modeling long-term variability and change of soil moisture

Modeling long-term variability and changeof soil moisture and groundwater level -

from catchment to global scale

Lucile Verrot

Department of Physical GeographyStockholm University

Stockholm 2016

c© Lucile Verrot, Stockholm University 2016Cover illustration: River Forth, Scotland, United Kingdom (Lucile Verrot)ISBN: 978-91-7649-387-8ISSN: 1653-7211Type set with LATEX using Department of Physical Geography thesis templatePublished articles typeset by respective publishers, reprinted with permissionPrinted by: Holmbergs, Malmö, 2016Distributor: Department of Physical Geography, Stockholm University

Abstract

The water stored in and flowing through the subsurface is fundamental for sustaining humanactivities and needs, feeding water and its constituents to surface water bodies and supportingthe functioning of their ecosystems. Quantifying the changes that affect the subsurface water iscrucial for our understanding of its dynamics and changes driven by climate change and otherchanges in the landscape, such as in land-use and water-use. It is inherently difficult to directlymeasure soil moisture and groundwater levels over large spatial scales and long times. Modelsare therefore needed to capture the soil moisture and groundwater level dynamics over such largespatiotemporal scales.

This thesis develops a modeling framework that allows for long-term catchment-scale screen-ing of soil moisture and groundwater level changes. The novelty in this development resides inan explicit link drawn between catchment-scale hydroclimatic and soil hydraulics conditions,using observed runoff data as an approximation of soil water flux and accounting for the effectsof snow storage-melting dynamics on that flux. Both past and future relative changes can beassessed by use of this modeling framework, with future change projections based on commonclimate model outputs.By direct model-observation comparison, the thesis shows that the developed modeling frame-work can reproduce the temporal variability of large-scale changes in soil water storage, as ob-tained from the GRACE satellite product, for most of 25 large study catchments around theworld. Also compared with locally measured soil water content and groundwater level in 10U.S. catchments, the modeling approach can reasonably well reproduce relative seasonal fluctu-ations around long-term average values.

The developed modeling framework is further used to project soil moisture changes due toexpected future climate change for 81 catchments around the world. The future soil moisturechanges depend on the considered radiative forcing scenario (RCP) but are overall large forthe occurrence frequency of dry and wet events and the inter-annual variability of seasonal soilmoisture. These changes tend to be higher for the dry events and the dry season, respectively,than for the corresponding wet quantities, indicating increased drought risk for some parts of theworld.

Sammanfattning

Vattnet som finns och strömmar under markytan är väsentligt för möta olika mänskliga vattenbe-hov samt föda in vatten och ämnen det bär med sig till olika ytvattenmiljöer och deras ekosys-tems. De förändringar som vattnet under markytan genomgår behöver kvantifieras för att vi skakunna förstå dess dynamik och hur det påverkas av klimatförändringar och andra förändringar ilandskapet, som den mänskliga mark- och vattenanvändningen. Det är dock svårt att direkt mätamarkvattenhalt och grundvattenytans läge över stora områden och längre tidsperioder. Därförbehövs tolknings- och beräkningsmodeller för att fylla i mätglappen och ta fram möjliga förän-dringsscenarier för framtiden rörande markvattenhalter och grundvattennivåer över stora rumsoch tidsskalor.

Denna avhandling utvecklar ett modelleringsramverk som möjliggör tolkning av långa tidsserierav klimat- och vattenflödesdata (hydro-klimatdata) med avseende på deras innebörd för förän-dringar i markvattenhalter och grundvattennivåer på avrinningsområdesskala. Det nya i dennautveckling ligger i den relativt enkla modellkopplingen av hydro-klimatdata med markens hy-drauliska förutsättningar på denna stora skala. Observerade avrinningsdata används för att upp-skatta avrinningsflödet genom marken till avrinningsområdets ytvatten och effekter av snölagrings-och smältningsdynamik på detta flöde. Både tidigare och framtida förändringar i markvattenhaltoch grundvattennivåer kan beräknas med detta modelleringsramverk, med framtida förändringarbaserade på klimatmodellresultat i stället för direkta mätningar av hydro-klimatdata.

Genom direkt jämförelse av modellresultat och observationer visar avhandlingen att detutvecklade modellramverket kan relativt väl representera observerade tidsvariationer i mark-vattenlagring från GRACE-satellitdata för de flesta av 25 studerade stora avrinningsområdenvärlden över. Även jämförelse med lokalt uppmätta data för markvattenhalt och grundvattennivåi 10 avrinningsområden i USA visar att modellramverket kan relativt väl representera tidsvaria-tionerna runt långsiktiga medelvärden.

