes and wetlands, as well as by dams, and long and meandering river stretches causes delays themselves. The proce-dure of modelling the runoff from its point of generation to an outlet is called routing, and is normally connected with calculations of these delays. A flow network is needed for the routing. Several global runoff networks exist (Table 2), from the 1 km resolution Hydro1k (USGS, 1999) to the 4° × 5° network by Miller et al. (1994). The low-resolution networks were used to route the runoff of the older, very low-resolution GCMs. Measured runoff is an integrated measure of the conditions in the whole basin and is useful for GCM validation. A routing scheme applied to runoff produced by GCMs grid cells can be compared to gauge data (Russell and Miller, 1990; Liston et al., 1994; Hagemann and Dümenil, 1998; Coe, 2000; Arora, 2001).

18

Table 2. Examples of global runoff networks. “www availability” indicates the data-sets that are directly downloadable over internet whereas other datasets are avail-able after contact with the responsible researcher.

Resolution Name Reference www availability

1 km Hydro1k USGS (1999) Yes 5� Coe (1998) Yes 5�, 0.5°, 1° Graham et al. (1999) 0.5° Hagemann and Dümenil (1998) 0.5° Renssen and Knoop (2000) 0.5° STN-30p Vörösmarty et al. (2000b) Yes 0.5° DDM30 Döll and Lehner (2002) 1° TRIP Oki and Sud (1998) Yes 2° × 2.5°, 4° × 5° Miller et al. (1994)

There are two main groups of routing models, the cell-to-cell models and the source-to-sink models (Olivera et al., 2000). The cell-to-cell models, where flow is accumulated along the flow net are the most common. Examples of such models (paper I) are the models of Miller et al. (1994), Liston et al. (1994), the HD model (Hagemann and Dümenil, 1998), TRIP (Oki et al., 1999), the model by (Arora and Boer, 1999) and RTM (Branstetter and Erickson, 2003). One or several linear reservoirs (Eq. 1) are commonly used (Liston et al., 1994; Miller et al., 1994; Hagemann and Dümenil, 1998):

outout QvdkQS �� (1)

The proportionality constant k, that regulates the outflow Qout from the stor-age S has the dimension of time and is related to travel distance, slope and roughness of the streambed and the length, width and depth of the stream (Liston et al., 1994). The distance d between cells is not constant and k= d/v, where v is the speed, is used since outflow can occur to one of eight possible directions in the flow network (Miller et al., 1994; Kaspar, 2004). The dis-tance is often multiplied by a meandering factor to get a representation of the true river lengths in large grid cells (Oki et al., 1999; Lucas-Picher et al., 2003). The speed v, which is in the order of 1 ms-1 can be set constant or vary between basins (Miller et al., 1994, Kaspar, 2004). Variable velocities were explored by Arora and Boer (1999), Arora et al. (1999) and Lucas-Picher et al. (2003) using the Mannings equation that relates the velocity to the hydraulic radius of the river and the slope. Geomorphological relation-ships between width and discharge and slope and discharge, were used to estimate the model parameters. Sushama et al. (2004) found that a simpler scheme that varies k instead of v could be used instead. A short time-step is needed in cell-to-cell routing to get numerical stable problems (Liston et al.,

19

1994; Coe, 1998; Kaspar, 2004; Sushama et al., 2004) which give long com-putation times.

Global source-to-sink routing models are represented by Naden (1999) and Olivera (2000). In cell-to-cell models, accumulated runoff can be picked out in any cell at the cost of long computation times, while in source-to-sink models the destination cells, such as the basin outlet or a cell with a runoff gauge, are decided beforehand and the time delays from the source to the sink is pre-processed. Within-cell routing can also be simulated in large grid cells, and this procedure is related to the source-to-sink routing (Olivera et al., 2000).

Routing is only necessary for very few rivers in monthly global-scale models if only river transport is considered (Sausen et al., 1994; Kleinen and Petschel-Held, 2007). Lakes, wetlands and dams are much more important for the delays (Vörösmarty et al., 1997; Coe, 2000). Ice damming can influ-ence the river flows as well (Graham, 2004; Shiklomanov et al., 2006). Re-cently Haddeland et al. (2006) and Hanasaki (2006) published algorithms for calculating operation strategies of dams. Irrigation dams are the focus in both studies.

Global water balance models The global water-balance models are simple models, transferring precipita-tion to evaporation and runoff. WASMOD-M, as presented here, is a new model in this category (paper II). One of the first global water balance model studies was published by Vörösmarty et al. (1997). Döll et al. (2003) describe this kind of models as “global hydrological models”. That notation can also be used for LSMs (Andersen and Hinderer, 2005).

The simplest global water balance model is probably the one by Kleinen and Petschel-Held (2007) which focuses on flooding. It uses a monthly time-step, only snow storage and no soil moisture storage. Other global water balance models are the model by Klepper, shortly described in (RIVM/UNEP, 1997), the model by Miller et al. (2003), WBM (Vörösmarty et al., 1989, 1996, 1998), Macro-PDM (Arnell, 1999c, 2003) and WGHM (Döll et al., 2003; Kaspar, 2004), a submodel of WaterGAP (Döll et al., 1999; Alcamo et al., 2003a). The latter three are the most well-known global models. Some of their main similarities and differences are listed in Table 3. WASMOD-M is simpler than these three models. WGMH is the most com-plex of the three. All four models work on a 0.5°×0.5° resolution but Macro-PDM is applied with 10� resolution in Europe (Schröter et al., 2005) and the coming WaterGAP3 will have 5� minute resolution (Martina Weiß, pers. comm.). Three three previous models use pseudo-daily climate data or calcu-lations. WBM uses a flow network but does only have routing with the addi-tional WTM water transport model. Macro-PDM has within-cell routing only and the runoff in the whole basin is summed and the discharge in a

20

specific measurement point could not be used until Schröter et al. (2005) added flow-net data to the basin boundaries. Routing is used in the version of Macro-PDM implemented by Meigh et al. (1999). WGHM calculates routing in rivers as well as in lakes, wetlands and reservoirs. Water with-drawal is also simulated with WaterGAP.

Table 3. Main similarities and differences between WASMOD-M and WBM (Vörös-marty et al., 1989, 1996, 1998), Macro-PDM (Arnell, 1999c, 2003) and WGHM/WaterGAP (Döll et al., 2003; Kaspar, 2004).

WBM Macro-PDM WGHM/WaterGAP2 WASMOD-M Spatial resolu-tion

0.5° x 0.5° 0.5° x 0.5° 0.5° x 0.5° 0.5° x 0.5°

Time-step Pseudo-daily (month)

Daily, output monthly

Daily, output monthly Monthly

Climate data Precip., temp. (mean, ranges, dewpoint), wind, percent sunshine

Pseudo-daily precip. and temp., vapour pressure, cloud, wind

Pseudo-daily precip., temp., wet days, cloud, and average sunshine hours

Precip., temp., vapour pressure

Within-cell distribution

- Soil moisture statistically, open water and land

Open water and land -

Routing In WTM Within-cell Within-cell, between-cells, lakes/wetlands

-

Flownet, basin orders

STN-30p Watersheds from RIVM

DDM30 STN-30p

Water with-drawal

- - Yes -

Parameters ? (>4) 13 � 36 6 Calibrated parameters

In WTM only Simple tun-ing

1, sometimes 1-2 addi-tional correction factors

5

Regionalisation - - Multiple regression Window Required physiographic dateasets

Soil map, land cover, topogra-phy, rooting depth

Soil map, land cover

Soil map, land cover (several), leaf mass, albedo, water holding capacity, slope, hydro-geology, digital chart of the world

-

The three main global water-balance models have different approaches to calibration or tuning (paper II). Calibration should ideally be avoided as a substantial part of the world is ungauged and since calibration is question-able when a model should be used for climate change studies (Arnell, 1999c; Hanasaki et al., 2007a), but because of limited data quality, complexity of processes, and subgrid spatial heterogeneity it can be considered necessary (Döll et al., 2003). Model performance of the land-surface models compared in the PILPS project was better for the calibrated models (Wood et al., 1998). This was true for conceptual as well as for physically-based models.

21

WBM has parameter values assigned a priori (Vörösmarty et al., 1998) and it is not calibrated. The parameter values are related to vegetation and soil properties, or assumed constant. Fekete et al. (1999a) apply runoff-correction factors in gauged cells to make inflow to downstream areas equal to measured flow. WTM, the water-transport model of WBM is however calibrated (Vörösmarty et al., 1989; Vörösmarty and Moore 1991; Vörös-marty et al. 1996).

Arnell’s (1999c; 2003) approach is to avoid calibration as much as possi-ble. Macro-PDM parameter values are estimated from spatial databases or assumed constant from literature values and using knowledge of previous applications of the model (Arnell 1999c; 2003). Six of the 13 parameters are globally uniform and 7 are functions of soil texture and vegetation (Arnell, 2003). When developing the model, Arnell (1999c) did some tuning to set values and test model sensitivity. The tuning process included tests of pre-cipitation datasets and potential-evaporation calculations and was done against long-term average runoff and long-term average within-year runoff patterns.

The approach of Döll et al. (2003) is to calibrate only the runoff regula-tion parameter of WGHM. Calibration is carried out against measured long-term average runoff to get a simulated maximum error of 1%. This goal is achieved for all 724 stations after applying one or two correction factors in 339 cases to ensure that the downstream stations get simulated runoff similar to the measured. Döll et al. (2003) regionalise their calibrated parameter with multiple regression. The other WGHM parameter values are globally uniform or related to land cover and other properties. A non-calibrated ver-sion of WGHM also exists (Martina Weiß, pers. comm.).

The models have been used for future global water resources assessments (paper I; Arnell, 1999a; 2003; 2004; Vörösmarty, et al., 2000a; Alcamo and Henrichs, 2002; Alcamo et al., 2003b) as well as for regional assessments (Arnell, 1999b; 2005; Schröter et al., 2005; Lehner et al., 2006). Kaspar (2004) and (Lehner et al., 2006) have investigated the validity of using WGHM for climate change studies. Lehner et al., (2006) studied WGHM’s ability to reproduce high and low flows before model simulations of hydro-logical extremes in a global change scenario and Kaspar (2004) found that the impact of climate scenarios on runoff was larger than the variations caused by parameter uncertainty.

WGHM/WaterGAP is probably the most well-tested model of the three. Model efficiency has been calculated with volume error (Eq. 19) and Nash (Eq. 20) efficiency measures for both monthly and annual time series, and observed and simulated high- and low-flow characteristics have been com-pared. Validation of the calibration and regionalisation are reported for 6 stations upstream of a calibration station and for 3 regionalised basins (Döll et al., 2003). Monte Carlo test of WGHM are made by Kaspar (2004) and Güntner et al. (2007b). Kaspar (2004) found, for most of the 35 tested ba-

22

sins, that the parameters related to lakes and wetlands were most sensitive, and that the impact of climate change scenarios is stronger than the uncer-tainty caused by the uncertainty in the parameters. Güntner et al., (2007b) investigate the sensitivity of the total water storage (sum of snow, soil mois-ture, groundwater and surface water storage) in 22 basins and find strong regional variations in parameter sensitivity depending on which processes that are important in different basins.

Although only few parameter values were tested, Arnell (1999c), in de-veloping Macro-PDM, show the effect on the average runoff of varying some parameter values between a few fixed values for 24 European model grid cells, before deciding upon a common best value. Arnell (2005) made a similar analyis for the Arctic rivers. Arnell (2003) compared volume errors of Macro-PDM with the calibrated and uncalibrated volume errors of Ni-jssen (2001a). Kleinen and Petschel-Held (2007) use these values for com-parison too, as they are easy to find and among the first to be published. Simulated results for all 663 validation basins are reported for WBM by Fekete et al. (1999b). These basins are also used by WASMOD-M.