Det utvecklade modellramverket används vidare för att studera möjliga framtida förändringari markvattenhalt på grund av förväntade klimatförändringar i 81 avrinningsområden runt om ivärlden. Markvattenförändringarna beror på vilket klimatförändringsscenario som studeras menfrekvensen i speciellt torra och speciellt våta händelser samt variationen i markvattenhalt frånår till år uppvisar generellt stora förändringar. Dessa förändringar tenderar att vara större föravrinningsområdenas torra händelser respektive torra årstider än för deras våta händelser ochregniga årstider, vilket indikerar ökad risk för torka i vissa delar av världen.

Thesis content

This doctoral thesis consists of a summary and four papers. The papers are referred toas Papers I to IV in the summary text:

I Destouni, G. and Verrot, L., 2014. Screening long-term variability and change ofsoil moisture in a changing climate. Journal of Hydrology, 516, pp.131-139.doi:10.1016/j.jhydrol.2014.01.059

II Verrot, L. and Destouni, G., 2015. Screening variability and change of soil moistureunder wide-ranging climate conditions: Snow dynamics effects. Ambio, 44(1),pp.6-16. doi:10.1007/s13280-014-0583-y

III Verrot, L. and Destouni, G., 2016. Data-model comparison of temporal variabilityin long-term time series of large-scale soil moisture. Journal of GeophysicalResearch - Atmospheres, in press.

IV Verrot, L. and Destouni, G., 2016. Worldwide soil moisture changes driven byfuture hydro-climatic change scenarios. Hydrology and Earth System SciencesDiscussions, doi:10.5194/hess-2016-165, in review.

The co-authorship of the papers reflects the collaborative nature of the underlyingresearch. For all papers LV was responsible of the numerical analysis. She was themain responsible of the study design in papers II, III and IV, and wrote the first draftof those three papers. GD designed, organized and wrote the study in Paper I, lead theorganization of the analysis in Papers II and III, and co-wrote the final version of PapersII, III and IV.

Contents

1 Introduction 1

2 Methodology 52.1 Modeling framework . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Account for snow dynamics . . . . . . . . . . . . . . . . . . . . . . . 72.3 Quantifying variability and change in soil water content and groundwa-

ter table level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Results 11

4 Discussion 21

5 Conclusion 25

6 Perspectives for future work 276.1 From lumped to semi-distributed modeling . . . . . . . . . . . . . . . 276.2 Identification of main drivers of large-scale long-term soil moisture change 276.3 More general perspectives on future soil moisture research . . . . . . . 28

7 Acknowledgements 29

References 31

SYMBOLS AND VARIABLES

CV Coefficient of variation α Measure of the pore-size distributionET Evapotranspiration β Soil parameter linked toFM Degree-day factor the pore-size distributionK Hydraulic conductivity γ Groundwater recharge coefficientKs Saturated hydraulic conductivity and partitioning coefficient overlandP Precipitation flow and soil infiltrationPeff Effective Precipitation θir Irreducible soil water contentPwater Liquid fraction of the precipitation θs Saturated soil water contentPsnow Snow fraction of the precipitation θuz Depth-averaged soil water content overq Vertical flux of water through the soil the unsaturated zoneR Runoff θz Depth-averaged soil water content overReff Effective runoff the depth zS Groundwater storageSM SnowmeltSWS Soil water storage (satu-

rated+unsaturated zones)SWSuz Soil water storage in the unsaturated

zoneTA Air temperatureTL Temperature below which the precipi-

tation is snow onlyTM Temperature above which the snow

starts to meltTU Temperature threshold above which the

precipitation is liquid onlyz Depth of soil layerzgw Groundwater levelzgw−0 Initial groundwater level

ERRATA

• Ks [L.T−1] is the saturated hydraulic conductivity (Paper I page 132)

• β = α/(3α +2) (Paper I page 132 and Paper II Supplementary Material page 2)

• θz(t) =zgw(t)θuz(t)+θs(z−zgw(t))

z (Paper I Equation 3)

1 Introduction

The water cycle lies at the heart of life on earth. Water is necessary to sustain lifeat all trophic levels, and humans are no exception: civilizations have developed aroundwater [Hassan, 2003], and, when easily available water was scarce, human societies haveengineered their environment to meet their direct needs as well as to develop agriculture.

But even our highly engineered societies cannot preserve themselves entirely fromextreme events. Up to a certain degree, droughts and floods can be mitigated by wa-ter retention systems, but major extreme events occasionally happen in regions of theworld, and can drastically affect agriculture or trigger water-borne diseases outbreaks[McMichael et al., 2006; Patz et al., 2005].

The need to know how the water is partitioned in our environment has led to a largevolume of scientific literature [Huntington, 2006], and remains a fundamental aspect ofhydrologic studies. This questioning has two components: First, it is crucial to knowhow and how much the water stored in a particular compartment of the environmentchanges with time. Second, we need to understand the time variability of water fluxes,in order to also be able to make projections of changes in the future that may be cru-cial for our survival. This is the subject of numerous studies focused on landscape andclimatic drivers affecting water fluxes [Zhou et al., 2015; Paul and Meyer, 2008; Singhand Woolhiser, 2002]. Global circulation models and assessments of hydrologic fluxcomponents have led to important findings for both past and future evolution of globaland regional water cycling and its changes and drivers [Hulme et al., 1998; Dai et al.,1999; Jaramillo and Destouni, 2015].

In modern times, nearly half of our sources of water, either for direct consumption,for industry, or for agriculture is mostly underground [Oki and Kanae, 2006]. Becauseof the volumes stored and their importance to humans and natural ecosystems, subsur-face water is a major field of research in hydrology. The underground can be separatedinto two main components: the unsaturated zone (UZ), where the pores are filled withboth water and air, and the saturated zone (SZ), where the pores are completely filledwith water. The saturated zone level where the water pressure equals the air pressure isreferred to as the groundwater table.

Quantifying changes in water volume and in water fluxes cannot be done in the samemanner for all spatial and temporal scales: the important fluxes for a given scale ofinterest have to be identified, depending on the specific research question, as well as onthe degree of precision necessary to describe the dominant physical processes [Klemeš,1983; Wood et al., 1988; Seneviratne et al., 2010]. Due to the difficulty of measuringvariables in both the unsaturated and the saturated zones, and to the inherent spatialheterogeneity of the soil, quantifying soil water fluxes and storage is a challenge [Alleyet al., 2002].

When measuring soil water fluxes and changes in stored water volumes, hydrologistsface a trade-off in terms of both time and spatial scales [Robinson et al., 2008]: Somemethods will allow for quantification of water storage change and associated fluxes in

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Modeling long-term variability and change of soil moisture and groundwater level - from catchment to global scale

a soil column, over a depth varying between a few centimeters down to several meters,and allow more or less continuous data, with frequency of measurement usually betweenthe order of magnitude of a second up to that of an hour. However, such quantificationat some selected locality in the landscape may not be representative of the conditionsaffecting a whole watershed. Other methods will allow for screening of large portions ofthe landscape, but may be representative of only a small soil depth (a few centimeters)and some time-average soil water content, for instance over several days.

The first quantification category includes mostly ground-based techniques. Of these,time domain reflectometry sensors (TDR) are probably the most widely used measure-ment technique [Vereecken et al., 2014]. They measure the dielectric permittivity of thesoil, which is related to the soil water content. Other sensors are also derived from theability of the soil to transmit a signal: frequency-domain reflectometry (FDR [Noborio,2001]) and time-domain transmission (TDT [Blonquist et al., 2005]) are some of them.These methods are all invasive: it is necessary to disturb the soil in order to set up theequipment. This may greatly influence the measurements [Walker et al., 2004]. The neu-tron scattering technique utilizes the high capacity of the hydrogen atoms in a moleculeof water to greatly lower the energy of a cloud of neutrons being injected in the soil froma radioactive source. This method can be used non-invasively (at the surface), but maymeasure soil water content over only a few centimeters or, if it is buried in the soil in theform of an emitting pole, it will represent soil water content over the height of the pole.

The second quantification category mainly includes satellite or air-borne microwavesensors that can collect soil-moisture related data based on the dielectric constant of thesoil. The soil dielectric constant is affected by soil water content, and is linked to thebrightness and scattering coefficient of the soil (passive and active signals, respectively).Infrared sensors on board some satellites can also indirectly provide soil moisture data.The reliability of both techniques to retrieve soil moisture values depends greatly on thevegetation cover [Prigent et al., 2005].

In between the two quantification categories mentioned above, hydrogeophysicalmethods (mostly electrical resistivity and ground-penetrating radar) can give a detailedpicture of the water content profile down to several meters in the soil, and of severalmeters of horizontal length [Daily et al., 1992; Lunt et al., 2005], but require heavyinstallation, are expansive, and usually cannot continuously monitor the field. They arebased on the speed of transmission and the electromagnetic or electrical signal betweena source and a receptor, depending mainly on soil water content.

To assess spatially and/or temporally complete data, mathematical representationsof the water cycle have always been central in hydrological science. Water fluxes in theunsaturated zone may be represented in various ways, depending on the required levelof complexity, and on the spatial and temporal scales of interest. The ability to representlarge-scale water fluxes and storage changes in the soil has become more achievable byincreasing computing power, which has drastically changed model capabilities [Boyleet al., 2000]. More specifically, conceptual, physically-based and empirical hydrologicalmodels have increased in number and complexity.