All three models have been used to test different ways to calculate poten-tial evaporation (Vörösmarty et al., 1998; Arnell, 1999c; Kaspar, 2004) as well as precipitation with and without correction or to use different precipita-tion datasets (Arnell, 1999c; 2005; Döll et al., 2003; Fiedler and Döll, 2007; Fekete et al., 2004).

Model performance can be compared to measurements other than runoff as a check of the model’s internal consistency. WGHM simulations are compared with water storage variations from the GRACE satellite observa-tions by Schmidt et al. (2006) whereas Werth et al. (2007) use these data for calibration. Comparison against satellite derived snow cover and runoff measurements are presented by Schulze and Döll (2004) in a test of a new, subgrid, snow routine for WGHM. Modified versions of WBM are used in comparison with remotely sensed snow (Rawlins et al., 2005; 2007) and isotope data (Fekete et al., 2006).

The global water balance models can be applied for a specific region as well (Vörösmarty and Moore, 1991; Vörösmarty et al., 1996, Arnell, 1999b; Arnell, 2005; Schröter et al., 2005; Lehner et al., 2006). Additionally, there exist several water balance models that have been applied over large areas but not globally. To identify the complete list is beyond the scope of this thesis, but some examples are the models by (Yates, 1997; Ewen et al., 1999; Graham, 1999; Guo et al., 2002; Yang and Musiake, 2003; Col-lischonn et al., 2007).

23

Uncertainties of GCMs and LSMs and the effect in studies of hydrological impact of climate change The development of the LSMs have raised the question of overparameterisa-tion (Hogue et al., 2006; Demaria et al., 2007) and the question if the LSMs despite their complexity perform as well as expected (Abramowitz, 2005). Even if the complexity sometimes can be motivated (Desborough, 1999) it does not help to have a good LSM, when the GCMs have big problems in simulating the precipitation which is the main driving force of runoff (Mearns et al., 1995; Arora, 2001; Paper I). Several scenarios have been set up that project future carbon dioxide levels based on, e.g., “business-as-usual” or more environmental-friendly world development together with population scenarios, for prediction of future climate conditions (Arnell, 2004). The differences between individual GCMs can be larger than between the scenarios (Graham, 2004). Because of the uncertainties in the GCMs the “delta change” approach is often used instead of the direct GCM output (e.g., Graham, 2004; Fronzek and Carter, 2007; paper I). This approach adds the relative change between a GCM’s climate prediction and its present climate simulations to a measured time series before feeding it to a hydrological model. It is assumed that relative climate changes are more reliably simu-lated by the GCMs than their absolute values (Hay et al., 2000).

Paper I describes six approaches to hydrological impact studies of climate change. These approaches are 1) direct usage of GCM output, 2) down-scaling with regional climate models, 3) global water balance models, 4) continental-scale water balance and hydrological models (including LSMs) 5) hypothesised scenarios, and 6) statistical downscaling. The interest in hydrological impact is often on local and regional scale, which the GCM resolution cannot depict. Downscaling methods are thus needed to get higher resolution projections of climate change impact. Regional climate models and statistical downscaling focus on an area of interest and translate the low-resolution GCM results to this area. These methods are seldom or never ap-plied globally. Hypothesized scenarios are quick solutions to modify existing climate time series without accessing GCM output data and considering the large errors in the GCM output. The approach is used in local and regional studies (paper I) but not in global water balance models, although it would be possible. Usage of “delta change” GCM output that gives some geo-graphical pattern should be slightly more realistic than, e.g., +2° for the whole globe, as long as several GCMs are used. It should be kept in mind that the GCMs are driven by global scenarios themselves, of CO2 and other emissions based on, e.g., assumed population changes (Arnell, 2004).

Impact of climate change needs to be studied locally and regionally, but the global analysis is also valuable. Global and continental water balance models, coupled or stand-alone LSMs and direct GCM output with routing can be used to study impacts on the continental scale. The uncertainty of the

24

GCMs is the main limitation of all approaches since it is the basis for the impact studies. Additional uncertainties come from errors in the regional climate models, errors in the hydrological models and lack of data (paper I). Further climate-hydrology feedback studies, including vegetation and further dialogue between modellers, the remote sensing community and other meas-urement communities will probably decrease the uncertainties (paper I; Gerten 2004; Overgaard et al., 2006).

25

Methods

The models used in this thesis are based on WASMOD1 (Water And Snow balance MODeling system) catchment model (Xu, 2002). While the original WASMOD is lumped, the two models used here are distributed. WASMOD-M, with M for macro-scale, is the monthly, global water balance model that is the focus of the thesis (paper II; III). The model version applied in paper IV, is a daily, distributed model, but it is still denoted WASMOD. It was developed to study the impact of spatial resolution for future versions and input-data sets of WASMOD-M. The simple structure and the few parame-ters of the original WASMOD were reasons why it was chosen for the first version of the new global water balance model. Additionally, different ver-sions of WASMOD have shown a high level of generality from applications at variously-sized catchments in Europe, Asia and Africa. Studies have shown that its model parameters can be correlated with catchment character-istics (Xu, 1999a; 2003; Muller-Wohlfeil et al., 2003) such as land-cover fractions and soil texture. WASMOD (Xu, 1999b), together with the models of Refsgaard and Knudsen (1996) and Donnelly-Makoweckia and Moore (1999), are also among the few water-balance models that passed the full split-sample-proxy-basin test proposed by Klemeš (1986).

Global data for WASMOD-M WASMOD-M requires gridded monthly precipitation, temperature and po-tential evaporation as input. A 0.5° � 0.5° latitude-longitude grid was used because data was easily and freely available for this projection and resolu-tion, and because it is used by other global water balance models (Arnell, 1999c; Döll et al., 2003; Vörösmarty et al., 1998). Additional data needed are flow networks with basin boundaries and areas. Compilation of gridded runoff results for continents requires their boundaries too. Measured runoff, at stations co-registered to the flow network, and gridded snow cover meas-urements have been used in the model tuning. 1 Not to be confused with WASMOD (Water and Substance Simulation Model) developed by Ernst-Walter Reiche, and described by, e.g., Rinker (2001) in Beschreibung der Wasser- und Stoffhaushaltsdynamik devastierter Flächen mit dem Simulationsmodell WASMOD am Bei-spiel des Braunkohlentagebaus Espenhain, Der Fakultät für Geowissenschaften, Geotechnik und Bergbau der Technischen Universität Bergakademie Freiberg

26

Climate-input data to WASMOD-M comprised gridded monthly values of precipitation, temperature and water-vapour pressure from CRU TS 2.02 (Mitchell et al., 2004) for paper II and CRU TS 2.10 (Mitchell and Jones, 2005) for paper III. Data covering 1901-2000 have been used. Precipitation-correction factors were calculated for gauge losses as quotients for each cell between corrected and uncorrected precipitation (Willmott et al., 1998; Leg-ates and Willmott, 1990) as a long-term average for each month.

Gridded potential evaporation ep was calculated from CRU air tempera-ture Ta (°C) and water vapour pressure ea (mbar = hPa) through the relative humidity RH (%) (Dingman, 1994, Xu 2002):

��

��

�

��

��

�

3.23727.17exp108.6

100)(

100

a

a

a

asat

a

TT

eTe

eRH (2)

� � RHTEep ac �� 1002 (3)

where Ta+=max(Ta,0), esat(Ta) is the saturated vapour pressure at temperature

Ta, and Ec (mm month-1 °C-2) is a non-calibrated model parameter. The cal-culation of esat(Ta) is an empirical formula (Dingman, 1994) which holds for momentary values. Theoretically it should not be used for monthly averages, but such errors are compensated for by the Ec adjustment factor. In paper II Ec was set to 0.018 globally, while in paper III distributed values of Ec were used. They were set in an inverse process, to get the average annual potential evaporation equal to the highest value in two potential evaporation datasets. This produced Ec values ranging from 2.61×10-4 (arid areas) to 0.999 (cold areas), with a median of 0.011.

Basin boundaries and areas, flow paths, and continent boundaries were taken from STN-30p (Vörösmarty et al., 2000b). 663 GRDC runoff stations have been co-registered to the flow network in ”UNH/GRDC Composite Runoff Fields V1.0” (Fekete et al., 1999a; 1999b; 2002). These stations have basin or inter-station areas sufficiently large to fit the 0.5° grid, and some stations with inconsistencies in the inter-station runoff were removed, while 28 stations with negative inters-station runoff more likely caused by evapo-ration and water withdrawal rather than measurement inconsistencies were kept (Fekete et al., 1999a). These stations belong to 257 basins discharging to oceans or large lakes. The gauged areas cover 50% of the 59132 STN-30p land-surface cells. Related to the actively discharging area only, the cover-age is 72% instead of 50% (Fekete et al., 2002).

It would have been useful to have regulation data since almost all large rivers are regulated (Vörösmarty et al., 2004; Nilsson et al., 2005) such that natural peak- and low-flow characteristics are modified. Regulation data are

27

often unavailable since dam and reservoir operation commonly involve competing economic interests and can also be in conflict with downstream water-supply needs (Brakenridge et al., 2005) and there exist no global data-base of naturalised streamflow, with flows recalculated to the natural behav-iour where anthropogenic effects like abstraction and damming have been subtracted. Neither regulation, nor natural routing delays by long river stretches, lakes and wetlands have been included in WASMOD-M. The long-term average runoff was used for model tuning to overcome this effect in paper II. We assumed that regulation did not affect average flow volumes, a non-valid assumption in warm and arid areas with substantial evaporation loss from river stretches and reservoirs, or where large withdrawals leads to losses. The average runoff of the 663 stations were taken from ”UNH/GRDC Composite Runoff Fields V1.0” (Fekete et al., 1999b) . The long-term aver-age within-year variations were also reported in the dataset and used in vali-dation. These averages are based on different time periods during the 20th century and some include data from the 19th century.

Model tuning against monthly time series was tried in paper III to better restrict the parameter values and avoid equifinality, despite the lack of rout-ing in WASMOD-M. Very few rivers have regulation delays longer than one year (Vörösmarty et al. 1997), and the model was also tuned against annual data to overcome the regulation delay. The time-series for the 663 stations were provided directly by GRDC (2007). This dataset contains two monthly time-series for some stations, which more or less overlap. These are “origi-nal” monthly data, and “calculated” monthly data. Only the “original” monthly data were used in paper III, restricting the number of time-series to 654.

The combination of precipitation and runoff data showed that some basins had physically unreasonable runoff coefficients (total runoff divided by total precipitation). Only stations with runoff coefficients between 1% and 85% were used in paper II and regions with abundant runoff coefficient problems were excluded altogether, e.g., Alaska and the Colorado River basin. All stations were included in paper III, even if they had data problems.

Calibration of snow parameters was performed against the 1986–1995 “Northern Hemisphere Monthly Snow Cover Extent” 0.5° × 0.5° latitude-longitude dataset from ISLSCP (2003) and the National Snow and Ice Data Center (Armstrong and Brodzik, 2005).

Simulation time periods, model windup times and initial values All simulations started with globally uniform initial values of land moisture and snowpack. Simulations in paper II always started 1901 and had at least a 14-year warm-up period. The parameter tuning procedure was applied for 1915–2000 and the simulations from the time period where gauge data were available for station were extracted. The time periods could not match when

28

the measured average runoffs included data from 1914 and earlier. Compari-sons with other estimates were calculated for the standard period 1961-1990. Gauge data before 1901 and after 2000 were shortened to match the climate data in paper III. Model warm-up always started at least 5 years before. The simulated and measured runoff time-series were divided in two for tuning and validation purposes, making the total windup time much longer for the validation. Snow calibration was made for the snow data period, i.e., 1986–1995, with a windup of 5 years.