Empirical models are based on statistical relationships derived from observed data.The detailed physical phenomena underlying an empirical representation of a system ofinterest are not the focus of this type of model. However, they have often built the foun-dations of many soil hydraulics representations [Clapp and Hornberger, 1978; Whitaker,1986; Arya and Paris, 1981]. Also, with increased computing power, statistical algo-rithms have become more diverse and powerful (see results from Pachepsky et al. [1996]for example).

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Lucile Verrot

Conceptual models represent processes in a compartmentalized box, and in a simpli-fied way, while physically-based models are mathematical formulations of natural pro-cesses. Also, models can be distributed or lumped, depending on whether they representthe system with spatial subunits or as a whole.

Distributed models may represent highly complex systems, but are subject to numer-ous limitations, due mainly to scarcity of data in time and/or space for many variables.Beven [2001] has summarized such limitations, inherent to the complexity of the dis-tributed models, and their high needs for calibration and uncertainty account. With theirspatiotemporal data requirements, distributed models are typically limited to relativelywell-monitored watersheds. Lumped models require various amounts of data, depend-ing on their complexity, and have the advantage of being relatively easily applicable tovarious monitoring conditions. However, their simplifications in terms of spatiotemporalvariation limits their use to only some specific questions [Beven, 2002].

Even considering the high number of available hydrological models, subsurface pro-cesses are still difficult to quantify. Models may represent soil water content in differentways, depending on the study aims. For instance, models based on mass balance havebeen used to investigate plant-soil interactions at watershed or field scales [Porporatoet al., 2004] and to quantify water flows through the landscape [Botter et al., 2007]. Othermodels are instead based on soil hydraulic properties, for example to describe transportprocesses in the soil compartment depending on its textural classification [Arya et al.,1999]. The overall water-balance, accounting for precipitation (P), evapotranspiration(ET ) and runoff (R) fluxes along with water storage changes, may not be consideredat the field or watershed scales in the models that are primarily based on soil hydraulicproperties and descriptions.Scaling issues are common to data and modeling of soil water fluxes and storage changesbecause soil properties, and not least hydraulic properties, are typically highly heteroge-neous in space [Famiglietti et al., 2008]. Models cannot represent the full spatial hetero-geneity of these variables, because of both computing limitations and lack of spatiallydistributed data [Young et al., 2001]. To allow for use of average soil properties oversome horizontal and vertical distances, it is fundamental to link local variable values,obtained by data or models, to average variable quantities on larger scales. Models ofupscaled soil water content may then display high sensitivity to parameterization values[Binley et al., 1989; Entekhabi and Eagleson, 1989].

Scaling issues may be addressed by geostatistics, exploring the field of spatial het-erogeneity from the data collection perspective, by statistically studying relationships inspace and time, between for instance soil water content and topography [Whittle, 1962]or rainfall patterns [Grayson et al., 1997]. Although geostatistical results may be consis-tent with spatially distributed data (remote sensing mainly), studies also suggest that theymay be site-specifically limited to the studied areas and not easily generalized [Westernet al., 2002]. Regarding the spatial heterogeneity of soil water fluxes, use of tracer testsand data may offer promising insights. Dissolved tracers that are carried by and travelwith the water through a whole catchment span the spatial variability and thereby repre-sent spatially averaged conditions over the catchment when relating the full tracer inputover the whole source (soil surface) to the full tracer output at the catchment outlet. Trac-ers can then be artificially deposited (dye for example) or be natural inputs to the system(water isotopes or radioactive atoms for example). Conservative tracers do not changetheir total dissolved mass in time, as opposed to reactive ones. Use of tracers may forinstance allow for identification of flow paths through a catchment [Tetzlaff et al., 2007]and/or for quantifying watershed-scale soil water in space and time [McDonnell et al.,2010]. However, also tracer concentrations cannot be monitored continuously in spaceand time, and results from one catchment may be difficult to extrapolate to others and to

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ungauged catchments.Despite efforts to characterize soil properties over whole catchments [Wagener et al.,

2007] and to relate the heterogeneity of soil water content to more readily measurablehydrological [Dai et al., 1999] and/or ecological [Korres et al., 2013] variables, the quan-tification of soil water content within and across watersheds has been identified as akey quantification challenge for hydrological models and data due to the complexityand scale-dependency of this variable over large scales [Tetzlaff et al., 2008; Sivapalan,2005]. This thesis addresses this quantification challenge with the main objectives:

Objective A: To develop a relatively simple, yet still physically based, modeling frame-work for quantifying variability and change of large-scale soil water content and ground-water table level over long (climatic) time periods and with applicability over a widerange of climatic and soil conditions (Papers I-II).