WASMOD-M Two versions of WASMOD-M have been used. The first, used in paper II, took its model equations directly from the code by Xu (2002). The changes in the latter version, used in paper III, were made to 1) avoid non-closure of the water balance by preventing the fast flow to exceed available water, 2) be able to regulate all evaporation by a parameter, by removing the non-parameter-governed direct loss. The model equations specific for paper II are denoted “a”, and those for paper III “b”.

WASMOD-M calculates, with a monthly time step, snow accumulation and melt, actual evaporation, and separates runoff into a fast and a slow component for each grid cell. Given the monthly time step, the model simul-taneously allows snowfall, rainfall, and snowmelt to occur in the same month. The model has 62 parameters of which 5 are calibrated and one is pre-set (Table 4). All units are mm month-1 unless stated otherwise.

Snow- and rainfall (snow and rain) as well as snowmelt (melt) and accu-mulation (sp) vary exponentially between two temperature thresholds (Tm and Ts, °C):

� � � �� 2/exp1 �� mssa TTTTPsnow (4)

snowPrain �� (5)

� � � � �� 2/exp1/ �� msamold TTTTsnowtspmelt (6)

� tmeltsnowspsp old �� (7)

where P is precipitation and �t = 1 month and {x}- means min(x,0).

2 In paper II 4-6 parameters as snow only was calculated for the “cold” cells, while the second model version (paper III) did not include this difference.

29

Direct water loss (dl) to the atmosphere was calculated from potential evapo-ration and rainfall in paper II. The variable “land moisture” (lm, in mm) represents the storage of water available for evaporation and runoff in the next time step. The name is introduced to make a clear distinction to the well-defined, local-scale, soil-physical entity “soil moisture”. Available wa-ter (aw) is calculated from active rain, i.e., rainfall minus direct loss, and snowmelt. Actual evaporation (evaptot) is calculated from land moisture, potential evaporation (ep), and direct loss:

� � ��

��

��

11/exp1

epepeprain

epdlepdl

(8a)

� �� dlrainactiverain (9a)

meltactiveraintlmaw old �� / (10a)

11}),1()min{( /(

��

��

��

dlepdlep

dlepevappartawAdlepevappart dl)epaw

c (11a)

�� }{ dlevappartevap (12a)

where Ac (-) is a tuneable parameter and {x}+ means max(x,0). The direct loss was removed to let Ac control all evaporation in paper III. Thus equa-tions 8a to 12a are substituted by 13b-14b

meltraintlmaw old �� / (13b)

}),1(min{ / awAepevap epawc�� (14b)

The slow runoff is a base flow, provided by land moisture whereas the fast runoff is provided by both land moisture and water added (i.e., melt + (av-tive)rain) during a time step. A water availability check was introduced in paper III. Both runoffs are described by linear reservoirs:

olds lmPslow �� (15)

)( activerainmeltlmPfast oldf �� (16a)

30

)( rainmeltlmPfast oldf �� (16b)

fastslowrunoff �� (17a)

)}(),min{( evapawfastslowrunoff �� (17b)

where Ps (month-1) and Pf (mm-1) are tuneable parameters. Finally the land moisture storage is updated.

trunoffevappartmeltactiverainlmlm old �� )( (18a)

trunoffevapmeltrainlmlm old �� )( (18b)

The first model version was written in Fortran 90, while the second was written in Matlab.

Model parameter tuning of WASMOD-M in gauged areas Two different parameter estimation procedures have been applied, one in paper II and the other in paper III. Focus of both has been to identify ac-ceptable parameter value sets.

Table 4. The complete set of parameters in WASMOD-M, and the ranges of the 5 parameters varied in the parameter tuning procedure. Ec is pre-processed.

Governs Eq. Fixed values (paper II) Range (paper III)

Sampling inter-val (paper III)

Ts (°C) Snowfall 4, 6 1.5, 3.5 0–4 Uniform Tm (°C) Snowmelt 4, 6 -1.5, -3.5 -4–0 Uniform Ac (-) Actual

evaporation 11a/14b 0.35, 0.55, 0.75 0–1 Uniform

Ps (mon-1) Slow runoff 15 5×10-5, 1×10-4, 0.0015, 0.004, 0.01, 0.025, 0.05, 0.14, 0.19, 0.25, 0.4, 0.6, 0.8, 0.9

e-14 –e0 a)

Logarithmic

Pf (mm-1) Fast runoff 16 5×10-6, 1×10-5, 1×10-4, 5×10-4, 0.001, 0.0025, 0.005, 0.0095, 0.0145, 0.025

e-18–e0 b) Logarithmic

Ec(mm mon-1 °C-2)

Potential evaporation

3 0.0018 2.61×10-4–0.999

Pre-processed

a) e-14 �8.31·10-7, b) e-18

�1.52·10-8

31

The sets were used for regionalisation only in paper II, while a single pa-rameter value sets was selected for a final simulation, but all acceptable sets were kept for all simulations in paper III. Monte Carlo-approaches were used. The model was first run with a combination of globally-uniform pa-rameter-value sets, covering the range of “reasonable” values for each pa-rameter (Table 4) in paper II. The most sensitive parameters were given the broadest range of possible values. The combination of the discrete values for all the parameters resulted in 1680 simulations. Only data from gauged areas were saved for further analysis. 15000 random parameter value combina-tions were tested for the whole upstream area of each basin in paper III. Parameter values were uniformly or logarithmically divided within the wide ranges and randomly combined.

Criteria The simulated long-term average runoffs were compared with the measured values, through the volume error (VE) in paper II. Abs(VE) varies from per-fect fit at 0 to plus infinity:

%100��

��

� �

timeobs

time timeobssim

runoff

runoffrunoffVE (19)

where runoffobs is the simulated runoff at every time step and runoffsim the corresponding simulated runoff. Parameter-value sets in paper II were con-sidered “acceptable”, if the simulated basin runoff differed by less than ±20%, or 5 mm in dry areas, respectively, from the measured value. Several limits were used in paper III (Table 5). Limitations of the state variables (snowpack and land-moisture) were used in paper II. Land moisture was not allowed to exceed 1000 mm in any month while the snowpack limit was 1200 mm. The average land moisture and snowpack respectively during the first simulation year (1915) was not allowed to differ more than 200 mm and 100 mm respectively compared to the average of the last simulation year (2000). The removal of the state-variable limits was also investigated.

The measured time-series were considered in paper III, in addition to VE. The Nash coefficient (NC), and the limit of acceptability (LA) were used. Tuning against snow cover data was also used, with a snow/no-snow criteria (SF). The model was calibrated against monthly as well as annual average time series for each basin in paper III. Simulations were always made with monthly input and monthly timesteps, but the monthly output was also aver-aged to yearly time series. Evaluation criteria were calculated separately for the two output time series.

NC varies from perfect fit at 1 to minus infinity:

32

��

�

��

timeobsobs

timesimobs

runoffrunoff

runoffrunoffNC

2

2

)(

)(1 (20)

where � denotes average. The limit of acceptability (LA) criterion is presented by (Beven, 2006). It

requires a modeller to predefine acceptable simulation errors, based on “ef-fective observation error” of input data and discharge measurements. These limits can vary in time. Simulated runoff that falls within the acceptable limits at a given point in time is weighted with, e.g., a triangular or a trape-zoidal function where a simulation close to the measured is given 100% weight whereas a simulation outside limits is given zero weight. The choice of predefined error limits was not obvious in the global case and subjective, wide limits were used. This was motivated since GRDC do not generally report rating-curve errors and the model-input data are uncertain. A symmet-rical, triangular weighting function (with a zero minimum and a unit maxi-mum) was used and LA was calculated as a time average.

We defined parameter-value sets to be “behavioral” in two ways. A first, relative definition was the selection of the best 1%, 3.3%, and 20% (150, 500, and 3000 of 15000) simulations for each criterion. A second definition used the absolute limits for each criterion (Table 5).

LA was defined by a range around the measured flow that simulated flows had to meet at least 95% of the time, i.e., less than 3 months in 5 years was allowed to fall outside of range. The initial range (LA75) was given as ±75% of the flow at each time step plus 3 mm to avoid high relative low-flow er-rors. If a sufficient number of simulations did not meet this criterion, we widened the range to ±99% of the flow plus 3 mm (LA99). If this was not enough, we widened the range until we got the requested number of simula-tions (LAmax).

Snow calculation in WASMOD-M is independent of the land moisture storage and evaporation and could thus be calculated separately by using the input precipitation and temperature only. Snow calibration compared the existence of snow or not. The snowpack (sp), in mm, simulated by WAS-MOD-M is a representation of the snowpack at the last day of the month, available for melting next month. The observations give the percentage of the weeks within a month with spatial snow coverage more than 50%. The 100% and some of the 0% values were used as only these have information on the situation at the end of the month while the intermediate values are not connected with any information about when snow cover occurred during the weeks of the month. The months with 0% values were not used during Dec-Feb and when they were adjacent to a month with some snow above 50% spatial coverage. During the other months the 0% months were assumed to

33

represent true no-snow conditions although the 0% value only imply less than 50% spatial snow coverage during the whole month. The snow-fit crite-rion was based on measured and simulated snow periods:

��

��

�

tot

correct

tot

correct

thsnonsnowmonthsnonsnowmon

snowmonthssnowmonthsSF ,min (21)

where snowmonthscorrect is the number of months with a simulated snowpack fitting months with measured snow and nonsnowmonthcorrect the number of simulated months with no snowpack fitting measured snowfree months, snowmonthstot is the total number of snowfree months and nonsnowmonthstot. The number of months is a total measure for all cells in the basin. SF varies from perfect fit at 1 to no fit at 0. Of the 344 northern hemisphere basins with snow measurements all had some cells with non-snow-classification, while 26 stations were lacking snow classification as none of the included measured cells had a snow cover for 100% of the time any month.

Inter-station areas Of the 663 runoff stations, 208 represent single-station basins and 234 headwater sub-basins. These 442 basins are geographically independent, and were calibrated independently from each other. The remaining 221 stations are downstream stations, each of which is associated with one geographi-cally independent inter-station sub-basin. Among the downstream stations, 90 are down-most and 13 of these have 10 or more upstream stations. The 1680 and 15000 simulations were applied with uniform parameter value combinations of the whole upstream area of each gauged station. An inter-station algorithm to tune the parameters of the inter-station areas was devel-oped in paper II. The inter-station runoff was calculated as the difference between the upstream and the downstream average runoff. Such a simple procedure could not be applied to the time-series used in paper III because of routing delays. All 654 basins were instead treated separately in paper III.

The inter-station algorithm of paper II focused on improving the runoff at the downmost basins compared to what was achieved with the uniform pa-rameter value combinations. It required that the runoff coefficient of the inter-station area was acceptable. Inter-station runoff was not considered if the sum of measured upstream and simulated inter-station runoff produced unacceptable results, i.e., VE larger than ±20%. The inter-station algorithm was also overruled if it increased the error at the downmost gauging station compared to a calibration for the whole basin against runoff at this station.

The single best parameter-value combination that was found for each sub-basin by the inter-station algorithm was used in the final, distributed parame-ter-value set.

34

Regionalisation of WASMOD-M’s parameter values to ungauged areas Around 50% of the model’s land-surface cells are ungauged. The method of assigning parameter values to ungauged areas is called regionalisation. A simple regionalisation procedure was used in paper II, using proximity only. A window 17 cells high and 39 cells wide was applied around each gauged cell and cells belonging to gauged basins within the window were identified. Common parameter value combinations of these gauged stations were identi-fied. The most commonly occurring parameter-value set among the gauged basins in this window was selected for each given cell, and if two or more parameter-value sets were equally common, the combination that gave the lowest error in the gauged areas was selected. Sub-areas that had been over-written with downstream parameter-value sets donated those sets in the re-gionalisation. Basins with no parameter value combinations got regionalised parameter values. Cells belonging to basins where the 20%-error limit was not reached was not used in the regionalisation and were given their best available parameter-value set with an error above 20% for the final distrib-uted parameter-value set.

Cells where no gauged basin or common parameter-value set was found within the moving window were given a single, default value. This default parameter-value set was subjectively derived from a map of acceptable pa-rameter values for all gauged and regionalised cells. The map showed a few dominating parameter-value sets close to the areas with missing values. The most abundant of these was chosen as default.

Evaluation and validation of WASMOD-M The within-year runoff patterns was used for model validation in paper II since parameter values were only tuned to the long-term average runoff. The long-term average within-year variations were plotted for all stations. A set of 15 gauging stations was especially studied since the result could be com-pared with results in at least two previous publications using other models. Total global and continental runoff with the final parameter value set was also compared with previously published estimates (Table 1). The availability of time-series allowed split-sample validation in paper III. Calibration was made against the first half of the available time-series and validation against the second half.

35

Routing of daily runoff produced by WASMOD The results of paper II and III highlighted the need for river routing in WASMOD-M. It was also found that newly started studies of the precipita-tion heterogeneity at different scales needed a scale-independent routing method. A new routing algorithm using aggregated time-delay-histograms was developed and compared to the widely used cell-to-cell linear reservoir routing in paper IV.

Site and data description The routing study was performed in the Dongjiang (East River) catchment, situated just north of Hong Kong in southern China (Figure 1). It is a tribu-tary of the Pearl River. Runoff was simulated for the catchment area of the downmost gauging station Boluo. Its catchment area is 25,325 km2. Climate data input was precipitation at 51 stations and daily air temperature, sunshine duration, relative humidity and wind-speed 7 at the meteorological stations. Final input to this WASMOD version was precipitation, temperature and potential evaporation. The potential evaporation was calculated with the Pennman equation for each climate station and then interpolated.

The global 1km flow network Hydro1k (USGS, 1999) was used. It has an equal area projection such that every cell is 1km2. Several topographic re-lated properties are included in Hydro1k and the slope was also used apart from the flow network and area. The Boluo discharge station was co-registered to Hydro1k by comparing coordinates and especially area. The best fit was achieved for a flow network of 25,886 cells (km2).

Resolutions Model simulations were carried out for 5�–60� resolution, with a 1�-step. The input climate data was interpolated to the cells of Hydro1k. Kriging with linear variogram was used to interpolate precipitation and inverse distance weighting was used to interpolate the other datasets. The data were then averaged to each resolution. Uniformly distributed climate inputs were also used at each resolution with both routing methods, to identify the pure rout-ing scale effect.

The linear reservoir routing requires an upscaled network. The network scaling algorithm (NSA) by Fekete et al. (2001) was used to generate a river network at each resolution consistent with the high-resolution Hydro1k. The proposed meandering factor to compensate for decreasing river-lengths with coarser resolutions was not used since this was implicitly accounted for in the calibration. Neither were the basin border cells considered to be either inside or outside of the catchment, but given the area that corresponds to the

36

actual catchment part of the cell. The runoff generating area thus remained the same for all resolutions.

The 30� network STN-30p delineates the Dongjiang catchment to 10 cells (Figure 1).

�

�

�

� � �

�

�

�

�

�

��

�

�

� �

�

�

� �

�

�

�

�

�

�

�

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�

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� �

�

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�

�

� �

�

�

�

�

�

�

�

�

�

�

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

!�� "#

$��

%��

�� &��

��

��

&��

'��

��

(�)��

&��

'��

��

&��

��

��

��

$�� '��

� ��

Figure 1. The Dongjiang catchment (dark grey) in the STN-30p network. The sur-rounding basins (black outline) gauging stations (black dots) and their upstream sub-basins (light grey) are also shown.

Daily, distributed WASMOD Dongjiang is a snow-free catchment and the snow algorithm was excluded from the model. The evaporation calculation was the same as in paper III. The fast and slow runoff calculations were changed to non-linear exponen-tial formulations for this daily model version:

� 1/exp1 clmSP old�� (22)

� SPevapPfast �� (23)

� � 2/exp1 clmlmslow oldold �� (24)

where SP is the percentage of the catchment which is saturated, and c1 and c2 are runoff parameters. The three parameter values were varied in 250 simu-

37

lations using a similar approach as in paper III. The 250 runoff simulations for each resolution were saved to be used in the routing.

Linear reservoir routing A linear reservoir approach is most commonly used in global cell-to-cell runoff routing and was implemented for comparison purposes. The linear reservoir (Eq. 1), which is a simplifcation of the Muskingum method without any influence of the inflow to the storage was combined with the water bal-ance of each grid-cell

outin QrunoffQdtdS

�� (25)

where t is time and Qin is inflow to the cell from surrounding cells and runoff is the runoff generated in the cell itself, to

outinout QrunoffQ

dtdQk �� (26)

Linear reservoir routing is often applied with a finite difference approxima-tion of Eq. 26 (e.g., Arora, et al. 1999) and was used here to determine the outflow of each cell. The travel time k between the grid-cells was set by the velocity and distance as in Eq. 1. The calibration of the velocity is described below.

Aggregated time-delay-histogram routing The aggregated time-delay-histogram routing is a new routing method based on the time-delay histogram of TOPMODEL (Beven and Kirkby, 1979). It uses the knowledge from a high-resolution flow network at lower spatial resolutions. A parameter that is easy to aggregate in space at different resolu-tions is wanted. The method is based on pre-processing, where the time from each Hydro1k cell to a downstream cell is calculated and then aggregated to a lower resolution. One downstream destination Hydro1k cell, the one with the co-registered Boluo catchment station, was used in paper IV. The source and destination cells are selected among the high-resolution cells for the most accurate time and area representation.

Two parameters are calculated for each upstream high-resolution cells, the delay time t, and the first-day percentage p. The delay time is the total accumulated time it takes for the water from the cell to reach the destination cell. The distances between the cells along the flow paths are denoted d1, d2,

38

..., dn, and the slope of each segment are tan(b1), tan(b2), …tan(bn). A theo-retical network velocity, v45, of the high resolution field at the slope tan(45°) is denoted v45. The network velocity is the only calibrated parameter in the method. The delay time is calculated from it and p is just a by-product of the model assumptions. The delay time from the reference point to the destina-tion cell is calculated as the sum along the flow path according to Beven and Kirkby (1979) but with the square root as Ducharne et al. (2003):

��

�n

i i

i

bvdt

1 45 )tan( (27)

The network velocity v45 is calibrated separately and requires the possible runoffs simulated with WASMOD as input in the calibration.

The runoff simulated by WASMOD was assumed to be evenly distributed in time during one day. This runoff will reach the sink during 24 hours of two consecutive days since no dispersion was assumed. The percentage of runoff that reaches the sink during the first day of arrival is denoted p. The remaining 100%-p arrives the following day. The delay time t is the time to the first arrival, and p describes how much of the day is left when this first runoff arrives.

The t and p of the Hydro1k cells in a low-resolution cell are combined to a time-delay histogram of the low-resolution cell instead of a coarse average. The time-delay histogram summarises the delays and first and second day percentages all Hydro1k cells in the low-resolution cell. An underlying as-sumption is that the runoff from the low-resolution cell is evenly distributed over all high-resolution cells. There is a possibility to include sub-grid varia-tion too, but that would complicate the comparisons presented here.

The final routing is simple. The aggregated time-delay histogram is used to partition the generated runoff into the corresponding delayed days of time series at the destination cell with the percentage share of each day.

Velocity calibration Both routing methods use one calibration parameter, the velocity, which is calibrated separately from the WASMOD simulations. The 250 runoff simu-lations of each resolution were combined with different velocities. Each tested velocity produced its own set of time-delay histograms in the time-delay-histogram method. Velocities and WASMOD parameters that gave the highest NC values compared to Boluo runoff were selected. Wide ranges of the velocities were initially tested to identify narrower ranges for the final calibration. For linear reservoir routing, the best velocity v was within [0, 1] ms-1, and the time-delay-histogram routing velocity v45 was found to fall within [7, 9] ms-1. These two velocities are not comparable as v45 gives the

39

velocity of a theoretical very steep river. A sampling interval of 0.1 ms-1 was used to select the velocities for the final calibration.

Benchmark The time-delay-histogram and the linear-reservoir routing are two very dif-ferent methods and simulation differences might be complicated to explain. A combined method, that applies a time-delay method to the coarse resolu-tion network, without the usage of the high-resolution data, was used to bet-ter differentiate between the resolution and methodological effect on the results. This benchmark routing was also applied at all scales and with the distributed and uniform climate input. The same velocity calibration proce-dure was applied.

40

Results

Tuning and criteria The simulations with 1680 globally uniform parameter-value sets produced acceptable results for the whole upstream area that comprises the main-stream sub-basins of 485 of the 663 stations in paper II. The 178 non-accepted stations were divided into the following four categories: In the first category, 57 stations lacked input and validation data that produced accept-able runoff coefficients. The other three categories were the result of either data or model deficiencies: No acceptable parameter-value sets could be found for 29 stations, i.e., they exceeded the 20% VE limit; 23 stations had unreasonable state variables for all parameter-value sets (e.g., the snowpack or the land moisture grew too large); 69 stations had no acceptable parame-ter-value set with acceptable state variables. After applying the inter-station algorithm, parameter values could be set for 531 of the total 663 stations. Since some of them were substituted by parameter values from downstream stations, the number of parameter-value sets was finally 429. The runoff was simulated with an absolute volume error less than 20% for the whole up-stream area of 455 basins, and within 1% for 276 basins, with the final, dis-tributed parameter value set.

Several different model evaluation criteria were calculated separately in paper III. The volume error was the easiest criteria to fulfil. All basins could be simulated with VE less than ±1% as long as the basins had reasonable runoff coefficients. The improvement in paper III compared to paper II could be attributed to the larger number of simulations, 15000 instead of 1680, and the removal of the “direct loss” in the model algorithms. A clear majority of the stations had parameter-value sets that fulfilled the LA75 crite-rion. The existence of snow or not was also well simulated. NC was the strictest criterion, with only 479 basins that could be simulated with a per-formance of at least 0.5. This number is comparable to the 485 acceptable basins in paper II.

The number of basins that fall within a certain criteria limit holds for the individual criteria. The combinations of two or several criteria were analysed in paper III. 52% of the basins could be simulated by parameter value sets that simultaneously fulfilled NC�0.5, VE�1%, SF�0.75, and LA75. It was possible to find good runoff parameter-value sets concurrent with the best 1% snow parameter-value sets for almost all snow-covered basins. It was

41

also possible to find common sets between the 1% best of NC and VE for 99% of all basins. NC and LA behave similarly in parameter space but com-mon sets between the 1% best of them were only found for 83% of all ba-sins. Common sets between the 1% best VE and LA were found for 52% of all basins.