Objective B: To test the applicability of this modeling framework against a range ofrelevant available observation data for different parts of the world (Paper III).

Objective C: To use the developed and tested modeling framework for investigatingthe implications of projected long-term scenarios of hydro-climatic change for possi-ble future variability and change of large-scale soil water content and groundwater tablelevel in different parts of the world (Paper IV).

The appended thesis papers address the above objectives. Papers I and II contributeto objective A by developing the basic modeling framework (Paper I) and its furtherextension to cold climate regions by also introducing a snow-dynamics module (PaperII). These papers exemplify the use of the modeling framework for two large watershedsacross a steep climatic gradient in Sweden, quantifying changes occurring in these catch-ments during the 20th century in terms of mean values and frequency of particularly dryand wet events of soil water content and groundwater level. Paper III contributes toobjective B by comparing output of the developed modeling framework directly withavailable observation data for various parts of the world. The comparison considerslarge-scale data for water storage change from the GRACE satellite, and local measure-ment data of soil water content and groundwater level. Finally, Paper IV contributes toobjective C by using the modeling framework to assess scenarios of future changes inthese variables on large scale across different parts of the world, based on climate changeprojections for the 21th century.

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2 Methodology

2.1 Modeling framework

This thesis develops, tests and uses a relatively simple modeling framework, based onobserved or modeled large-scale water fluxes as inputs. The developed model links thelarge-scale water balance and water storage change implied by these fluxes with pre-vailing soil hydraulic parameters to determine the temporal variability and change oflarge-scale soil moisture, expressed in terms of both unsaturated soil water content andgroundwater table level over some arbitrary soil depth of interest (Fig. 2.1). This frame-work thus requires only input data that are commonly available, and by its simplicity en-ables screening of long-term input data series of the large-scale water fluxes to determinethe variability and change of large-scale soil water content groundwater level in the soil.The large-scale fluxes used as inputs in the model imply that these soil-moisture out-put variables are spatially averaged over a whole catchment area, and a snow-dynamicsmodule in the model implies that various climatic conditions can be considered.

In the model development, we define the vertical z-axis positive upwards, and theland surface at the height z = 0 [L]. The depth of the groundwater level zgw defines thelower vertical boundary of the unsaturated zone, and the upper vertical boundary of thesaturated zone. z refers to the total depth of the soil, and it is set below zgw (|zgw|> |z|).θuz [-] is the soil water content averaged over the unsaturated zone, and θz [-] is the soilwater content averaged over the total considered soil depth z (see Fig. 2.1). Brooks andCorey [1964] defined a constitutive relationship for relating the unsaturated hydraulicconductivity K [L.T−1] in the soil to its water content:

K(θuz) = Ks

(θuz−θir

θs−θir

)1/β

(2.1)

where Ks [L.T−1] is the saturated hydraulic conductivity, θir [-] is the irreducible watercontent, θs [-] is the saturated water content, and β = α/(3α +2) [-] and α [-] are char-acteristic parameters, linked to the pore size distribution of different soil types [Rawlset al., 1982; Saxton et al., 1986]. Van Genuchten [1980] and Morel-Seytoux et al. [1996]described similar relationship between K and θuz.

Dagan and Bresler [1979], and Bresler and Dagan [1981] used the possibility ofrelating the field-scale average unsaturated hydraulic conductivity K in equation 2.1 tothe average vertical soil water flux q [L.T−1] of groundwater recharge, by assumingprimarily gravity-driven flow and unit hydraulic gradient, as:

θuz =

(qKs

)β

(θuz−θir +θir) (2.2)

Dagan and Bresler [1979], Bresler and Dagan [1981] and multiple subsequent stud-ies (e.g., Destouni and Cvetkovic [1989, 1991]; Destouni [1993]; Destouni and Graham

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Meanzuz

Fixedz

0

Variableunsaturatedzonedepthzuzwithwatercontentθuz

Variablesaturatedzonedepth(z-zuz)withwatercontentθs

Depth

Temporallyvariablewatercontentθzoverfixeddepthz

Time

Meangroundwatertable

Variablegroundwatertable

Figure 2.1. Schematic conceptualization of different soil moisture quantities

[1995]) found this model sufficiently applicable for statistically (i.e. in relative terms)representing average large-scale soil water fluxes through the unsaturated zone, albeitits relative simplicity. Numerical studies conducted by Destouni [1991] showed that,for periods ranging from four months to five years, the average groundwater recharge qcould be well represented by equation 2.2.Depending on the climatic conditions prevalent in the catchment(s) studied in each thesispaper, the change in soil water storage per considered unit time ∆S [L.T−1] can furtherbe described in two different ways:

(a) Neglecting snow dynamics effects: only a part γ [-] of the area-normalized to-tal observed runoff R represents runoff through the subsurface water system, with thesoil water flow q in equation 2.2 then approximated as q ≈ Reff = γR, and ∆S furtherexpressed a:

∆S = γ(P−ET )−Reff (2.3)

where P [L.T−1] and ET [L.T−1] are the area-normalized precipitation and evapotran-spiration, respectively.