Table 5. Number of basins with at least one parameter-value set resulting in simu-lated results fulfilling different evaluation-criteria limits for Nash (NC), volume error (VE), limit of acceptability (LA), and snow fit (SF) when evaluated against monthly and annual observations in paper III. There were 654 basins with runoff measurements and 344 with snow measurements. Percentages relate to these totals. Criterion Monthly Annual Type Limit Name No % No % NC � 0.8 NC0.8 157 24 103 16 � 0.5 NC0.5 479 73 363 56 � 0 NC0 642 98 560 86 VE � 1% VE1 632 97 630 96 � 20% VE20 643 98 643 98 � 50% VE50 651 100 651 100 LA ± 75% of obs. LA75 580 89 650 99 ± 99% of obs. LA99 654 100 654 100 SF � 95% SF95 274 77 - -

� 75% SF75 321 91 - -

� 50% SF50 339 96 - -

Parameter-value behaviour Being the criteria that is easiest to fulfil, VE, is also the least restrictive. It normally leaves most parameter spaces unconfined (Figure 2). The dynam-ics criteria NC and LA commonly confine the parameter spaces of the evapo-ration and runoff criteria. NC has a slight influence on the two snow parame-ters Ts and Tm but SF was needed to get a substantial constriction of them. The constriction was clear for Ts but less so for Tm. Criteria and parameter behaviour differed between snow-covered and non-snow covered (arid and tropical) basins. VE easier confined the evaporation parameter Ac in non-snow basins and the runoff parameters Ps and Pf in snow basins. Ac was also better confined by LA and NC for the non-snow basins, while the runoff pa-rameters were better confined for non-snow basins by the 1% best NC and LA values, but for snow-covered basins with the 20% best NC and LA val-ues.

42

0 0.5 10

0.5

1N

C, m

on

0 0.5 10

0.5

1

NC

, yr

10−6

10−3

100

0

0.5

1

10−6

10−3

100

0

0.5

1

10−6

10−3

100

0

0.5

1

10−6

10−3

100

0

0.5

1

0 0.5 1

0

5

10

VE

Ac

10−6

10−3

100

0

5

10

Ps

10−6

10−3

100

0

5

10

Pf

Figure 2. Runoff performance for River Sénégal at Bakel 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 calibra-tion time period (1904 – 1951). Values for the 500 (3.3%) best sets are shown as large dots. (Paper III)

Time aggregation Equifinality of both runoff parameters, and also of the evaporation parame-ter, increased when successively calibrated against monthly, annual, and long-term average runoff (Figure 2). The trend was very clear when going from annual to long-term average aggregation but less clear when going from monthly to annual aggregation. Equifinality decreased in some cases from monthly to annual aggregation, especially for the evaporation parame-ter. It was also evident that LA75 was too permissive in combination with annual data (Table 5).

43

Regionalisation The 17×39 window reached the majority of the ungauged cells in paper II (Table 6). The regionalisation was successful since a majority of the region-alised cells got parameter values that were found among all or at least the majority of the surrounding basins.

Table 6. Number of cells that fall into the different regionalisation categories in paper II.

Category Cells

No station found within the window =>default value 6,337 Only one station (with accepted values) within the window 3,997 No common values was found between the stations (2 or more stations) =>default value 1,674 A common value between up to 50 % of the stations (4 or more) 2,917 A common value between more than 50 % but less than 100% of the stations (3 or more stations) 10,272 Common value for all stations (2 or more stations) 7,349 Value set from own station 24,641 Value set from own station, not used in regionalisation 1,945 Total land cells 59,132

Routing The performance of the aggregated time-delay histogram remained constant over all resolutions while the performance of the linear reservoir routing decreased with decreasing resolution and exhibited a zigzag pattern, with dramatically changing performances between small resolution differences (Figure 3). The combined benchmark simulation is somewhat better than the linear reservoir method but it has the same variability and performance de-crease with decreasing resolution.

The optimum velocity was constant the over the different scales with the aggregated time-delay histogram, while it varied somewhat with the linear reservoir method. The best WASMOD parameter values were the same with all spatial resolutions with the aggregated time-delay-histogram method while a wide range of parameter values were selected as best for different resolutions with the linear routing algorithm.

The difference between the simulations to distributed and uniform climate forcings were minor compared to the large differences between the different routing models.

44

10 20 30 40 50 600.65

0.7

0.75

0.8

0.85

0.9

Cell size (minute)

N−

S co

effic

ient

TDH, V45

= 8 m/s

TDHuni

, V45

= 8 m/s

LRR, V = 0.4 m/sLRR

uni, V= 0.4 m/s

Bench, V = 0.45 m/sBench

uni, V = 0.45 m/s

Figure 3. Best simulated runoff performance at Boluo in the Dongjiang basin with the NC criterion. TDH = aggregated time-delay histogram, LRR = linear reservoir routing, bench = benchmark run with time-delay calculated from the low resolution network. Both distributed (straight lines) and uniform (dotted) climate data are used for all three simulations. (Paper IV)

Validation Within-year runoff patterns The tuning against the long-term VE in paper II was compared with the within-year runoff dynamics. These were reasonably well captured for most of the 663 stations. There was a general tendency that simulated runoff var-ied more than the measured (Figure 4), while there were a few examples of the opposite. There was also a tendency for around 40% of the gauging sta-tions that the simulated peak flows occurred earlier than the measured (Figure 4), while a delayed peak only occurred at 15% of the stations.

45

Jan Apr Jul Oct0

10

20

30

40

50Mackenzie

Jan Apr Jul Oct0

20

40

60

80

100

120Mississippi

Jan Apr Jul Oct0

1

2

3

4Loire

Jan Apr Jul Oct0

50

100

150

200

250Congo

Jan Apr Jul Oct0

2

4

6

8Wisla

Jan Apr Jul Oct0

20

40

60

80

100Yenisey

Jan Apr Jul Oct0

5

10

15

20

25

30Huang He

Jan Apr Jul Oct0

20

40

60

80

100

120Chang Jiang

Jan Apr Jul Oct0

20

40

60

80Lena

Jan Apr Jul Oct0

0.5

1

1.5Guadalquivir

Jan Apr Jul Oct0

0.5

1

1.5Maas

Jan Apr Jul Oct0

5

10

15

20

25

30

35Sénégal

Jan Apr Jul Oct0

100

200

300

400

500Amazon

Jan Apr Jul Oct0

10

20

30

40Danube

Jan Apr Jul Oct0

20

40

60

80Brahmaputra

Figure 4. Long-term within-year variations in runoff and precipitation (grey bars) from 15 representative gauging stations at 6 continents averaged over different time periods (in units of 1000 m3 s-1). Measured monthly runoff (white dots) and simu-lated with WASMOD-M (black dots) based on a parameter-value set tuned from 485 globally-distributed gauging stations. Note different ordinate scales. (paper II)

Global and continental water balances Globally, nearly half of the 1680 parameter-value sets in paper II produced runoff within ±20% of the measured values integrated over all gauged areas. However, none of these globally-uniform sets could produce acceptable simulations of runoff from all continents. All acceptable globally-uniform parameter-value sets produced overestimated runoff from Europe and all sets caused state-variable problems at some point.

Continental and global runoff values with the distributed parameter-value set of WASMOD-M were in the same range as measurement compilations and comparable investigations (Table 1). Runoff was simulated better for individual continents with continentally-uniform parameter values, than with the globally distributed parameter-value set, but at the cost of compensating errors at the basin scale.

Split-sample validation The access to time-series data in paper III provided the possibility of split-sample test. The best parameter-value sets identified during the calibration

46

period produced the among best validation period results for all criteria (Figure 5), although the absolute criteria value could differ.

Figure 5. Modeled runoff performance for validation (second half) versus calibra-tion (first half of observation) periods for three evaluation criteria (Nash, NC; limit of acceptability, LA, and volume error, VE). Top row shows performance for Sé-négal River at Bakel (observations 1904 –1989) and bottom row for Ob River at Salekhard (observations 1930 – 1999). Simulations based on the best 150 (1%) cali-brated 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 III)

Comparison with other models The capacity to mimic observed runoff vary largely between present-day global water-balance models (Figure 6). The varying number of models per basin reflects the lack of easily available simulation data and model inter-comparisons. The non-calibrated models generally perform worse than the calibrated but also the latter can have large volume errors.

47

Sénégal Huanghe Mackenzie Wisla Mississippi Lena Yenisei Loire Maas Danube Zaire Changjiang Amazon−100

−80

−60

−40

−20

0

20

40

60

80

100

VE

Model deviations rangingfrom −14% to 424%

WBM

WGHM, final

WGHM, before corr.

MacPDM

VIC, uncalib.

VIC, calib

K&PH

WASMOD−M; WN07

previously published

150 best with NC

150 best with VE

Figure 6. Volume errors (%) for WASMOD-M and 5 other global water-balance models at 13 major basins sorted after increasing specific runoff at their down-most discharge stations, from low (Sénégal) to high (Amazon). Published results (left-hand) of calibrated models are marked with filled symbols and non-calibrated mod-els with open symbols. WASMOD-M results from paper III (right-hand) relate to runoff ranges simulated with the 150 (1%) best parameter-value sets based on vol-ume error (VE) and the Nash criterion (NC). Reported runoff can come from differ-ent stations in the system, but with small area differences. Models are VIC with and without calibration (Nijssen, et al., 2001a), “K&PH” (Kleinen and Petschel-Held, 2007) and WASMOD-M “WN07“ (paper II). Additionally, with error percentage calculations from reported measured and simulated flow; WBM (Fekete et al. 1999b), WGHM before and after additional correction factors (Döll et al., 2003) and MacPDM with lowest absolute volume errors when several values are reported (Ar-nell, 1999; 2003; 2005) and with approximate values from figures for the European basins (Arnell, 1999).

48

Discussion

A major difference between global and catchment water balance modelling is that when studying a specific catchment only, there is normally a possibil-ity to gather catchment-specific information that can be utilised in the mod-elling. Global-scale water balance modellers are referred to and dependent on global datasets and detailed information about each catchment is not available. The analysis must focus on the general picture and unexpected results for single basins cannot be explored in detail.

Data problems Several types of data problems face the global water balance modeller. These errors were grouped into three classes in paper II: (i) geographical boundaries and positions, (ii) runoff- and climate-data quality, differing time periods and (iii) unknown or unavailable anthropogenic runoff influences.

Geographical boundaries and positions Basin areas for given gauging stations can sometimes differ considerably (Renssen and Knoop, 2000), which causes problems in validation of digital river networks and results in different runoff estimates in model compari-sons. One reason for the difference in arid areas is that digital flow networks normally calculate the whole upstream area, while station-based estimates can report values on the actively discharging area only (Fekete et al., 1999a). The area differences can introduce large differences in calculated runoff volumes (Arnell, 2005; Döll et al., 2003). Comparison of different runoff data-bases such as STN-30p/GRDC (Fekete et al., 1999b) and GHCDN (Dettinger and Diaz, 2000) reveal that reported gauging stations positions can differ as well.

Inconsistent runoff and climate data and differing time periods The measured average runoff is higher than the precipitation in some basins (paper II; III; Fekete et al., 1999a; Nijssen et al., 2001a). Two main reasons are the sparse precipitation gauge network in mountainous areas where pre-cipitation amounts are higher compared to lowlands, and the gauge under-

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catch of precipitation (Adam and Lettenmaier, 2003; Adam et al., 2006; Legates and Willmott, 1990). Despite the runoff coefficient problems the precipitation correction is too high in some areas. The correction factors by Legates and Willmott (1990) used in this study are known to be too high for Europe (Arnell, 1999c; Döll et al., 2003). They also cause a double-correction in Russia since the stations that form the reference climatology for the CRU time series already are corrected for gauge undercatch (New et al., 1999). Some small Russian basins show too high runoff coefficients despite the double corrections. Another possible reason of too high runoff coeffi-cients is glacier melt. The melting Alaskan glaciers studied by (Arendt et al., 2002) are however not situated in the same Alaskan basins where paper II and III present too high runoff coefficients.

The globally-uniform parameter Ec in the potential evaporation calcula-tion caused too high values in arid areas and too low in arctic areas in paper II. The usage of published potential evaporation datasets in paper III im-proved the calculations, but very high dryness indices (potential evaporation divided by precipitation) indicated that the potential evaporation was still too high in some arid areas, possibly in combination with too low precipitation. The simplest work-around would be to use the minimum instead of the maximum from the two reference datasets while a more detailed approach would be to use additional data, such as radiation, and utilise the knowledge about the effect of the different potential evaporation calculations (Vörös-marty et al., 1998; Arnell, 1999c; Kaspar, 2004).

Average runoff and precipitation are not constant in time and data from different time-periods can cause differences and complicate the calculation of inter-station runoff (paper II). Mismatch between measured upstream and downstream discharge are also caused by measurement errors (Fekete et al., 1999a), water withdrawal and river-bed seepage, and evaporation from open water bodies in warm climate (Döll et al., 2003). All global runoff estimates does not include information about the time period for the calculation (Table 1).

Unknown and unavailable anthropogenic runoff influences. Most hydrologic models mimic natural variations of water-balance compo-nents (paper II). Regulation of rivers by dams, re-routing of water to other basins, and water extraction are major anthropogenic influences that consid-erably disrupt the natural water balance. Vörösmarty et al. (1997) and Nils-son et al. (2005) quantify the influence of dams and the degree of regulation of large rivers and find that dams globally impact 83% of the global runoff, and represent a 700% increase in the standing stock of natural river water, with residence times for individual impoundments spanning from one day to several years. We are still far away from a trustworthy global database of time series accounting for anthropogenic influences of the global water cy-

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cle. Hence, even a perfect fit between simulated and measured runoff needs to be evaluated critically and should not be overrated.

Parameter behaviour It was found in paper II that globally uniform parameter-value sets could produce good global runoff estimates, but at the cost of compensating errors at the continental scale, and that continentally uniform parameter-value sets could produce good continental runoff estimates, but at the cost of compen-sating errors at the basin scale. Similary, Arnell (2005) found large discrep-ancies for individual basins simulated with MacroPDM, although the total runoff fitted well. Optimal parameter-value sets can differ between upstream and downstream sub-basins in the same system (paper II; III; Döll, et al., 2003) but the tuning against inter-station runoff is complicated, especially for time-series, but also for average values. Inter-station sub-basin cover 63% of the gauged areas in “UNH/GRDC Composite Runoff Fields” and inter-station tuning is thus an important, but rarely discussed task. Some problems to tackle are mis-matching time-periods of upstream and down-stream gauges, non-modelled losses such as evaporation and water with-drawal, and the question if bad simulated upstream runoff should be cor-rected or not to provide good inflow to the downstream area.

All parameters are assigned uniform values over large areas in WAS-MOD-M, as opposite to the other global water balance models where some parameters vary with, e.g., the properties of vegetation and soil. These dif-ferences complicate cell-by-cell model comparison (paper II) and make model estimations from WASMOD-M less reliable for, e.g., a country. Fur-ther distribution of the parameter values is a future model development goal.

The assumption in paper II that WASMOD-M is overparameterised when tuned only against VE was confirmed in paper III. The model evaluation criteria NC and LA focusing on the runoff dynamics confined the evapora-tion- and runoff-parameter spaces to a much higher degree than VE. The evaporation and slow-flow parameters Ac and Ps could not be simultaneously well confined by any criteria. Ac was more confined by all runoff criteria for non-snow than snow basins, and the opposite was partly true for Ps and Pf. These climatic differences between parameters need further attention in fu-ture studies, and the low number of parameters might still need reduction.

The evaluation against snow-covered data through SF in paper III showed that the snow parameters Ts and Tm were confined by SF. All equifi-nality could not be removed and future model versions might use a fixed Tm value. This finding might be challenged with snow-water equivalent data or snow cover data that can be used also at the start and end of the snow season. Evaporation data would also be very useful for model evaluation and tuning.

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The number of basins with VE values within 20% simulated by the final parameter value set in paper II increases to 455 from the used 429. This is however lower than the 485 basins which were well modelled with the uni-form parameter-value-sets. The decrease is caused by the overwriting by downstream sets and the usage of the upstream measured runoff in the re-gionalisation algorithm. The latter approach was chosen to avoid compensat-ing errors downstreams, and because usage of the whole range of upstream accepted parameter value sets combined with the downstream sets would give too many combinations.

Time aggregation and criteria relationships Generally, the equifinality of the runoff and evaporation parameter values increased when the model was tuned successively against monthly, annual and long-term average runoff (paper III). The most common exception was the evaporation parameter Ac, that on average was slightly more confined by the annual NC and LA values than by the monthly. Generally the monthly and annual NC and LA criteria confined the parameter values to about the same parameter-value space, although the selection of the 1% best parameter values could differ.

NC and LA values are not comparable between the time aggregations. NC is normally lower for annual time-series because of their lower variability. The majority of the stations had short time-series which made the annual NC values uncertain. Usage of whole time-series, instead of only the first period might partly solve this problem.

Just as NC and LA are not comparable between time aggregations, they are not fully comparable between basins either. NC depends on the observed runoff variability and high values can be achieved also with poor models (Schaefli and Gupta, 2007). The improvement over a benchmark, calculated from, e.g., scaled precipitation is worth exploring.

In many senses NC and LA behaved similarly, but the best NC values fit-ted much better than the best LA values with the best VE values. The LA criterion needs further investigations before it can be fully utilised on the global scale. It is likely that narrower limits easier would identify good pa-rameter value sets of the well-simulated basins. Further studies are also needed of the not so well modelled stations, both regarding the inclusion of additional processes to the model, and the criteria behaviour.

The larger equifinality of the VE criterion also resulted in a wider range of possible runoff dynamics, while the constriction of the snow parameters though SF only marginally influenced the runoff. Also Dunn and Colohan (1999) and Udnæs et al. (2007) find that internal model consistency can improve with snow data in addition to the runoff data, but that the total run-off is only marginally affected.

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The VE criterion was combined with limits for the state-variables in paper II. The usage of criteria focusing on the dynamics minimised these problems in paper III and no state-variable limits were used. The few stations that still experienced problems coincided with low NC values and warm-up times much longer than for other stations. Preparation of a distributed initial state-variable set, in combination with continued usage of criteria focusing on the dynamics, might eliminate the problem.

Validation The model performance tuned against VE only was compared against within-year dynamics in paper II whereas the access to time-series data enabled validation against an independent time-period in paper III. Comparison with other global runoff estimates and the performance of other models in indi-vidual basins were also used for comparison in papers II and III. Compari-son against other models and estimates can, strictly speaking, not be called validation in a Popperian sense. When simulations agree with those of earlier models, it does not prove that the simulations are right since all earlier mod-els might be wrong.

Within-year dynamics and split-sample validation The present version of WASMOD-M does not account for, e.g., time delays along river networks, evaporation losses from dams and rivers, flood inunda-tion, anthropogenic water abstraction, river regulation, river routing, subgrid variability, glacier dynamics, permafrost and capillary rise. Future model development may include additional processes and input data if validation data and consistency checks can substantiate them (paper II). The missing routing (both natural and anthropogenic though dams) is a main reason why WASMOD-M often simulated peak runoff too early (paper II). The within-year dynamics however agreed reasonably well with the measured. Altera-tions by humans, which are more common during the validation period, as well as climatic variations, affected the split-sample test (paper III). The best parameter of the calibration period values were the best, or among the best also for the validation period. For some basins was the whole set of 15000 parameter value combinations improved for the validation period, and for some basins were all impaired.

Model shortcomings were not always easy to explain, but some reasons were non-modelled lakes, that gave NC values below 0 and too high runoff coefficients that gave too high VE values and extreme values of the evapora-tion parameter Ac (paper III). Larger basins were normally easier to model since different errors could cancel each other.

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Comparison with other models and estimates A total global runoff of 38,605 km3yr-1 was simulated in paper II (Table 1). This was in the same range as previous model- and measurement-based es-timates. It was higher than the estimate by Döll et al. (2003), which can be expected as they do not apply correction factors to the CRU precipitation, but lower than the estimate Gerten et al. (2004) who also do not correct the CRU precipitation. There is a tendency that measurement-based estimates are higher than the model-based, although the opposite should be expected. The runoff from Europe approached earlier estimates when uncorrected pre-cipitation was used, and the runoff from South America was well simulated if the state variable were allowed to exceed their limits.

All global water balance models perform “reasonably well”, but every model still has large errors in some areas, and these do not necessary coin-cide (Figure 6). The development of global water balance models would benefit from model intercomparisons, with, e.g., similar input data and river networks. Gerten et al. (2004) and Hanasaki et al. (2007a) compare the cur-rent results of some of the models.

WASMOD-M is a simple global water balance-model, and the simplicity introduces limitations in the possible uses of modelled data. WASMOD-M, together with Macro-PDM and WBM, only simulate natural runoff, without any major human alterations. As humans affect a major part of the global river runoff (Vörösmarty et al., 2004; Oki and Kanae, 2006) this is too sim-plistic in most river basins. It was shown in paper III, that WASMOD-M, despite being very parsimonious, still suffer from equifinality. Except for the model by (Kleinen and Petschel-Held, 2007) WASMOD-M use the fewest number of paramters, and it can be questioned if the other water balance models are not overparameterised as well. This question might be weakened by the fact that WASMOD-M has the highest number of calibrated model parameters. Parameter values are commonly estimated from physiographic datasets instead of being calibrated (Arnell, 1999c; Döll et al., 2003; Vörös-marty et al., 1998). Theoretically this is better than calibration, but the un-certainties introduced by these datasets (Hannerz and Lotsch, 2006; Peel et al., 2007), must be taken into account.

An interesting question, which has no clear answer, is whether additional correction factors should be applied when a model fails. When a correct upstream input is wanted for a downstream station, corrections are applied by Döll et al. (2003) and Fekete et al. (1999a). Arnell (2003) who only evaluate runoff against the downmost station do not use any correction. The overwriting of the upstream best parameter-value sets by the downstream best, as used in paper II and by Nijssen (2001a), can also be seen as a cor-rection.

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Routing The new aggregated time-delay-histogram routing is not dependent on the flow network scale and can be used for further studies of the impact of pre-cipitation heterogeneities at different resolutions. The widely used linear reservoir routing can however introduce much larger errors than the uncer-tainties caused by low-resolution climate data. The variability of the linear river routing and the benchmark simulation is most likely caused by the large changes of the flow networks between the different resolutions and the relocation of the gauging station (paper IV). Decreasing model performance with decreasing resolution is also noted by (Guo et al., 2004), but while the performance of aggregated time-delay-histogram remained constant with decreasing resolution their proposed multiple-outlet approach of the low-resolution network also decrease in performance, although as not as much as the standard single-cell outlet network. The zigzag pattern can however not be seen in their result. One possible reason is that they test much fewer reso-lutions.

The variable identification of the best WASMOD-M parameter values in the calibration procedure with the linear reservoir routing implies that non-optimum runoff parameters are selected to compensate for errors in the rout-ing procedure.

The work in paper II and III highlight the need for routing in WASMOD-M. The aggregated time-delay-histogram method has potential to be applied globally. One advantage is that lakes are implicitly represented with their almost zero slope. One drawback is the calibration, but as the velocity pa-rameter was constant over the scales in the Dongjiang catchment it can be speculated that it will remain constant also in other basins. The preparation of the time-delay histograms will be computationally demanding, but once this data is prepared, the routing itself much quicker than cell-to-cell routing.

It should be stressed that the time-delay-histogram method can be applied for any destination cell, not just the basin outlet. Maps of accumulated dis-charge, as provided from cell-to-cell routing, can be produced by applying the method with a destination cell in each low-resolution cell. The high-resolution destination cell should be the cell with the largest upstream area within the low-resolution cell. The time-delay-histogram method can be methodologically classified as between source-to-sink and cell-to-cell rout-ing.