(b) Accounting, in addition to the above, also for snow dynamics effects, an effectiveprecipitation Peff [L.T−1] may be used to represent the liquid water part of total P, whichis the only part that can infiltrate the soil, and expressing ∆S accordingly as:

∆S = γ(Peff−ET )−Reff (2.4)

Previous studies have shown that the factor γ may be close to 1 in many cases fromtemperate to cold climate conditions [Bosson et al., 2012], such as in one of the studiedcatchments in Sweden, without major snow-dynamics effects (Norrström drainage basinin Papers I-II). In colder conditions, simulations have shown that γ may be between0.53 for cold regions and 0.73 up to 1 for temperate regions [Bosson et al., 2012] (thisvariation range is, for instance, considered, for the Piteälven River basin in Paper II).

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Lucile Verrot

In the following, ∆S is expressed in terms of Peff, for generality. However Peff ≈ Phas been used in Paper I, for some catchments in Paper III, and in Paper IV. The method-ology for calculating Peff (Paper II and some catchments in Paper III) is presented in theparagraph 2.2 "Account for snow dynamics". At any time t, the cumulative groundwaterstorage from any arbitrary starting time t0 is then:

S(t; t0) =∫ t

t0

(γ[Peff(τ)−ET (τ)]−q(τ)

)dτ, (2.5)

where τ is the dummy integration variable. The associated change in the depth of thegroundwater table can further be estimated by distributing the storage change ∆S at eachpoint in time over the available unsaturated pore space (θs− θuz) and integrating theresult from initial time t0 to time t:

zgw(t; t0) = zgw−0(t0)+∫ t

t0

γ[Peff(τ)−ET (τ)]−q(τ)θs−θuz(τ)

dτ, (2.6)

where zgw−0 is the initial groundwater level position at time t0. The average soil watercontent over the depth z is finally obtained as the weighted average of the soil moisturein the unsaturated zone and the saturated zone down to depth z:

θz(t) =zgw(t)θuz(t)+θs(z− zgw(t))

z(2.7)

2.2 Account for snow dynamics

Where and when snow dynamics play an important role, the precipitation fraction thatcan infiltrate the soil and contribute to ∆ is not the total measured precipitation P butthe sum of the liquid fraction of the precipitation, Pwater [L.T−1], and the snow-meltcontribution, SM [L.T−1], to that liquid water. The quantities Pwater and SM are obtainedfrom a simple degree-day modeled presented by Rankinen et al. [2004a]. This particu-lar model has been originally tested in Finland [Limbrick et al., 2000; Granlund et al.,2004; Rankinen et al., 2004b], but the conceptualization of degree-day model has beenused widely in different conditions [Braithwaite and Zhang, 2000; Tobin et al., 2011],including other Scandinavian countries [Mörth et al., 2007; Juston et al., 2009].

Following this approach, the liquid water Pwater from the precipitation P is definedas the difference between P and the fraction of P that falls as snow Psnow [L.T−1]:

Pwater = P−Psnow (2.8)

The value of Psnow depends at any point in time on the air temperature TA [Θ]:

Psnow = 0 f or TA > TU (2.9a)

Psnow = PTU −TA

TU −TLf or TL ≤ TA ≤ TU (2.9b)

Psnow = P f or TA < TL (2.9c)

where TU [Θ] and TL [Θ] are the temperature above and below which P is considered tofall entirely as water (equation 2.9a) or as snow (equation 2.9c), respectively. BetweenTL and TU , the precipitation falls partly as water and partly as snow (equation 2.9b).The degree-day model includes also the temperature threshold TM [Θ], above which the

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snow starts to melt, at a rate FM [L.T−1Θ−1] (the degree-day factor), producing the fluxof meltwater SM:

SM = FM(TA−TM) (2.10)

The original model presented by Rankinen et al. [2004a] also accounts for evapora-tion from the snowpack. However, this evaporation is here already accounted for as partof the total catchment-scale evapotranspiration ET in equations (2.3), (2.4), (2.5) and(2.6).

2.3 Quantifying variability and change in soil water contentand groundwater table level

Based on observed monthly time series of P, ET and R and hydraulic properties derivedfrom soil textures, equations (2.2), (2.6) and (2.7) are quantified and provide correspond-ing time series of monthly values of θuz and zgw. The datasets used for all model inputvariables in all theses papers and their considered study catchments are listed in Table 1.Table 1 also shows the climatic periods (p1 and p2), between which changes in long-termaverage output values are assessed in parts of the thesis, for past or projected climaticconditions.

Comparison between the mean monthly values of soil moisture for the average yearin each of the two studied climatic periods (p1 and p2), and of the corresponding tempo-ral inter-annual variability around these values (in terms of the temporal standard devia-tion (ST D) or associated coefficient of variation (CV ; ST D divided by the mean value)show the changes in long-term average and temporal variability conditions occurringbetween the climatic periods in terms of both intra-annual and inter-annual variabilitycharacteristics. In Papers I and IV, relative changes in the occurrence frequency of raredry and wet events are also calculated and relate to changes in drought and flood riskbetween the considered climatic periods. Rare events have then been defined as valuesthat for wet events exceed (and for dry event are less than) a considered Xth percentile([100−X ]th percentile); for example, X may here be 95% (Paper IV) or 99% (Paper I).

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Lucile Verrot

Table 2.1. Summary of the input datasets used in the four thesis papers

Paper I Paper II Paper III Paper IV

Studiedcatchments

Norrström (Swe-den)

Norrström andPiteälven (Swe-den)

(a) 25 catchments world-wide (b) 10 catchments inthe United-States

81 catchmentsworld-wide

Entire timeperiod,

p1 and p2

1901-2002p1: 1901-1921p2: 1992-2002

1950-2009p1: 1950-1969p2: 1990-2009

Specific to each catchment2006-2099

p1: 2006-2025p2: 2080-2099

P time se-ries

Monthly valuesfrom CRU TS2.1, [Mitchelland Jones, 2005]

Daily valuesfrom E-OBSdataset of theEU-FP6 projectENSEMBLES[Haylock et al.,2008]

(a) Monthly values fromthe Global Precipitation Cli-matology Center [Schnei-der et al., 2011] (b) Dailyvalues from National Cen-ter for Atmospheric Pre-diction [NCEP, 2004], cor-rected with monthly val-ues from the CPC Uni-fied Gauge-Based Analysisof Daily Precipitation [CPCUS, 2015]

Monthly valuesfrom CoupledModel Inter-comparisonProject CMIP5[Taylor et al.,2012] and fromthe GlobalPrecipitation Cli-matology Center[Schneider et al.,2011]

ET time se-ries

Yearly values:Water-balanceconstrainedMonthly values:extrapolatedfrom MODIS-16 ET [ORNLDACC, 2011]

Yearly values:Water-balanceconstrainedMonthly values:extrapolatedfrom MODIS-16 ET [ORNLDACC, 2011]

(a) and (b): Monthly valuesfrom MODIS-16 ET [ORNLDACC, 2011]

Monthly valuesfrom CoupledModel Inter-comparisonProject CMIP5[Taylor et al.,2012]

R time se-ries

Daily dischargevalues fromSMHI [2010]

Daily(Norrström)and monthly(Piteälven) dis-charge valuesfrom [SMHI,2010]

(a) and (b): Monthly valuesfrom the Global Runoff DataCenter [GRDC, 2015]

Monthly valuesfrom CoupledModel Inter-comparisonProject CMIP5[Taylor et al.,2012]

Temperaturetime series -

Daily valuesfrom E-OBSdataset of theEU-FP6 projectENSEMBLES[Haylock et al.,2008]

(a) Monthly values from theGlobal Historical Climatol-ogy Network GHCN-CAMS[Fan and Van den Dool,2008] (b) Daily values fromNational Center for Atmo-spheric Prediction [NCEP,2004]

-

zgw0

Database fromSLU [2012]

(Empirical deter-mination)

(a) calibrated from GRACE-satellite monthly valuesof ∆S (CSR-RL05, fromSwenson [2012]; Landererand Swenson [2012]; Swen-son and Wahr [2006]) (b)Monthly values from USGS[2015]

-

9


Table 2.1 (Continued)

Paper I Paper II Paper III Paper IV

Coefficientγ

From per-mafrost andnon-permafrostsoils in Sweden[Bosson et al.,2012]

(From per-mafrost andnon-permafrostsoils in Sweden[Bosson et al.,2012]

(a) Not applicable (b) Ex-trapolated from permafrostand non-permafrost soils[Bosson et al., 2012]

-

Soil hy-drauliccharacter-istic values(θir,θs,Ks,α)

Calculation ex-emplificationbased on samplesfrom Swedishsoil [Destouni,1991]

Calculation ex-emplificationbased on samplesfrom Swedishsoil [Destouni,1991]