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Conclusions

Model calculations of global runoff differ a lot between different models. The errors of simulated river runoff can be large and do not always point in the same direction. Global water balance models perform “reasonably well”, and do not show as good performances as can be found when investigating a single well-monitored basin. Data access and quality is a main limitation. Precipitation and river regulation are major sources of uncertainty.

It was shown that the new simple global water balance model, WAS-MOD-M, could simulate the global runoff “reasonably well”. A simple re-gionalisaiton procedure that utilised proximity only contributed to calculate a global runoff estimate in line with earlier estimations. Already tuning against the volume error produced reasonable within-year patterns produced in most basins, but the volume error was not enough to confine the parameter space. The parameter space and the simulated hydrograph could be better confined by, e.g., the Nash criterion. Calibration against snow-cover data could con-fine the snow parameters better, although some equifinality still persisted. Thus, even the simple WASMOD-M showed sign of being overparameter-ised. At the same time it was shown that global uniform parameter value sets produce reasonable global runoff, but at the cost of compensating errors at the continental scale.

A new aggregated time-delay-histogram routing method, that utilised high-resolution flow network information in low-resolution calculations performed equally well over all scales in the Dongjiang catchment, while the standard linear reservoir routing decreased in performance with decreasing resolution. This algorithm was developed for later improvement of WAS-MOD-M. The somewhat ambiguous runoff evaluations against monthly and annual observations will be easier to analyse when the routing is imple-mented.

The development of global water balance models would benefit from bet-ter precipitation data, both in terms of coverage and gauge corrections. Lar-ger spatial and temporal coverage and less error in runoff data would also be very useful, together with estimation of other properties, such as evaporation and snow, for further model consistency checks. A global data-base of dam-operation schemes is probably not possible, because of company secrets, but would be very useful for the research community. Model intercomparisons and model ensembles that use the same standardised inputs, would also con-

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tribute. Estimates of global runoff should be followed by information about time period and included flows.

Possibilities for future work Further work with WASMOD -M could continue along three paths, testing, development, and application. These are no separate paths and numbers eventually presented from the application path should be given together with uncertainty estimates. Model testing will point out important parts of the model to improve, and new model versions should be thoroughly tested as well.

Testing could be continued in different directions. One example is cli-matic split-sample tests to improve trust in model applicability for climate-impact studies. When improved regionalisation methods have been incorpo-rated they should be tested with cross-validation techniques. The simulations results from paper III could be further analysed in a proxy-basin context. A forthcoming model version with the new routing algorithm could be ex-pected to behave differently when evaluated against monthly versus annual observations so the time-aggregation tests should be repeated. Since the study of model efficiency is not an absolute science, development of bench-marks along the suggestions of Schaefli and Gupta (2007) should be tested, not only against WASMOD-M simulations but also against simple statistical models to verify that model performance is not just the effect of pure luck.

The input data used has well-known shortcomings and the model simula-tions will improve with better data, especially for precipitation. Usage of several driving datasets will provide another uncertainty assessment. Addi-tional data on, e.g., evaporation and snow-water equivalent will provide both testing and further calibration possibilities.

Global water balance models, as being applied everywhere, might be use-ful for exploration of advantages and disadvantages of more general models (Andréassian et al., 2006) compared to models with adoptions to the condi-tions and data availability at each sites (Beven, 2007). The learning from the model applications is central to both approaches.

Model development could first of all be continued with regionalisation and routing. Regionalisation could encompass methods based on independ-ent physiographic datasets to get reasonably distributed parameter-value datasets both within and between basins. Distributed parameter-value sets are expected to produce better inter-station runoff. The model algorithms could be reformulated to avoid calibrated parameters. The evaporation for-mulation could be revisited on the basis of physically reasonable limits in various parts of the world. Routing could be included that account for forth-coming databases of dams (Reidy Liermann, 2007). Rivers like Colorado, Huang He, Nile, and Amu Darya and Syr Darya (Gleick, 2003) will not be

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well simulated unless water losses withdrawal and open water evaporation are modelled. Long-term effects of melting glaciers in the world, especially in Asia, could be studied through inclusion of these processes.

Investigations of many large-scale water-resource problems such as water conflicts between nations, trans-boundary water management, virtual water trade, population growth in relation to water scarcity, changed land use and climate change are possible applications after model improvements.

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Acknowledgements

Welcome to the most read part of every thesis! It is an important part since there are so many that have their share in this work. I wouldn’t have made it without all of you!

First of all, my supervisors Sven Halldin and Chong-yu Xu: I’ve been for-tunate to have very kind supervisors that also have been available almost all of the time. Your doors were always open and quick e-mail answers came from Chong-yu in Oslo as well as in Hongkong. Sven, every text suggestion that passed you improved and I appreciate that help a lot. Remaining errors in this thesis are my own. You also managed to find the general picture among all the details that I provided to you with. But when it comes to ad-ministrative peculiarities we were commonly interested! Thanks also to Bitte for selecting your vacation in such a way that Sven was available to check my texts almost anytime during the last week!

I’m happy to have had Lars-Christer Lundin as my third supervisor. As you did not participate in the daily work you could see everything with some distance and always had good suggestions at the formal meetings where we gathered.

Lebing Gong, already the day I got to know that I would get you as fellow global modeller I started to think about what to write about you here as I knew that your addition would speed-up and improve my work a lot – and it certainly has. You’re smart, quick and ambitious. You are also very kind – I do not know how many times you told me not to worry this last autumn. As the first author of the routing paper you also got very much pressure on you this last month because of my thesis deadline, together with the other tasks you had to fulfil.

Keith Beven, I appreciate that you have taken your time in reading and correcting my papers. Although we didn’t meet so much during your year here in Uppsala I’ve noticed how you really have inspired my modelling colleagues.

Visualisation is very important for understanding model data. Andreas G and Dan helped me with GIS program tricks.

The global modeller is dependent on datasets gathered and made avail-able. I’m very grateful to all those individuals and groups that freely provide their data. The data used in this thesis come from: Tim Mitchell and David Viner at Climate Research Unit (CRU) at University of East Anglia, Will-mott, Matsuura and collaborators at University of Delaware, GRID-Tsukuba

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at National Institute for Environmental Studies and Chung-Hyun Ahn and Ryutaro Tateishi at Chiba University, Water Systems Research Group at University of New Hampshire, Thomas de Couet at Global Runoff Data Centre (GRDC), Michael Dettinger and Henry Diaz though Byron Bodo and the Data Support Section at the National Center for Atmospheric Research, International Satellite Land-Surface Climatology Project (ISLSCP) and the National Snow and Ice Data Center (NSIDC) at University of Colorado, Boulder.

My calculations have sometimes been computer demanding and several LUVA co-workers have let me use their computers. Some of the computa-tions in paper III and IV were performed on UPPMAX resources under Pro-ject p2006015.

The major part of the funding for this project came from Swedish Re-search Council on contracts 629-2002-287 and 621-2002-4352. Additional funding came from the Department of Earth Sciences, the National Graduate School in Scientific Computing and Liljewalchs traveling scholarship. The 3 start-up months after a parental leave decided by our faculty is well worth exporting to other universities.

When I started in the hydrology group, it was me, Auli, and “It’s raining men, hallelujah!” for the rest, and the lunches even more so (Fredrik – the vacation in Paris, Fritjof, Johan Ö, Klas, Magnus, Niclas, Tony, Andreas G and Micke). I miss you guys! Tomas Nord has been a reliable lunch compan-ion over the years. You, later with the aid of Johan T, also keep our com-puter system running and free from viruses, worms, trojans etc. so we do not have to worry. It is also always nice to stop at your open door for a chat.

In this world of men I noticed after a while that I had to giggle sometimes and that was best made with the meteorologists (Anna S, Cicci, Karin T – the company, Xiaoli – the game evenings). Hanna Z, I’m happy that you joined the hydrology group (and started your own process of smoothing the educational background among the Ph.D. students). Hanna was later fol-lowed by Zairis and Ida (the limit of acceptability inspiration) so if Julia (belonging to all old divisions!) is counted in we are five women and four men (José Luis, Lebing, Martin, Michael) as long as I’m not a doctor!

From Erik K to Elias, the list of nice young researchers that has passed the “LUVA(L) Challenge” group is long: Andreas B, Angelica, Anna L, Aziz, Dan, Håkan, Jenny, Karin J, Sara-Sofia, Toddy (die Gespräche), Anna R, Andreas K (the evening talks), Babatunde, Björn C, Erik S (the practical thesis information), Igor, Kim, Maria, Mathias, Wasana, Abdulhadi, Anne-Marie, Björn S, Hanna R, Jim, Karin A, Marcus, Flora, Fredrik H, Louise, Markus, Stefan. From other parts of the department I’m happy for the coop-eration and friendship with Camilla P, Chris A and Mattias L. Thanks also to all colleagues that have checked that I’m doing all right during these last stressful months (Allan, Cicci, Hélène, ...). Our very quick printing office also has an important share in that it was possible for me to finish this work.

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I have learnt a lot from teaching (including the complexity of reverse park-ing in snow) in the co-operation with other teachers (Allan, Rajinder, Roger, ...) and contacts with students. The UVC years were also fun. It has been inspiring to meet other researchers at conferences and courses (the birthday and football in Umeå).

The soil science project during my undergraduate studies, under the guid-ance of Petra Bergkvist and Nick Jarvis at SLU was very important for my wish to do a Ph.D. I’m also very happy for the year I spent with Per-Erik Jansson and co-workers at KTH, in cooperation with the Uppsala limnolo-gists, where I got both practical measuring experience and some SVAT knowledge. Further back, the advanced environmental science course by Jack-Sture Börjesson and Sten Willstrand at Nils Ericsonsgymnasiet stands out in my memory – not only because of the fika! The projects during that course I carried out with Kajsa, which leads me over to all my friends among the “theatre people”, whom I met both at lunches, courses and fully outside of work. This text is becoming lengthy but at least I want to mention Sara J, Kneppers, KTF and Uppsala baptistförsamling too, and my (lunches with Tove) and Daniels relatives.

My parents and parents-in-law have a large share in this work. They have travelled several hours during many weekends of this autumn to come and help us at home such that I could focus on working. Thanks for all the love and support! Gustav and Anders, it is quite fun that we end up doing pro-gramming all of us, isn’t it? Maybe it is something in the genes from Rosa, Arne, Britt-Marie and Conne?

Daniel, my love, you’re the best! You answered computer questions, dis-cussed practical, theoretical and philosophical research question with me and took care of Ture day and night while I was working. Without you and your hugs this had not been possible. (For those of you that share my interest in details: I’m married Widén Nilsson but I publish as Widén-Nilsson.)

Ture – dina leenden är de finaste jag någonsin sett. Nu skall vi leta efter roliga lekplatser i Bern tillsammans!

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”Vatten som rör sig i en flod antingen lockas, jagas eller rör sig av sig självt. Om det lockas, eller begäres, vem är den begärande? Om det

jagas, vem är den som jagar det? Om det rör sig av sig självt visar det prov på förnuft, vilket är omöjligt hos kroppar som ständigt föränd-

rar form, ty i sådana kroppar finns inte något förstånd.”

Leonardo da Vinci, 1452-1519, “vatten och vind”, sidan 161, texter av Leonardo da Vinci utvalda och översatta av Astrid Hjort. bokförlaget skara-

bé, 1995. Lund.

“Bara en vattenpuss ville jag vara

och spegla himlen”

Dom Helder Camara. 1982. Tusen skäl att leva. Översättning av Chatari-na B Broomé. Proprius förlag.

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Sammanfattning på svenska (Summary in Swedish)

Vatten är nödvändigt för allt liv på jorden. Vi människor behöver vatten inte bara för mat, dryck och hygien, utan även för våra djur, bevattning av grö-dor, elkraft och industriellt bruk. Vi tjänar även på väl fungerande ekosys-tem, men alltför stort uttag av flodvatten kan orsaka stor skada på naturen och därmed våra egna livsbetingelser. Redan idag saknar mer än en miljard människor tillgång till rent dricksvatten (WHO/UNICEF, 2000) och antalet drabbade människor riskerar att öka med befolkningsökning och klimatför-ändringar (Vörösmarty m. fl., 2000a; Alcamo och Henrichs, 2002; Arnell, 2003). Förutom koldioxidutsläppens förutspådda indirekta påverkan på den globala hydrologiska cykeln sker en kraftig direkt påverkan redan idag ge-nom bland annat bevattning och dammar (Vörösmarty m. fl., 2004; Gordon m. fl., 2005; Oki och Kanae, 2006, Haddeland m. fl., 2007). Datormodeller är ett användbart verktyg vid förutsägelser om framtida effekter av t.ex. kli-matpåverkan och globala problem kräver globala datormodeller (Eagleson, 1986; Shuttleworth, 1988). Ingen datormodell kan dock beskriva verklighe-ten exakt, utan alla är förenklingar. Modellerna begränsas av dessa förenk-lingar, liksom av osäkerheter i de mätdata som de bygger sina beräkningar på. Är dessa modeller tillförlitliga? Hur bra kan de återge dagens förhållan-den och klarar de att räkna på morgondages förändrade förhållanden? Den globala avrinningen från floder till oceanerna anges ofta till värden runt 40 000 km3 per år, men de olika beräkningarna skiljer sig lika mycket som flödet motsvarande en hel kontinent. Dessa beräkningar görs endast baserade på mätdata, eller med hjälp av datormodeller. Skillnaderna kommer från olika typer av beräkingsmetoder, olika definitioner av vilka flöden som skall räknas in och olika tidsperioder som används.

Vattenföringen i alla jordens floder kan beräknas med olika sorters mo-deller, inklusive de globala klimatmodellerna. Trots att många modeller är mycket avancerade är deras simulerade resultat inte så bra som man skulle kunna önska. De globala klimatmodellerna har framförallt svårt att simulera nederbörd korrekt. Denna avhandling fokuserar på de enklare s.k. globala vattenbalansmodellerna. Dessa modeller beräknar tidsserier av flodernas vattenföring från tidsserier av bl.a. nederbörd och temperatur. Avhandlingen handlar till stora delar om en ny global vattenbalansmodell, WASMOD-M, och hur man kan få den att räkna ut vattenflödena så korrekt som möjligt.

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WASMOD-M är en enkel global vattenbalansmodell som använder färre parametrar än de flesta andra liknande modeller, vilket är en fördel. I en modell med många parametervärden är risken för överparameterisering stör-re. I en överparameteriserad modell kan flera olika parametervärdeskombi-nationer ge lika gott resultat, s.k. ekvifinalitet. WASMOD-M beräknar inte heller lika många processer som flera andra modellerna, vilket snarare är en nackdel, men fler processer kräver också fler parametrar. Om man arbetar med hela jorden behöver man få tillgång till data över hela jorden. Att göra den sammanställningen själv är alltför omfattande och globalmodelleraren är därför till största del beroende av andras sammanställningar. Man kan inte heller, som i en studie av ett enskilt avrinningsområde, gå ut och göra fler mätningar vid behov, utan är begränsad av att vissa områden på jorden sak-nar mätningar av vattenflöden och nederbörd. WASMOD-M beräknar vat-tenbalansen för alla jordens landytor, utom Grönland och Antarktis, i rutor som har storleken 0,5° latitud × 0,5° longitud. Jordens rundning gör att ru-torna är större vid ekvatorn än vid polerna. Modellen använder månatliga värden på nederbörd, temperatur och ångtryck för beräkningarna. Dessa data kom från Climate Research Unit i England. Modellen behöver också ett flö-desnät, som talar om vilken ruta som hör till vilket avrinningsområde, och här användes STN-30p från University of New Hampshire i USA. Uppmätta vattenflöden behövs för att jämföra modellens resultat med verkligheten. Flödesdata från 663 mätstationer i 257 huvudavrinningsområden kom från Global Runoff Data Center i Tyskland. Nederbörds- och flödesmätningar är behäftade med stora mätfel. Mycket stora fel fås även om modellerna drivs med nederbörd beräknad av en global klimatmodell. Ett ytterligare problem är att vattenföringen i en stor del av vattendragen är påverkad av dammar och vattenavledning för bevattning. De flesta modeller, inklusive WAS-MOD-M, inkluderar dock inte denna mänskliga påverkan eftersom den är svår att beräkna. Det gör att simulerade och uppmätta flöden inte är helt jäm-förbara. Typiskt simulerar modellerna toppflödena en månad tidigare än de uppmätta värdena, p.g.a. fördröjning som sker i dammarna. Fördröjning av vattnet sker inte bara i dammar utan även vatten som genereras högt upp i avrinningsområdet tar längre tid på sig att nå utflödespunkten än avrinning som genererats längre ned i systemet. WASMOD-M inkluderar inte denna fördröjning än, men i artikel IV utvecklas en ny sådan metod för ett enskilt avrinningsområde i Kina.

Det finns en uppsjö av utvärderingsmått som anger hur bra en viss simu-lering är jämfört med mätdata. Utvärderingsmåtten används både för att ana-lysera modellens beteende och för att välja ut de parametervärden som ger bäst resultat (kalibrering).

Fem av de sex parametrarna i WASMOD-M behöver kalibreras, medan den sjätte bestäms i förväg. Parametrarna är begreppsmässiga och kan där-med inte mätas utan måste kalibreras. Två parametervärden används för snöberäkningen, en för avdunstningen och två för avrinningen. Den sjätte,

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icke-kalibrerade parametern, används före själva modellberäkningarna för att räkna ut den potentiella avdunstningen, som förutom nederbörd och tempe-ratur driver modellen.

Monte Carlo-metoder som tar hänsyn till parametervärdenas möjliga ek-vifinalitet har använts vid kalibreringen. 250-15000 parametervärdeskombi-nationer har använts i de olika delarbetena. Många utvärderingsmått jämför simulerat och uppmätt resultat för varje tidpunkt. Men tanke på tidsfördröj-ningarna som WASMOD-M inte simulerar, användes endast volymfelet som jämför den totala simulerade avrinningen med den uppmätta i artikel II. Vo-lymfel som var lägre än 20% klassificerades som acceptabla. Volymfelet är ett grovt mått som inte är så användbart om man vill finna de entydigt bästa parametervärdena och i artikel III studerades även två mått som jämför hela simulerade och uppmätta tidsserien med varandra. Det första, Nashs kriteri-um, är välanvänt inom hydrologin sedan 1970-talet. Det andra, ”acceptabelt gränsvärde” introducerades av Beven (2006). Utöver dessa tre mått som jämför vattenflöden jämfördes även den simulerade snön med data på snö-täckningen över norra halvklotet från ISLSCP och National Snow and Ice Data Center i USA. Dessa data kommer från satellitövervakning och motsva-rar inte snömängden som simulerars i WASMOD-M. Ett mått användes som jämförde om snö simulerades och inte vid samma tider som snö var uppmätt och ej. De två tidsseriebaserade utvärderingsmåtten beräknades både på må-nadsgången och årsgången.

Flödesdata fanns att tillgå från ungefär 50% av jordens landområden, eller 72% om man endast räknar de områden som producerar avrinning (Fekete m.fl., 2002). Kalibrerade parametrar behöver alltså överföras till de områden där kalibrering inte kan göras. Detta kallas regionalisering. En mycket enkel kalibreringsmetod utvecklades, som söker efter parametervärdeskombinatio-ner i närliggande områden till en ruta som saknar parametervärden. De viktigaste slutsatserna i avhandlingen är: � Modellberäkningar av flöden i floder varierar kraftigt mellan modeller.

Felen i de olika modellerna är stora och inte alltid entydiga. Även WAS-MOD-M, som är en mycket enkel modell, visade indikationer på att vara överparameteriserad och särskilt snöberäkningen skulle kunna förenklas. Modellutvecklingen skulle främjas av en studie som jämför de olika mo-dellerna, när de använder samma data. Osäkerhet i data är en stor bi-dragande orsak till modellosäkerheten. Osäkerheterna finns i alla utnytt-jade data, men felen i uppmätt nederbörd är viktigast eftersom den främst av allt styr den simulerade avrinningen.

� Volymfelet är det vanligaste måttet på en modells förmåga att simulera flödet förbi en viss mätpunkt. När WASMOD-M kalibrerades endast med hjälp av volymfelet gick det att även få en ganska bra inomårsvariation, men parametervärdena kunde inte bestämmas entydigt. Med ett mått som

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även tar hänsyn till inomårsvariationen blir både parametervärdena och den möjliga simulerade avrinningen begränsade till ett snävare intervall.

� Genom att använda sig av andra data än vattenföring, i det här fallet snö, kan antalet möjliga parametervärdeskombinationer begränsas. De förbätt-rade parametervärdena behöver dock inte ha så stor effekt på den simule-rade avrinningen. Tillgång till globala avdunstningsdata skulle vara my-cket användbart för vidare studier.

� Den enkla regionaliseringsmetoden fungerade såtillvida att den globala och kontinentala avrinningen som beräknades med WASMOD-M var i linje med flertalet tidigare beräkningar. Resultaten från WASMOD-M kunde användas för att visa att den av de tidigare beräkningarna som skil-jde sig mest från de övriga (Oki, 2001) till stor del berodde på den speci-fika, korta tidsperioden som användes. Eftersom den globala avrinningen varierar mellan olika år är det anmärkningsvärt att inte alla redovisade uppskattningar av den globala avrinningen innehåller uppgifter om vilka år de baseras på. Det saknas även ofta uppgifter om vilka olika flöden som ingår, såsom avrinning till interna landområden, grundvattenutflödet i haven och avdunstning från floder och sjöar.

� En ny metod för att fördröja vattenflödet visade sig prestera lika bra även med rumsligt lågupplösta beräkningar eftersom underliggande högupplös-ta data kunde utnyttjas väl. Det visade sig också att den vanligaste meto-den, linjär reservoar, ger sämre modellresultat med minskande upplös-ning. När denna metod har inkluderats i den globala modellen kan en för-bättrad studie av effekten av tidsupplösningen på olika utvärderingsmått genomföras. Innan dess kan man endast spekulera i orsakerna till att ka-librering med hjälp av årsgången var något bättre på att begränsa det möj-liga intervallet för avdunstningsparametern än kalibrering med månads-värdena. I huvudsak var dock månadsvärdena mer begränsande, precis som förväntat. En global databas över hur flödet från olika dammar regle-ras vore mycket användbar för att bättre simulera tidsfördröjningen i flo-derna, men med tanke på hur ofta detta är företagshemligheter är det inte troligt att en sådan databas ser dagens ljus.

Det tar tid att bygga upp vattenbalansmodeller och det finns många möjliga vidareutvecklingar av modellen. Det är också viktigt att fortsätta att kritiskt testa modellen på fler sätt än vad som hittills gjorts. När modellen börjar tillämpas för att t.ex. studera gränsöverskridande vattenresurser, virtuell vattenhandel, befolkningstillväxt och vattenresurser samt effekterna av för-ändrad markanvändning och förändrat klimat är det viktigt att även informe-ra om osäkerheterna i beräkningarna.

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