(a) and (b): from Rawls et al.[1982]

From Rawls et al.[1982]

Soil texture

Sample anddepth-averagedvalues fromDestouni [1991]

Sample anddepth-averagedvalues fromDestouni [1991]

(a) Harmonized World SoilDatabase v1.1 [Nachtergaeleet al., 2008; FAO, 2012](b) First Most PredominantSurface Soil Classes OverNLDAS Domain issued byNorth-American Land DataAssimilation system [Xiaet al., 2012]

-

Degree-dayparameters(FM ,TU ,TL)

-

Based on cli-matic similaritieswith sites inRankinen et al.[2004a]

(a) Not applicable (b) Basedon climatic similarities withsites in Rankinen et al.[2004b]

-

10

3 Results

Paper I

This study develops and presents the basic modeling framework and focuses its appli-cation on the analysis of the frequency of dry and wet events in the Norrström drainagebasin in Sweden. Results are derived from calculation of θuz and zgw statistics in 20-yearwindows over the 20th century. Dry and wet events defined as the values below the 1%and above the 99% percentile, respectively, based on the values from the first time win-dow (1901-1921). Results show a major increase in the frequency of dry θuz events: bythe end of the 20th century, the fraction of months with such dry soil moisture conditionshas increased, from the original 1% in 1901-1921 up to more than 10% in 1981-2001,while the fraction of days with such dry soil moisture conditions has increased to almost35% (Fig. 3.1a). The corresponding increases for low groundwater level, zgw, condi-tions are not as large. The increases in the frequency of wet conditions for both θuz

and zgw (Fig. 3.1b) are similar and considerably smaller than for the dry θuz conditions.An explanation for the increases in the frequency of dry θuz events is an increase in thelong-term average ET (along with with a corresponding decrease in R) reported to haveoccurred in the Norrström drainage basin during the 20th century [Destouni et al., 2013;Jaramillo et al., 2013].

Furthermore, comparison of the average year in the first 20-year window (1901-1921) to that in the last 20 year window (1982-2002) of the 20th century, shows thatthe intra-annual variability of θuz and zgw has changed: θuz has become noticeably dryerbetween May and October, especially in sandy soils, also as a consequence of an increaseof ET in these months. Changes in the overall intra-annual pattern of water storagechange, with a decrease in available water in spring and in August, correspond to similarchanges in the intra-annual variability of groundwater level zgw.

The calculations are made for two representative soil types in the Norrström basin(clay loam and sand), and for two comparative values of initial groundwater level zgw−0(-2m and -1m). Results for both soil types are similar with regard to the changes inoccurrence frequency of wet and dry events. However, the clay loam texture is overallassociated with higher soil moisture values and therefore less marked relative decreasein intra-annual values. The absolute value of zgw−0 does not impact the results of relativetemporal variation and associated statistics of interest; they are similar for both investi-gated values of zgw−0.

11


1920 1940 1960 1980 20000

5

10

15

20

25

30

35

Day/Month

fraction[%

]

Water content in unsaturated zone θuz

Below original 1st percentileMonthly statisticsDaily statistics

1920 1940 1960 1980 20000

1

2

3

4

5

Day/Month

fraction[%

]

Water content in unsaturated zone θuz

Above original 99th percentileMonthly statisticsDaily statistics

Figure 3.1. Frequency of days (green lines) and months (red lines) with water contentin the unsaturated zone θuz that are below the reference (original, 1901− 1910) 1stpercentile (a) and above the corresponding reference 99th percentile (b) for differentclimatic 20-year periods. Results for contrasting soil types sand and clay loam largelyoverlap, with only one set of results shown in the figure.

12

Lucile Verrot

Paper II

This study further develops the modeling framework to also include snow-dynamicseffects, and exemplify its application for two different catchments along the steep hy-droclimatic gradient in the north-south direction of Sweden (Fig. 3.2). Results may bedivided into three categories, each addressing a distinct issue: snow-dynamics effects,temporal variations in each catchment, and comparison between the two catchments.

Figure 3.2. Location of the two study basins: Norrström in green and Piteälven in blue.The base layer is a Digital Elevation Model provided by the European EnvironmentAgency (EEA 2012)

First, as expected, the northern basin (Piteälven, Fig. 3.2) displays stronger snowstorage and melting dynamics than the southern basin (Norrström, Fig. 3.2) over theentire period of study (1950-2009). Second, the relative changes occurring in each basinbetween the two 20-year windows 1950-1969 and 1990-2009 are that the mean soilmoisture over the unsaturated zone θuz has only slightly increased in Piteälven (Fig.3.3a and 3.3c), following an increase in average R, while the fixed-depth water contentθz (Fig. 3.3b and 3.3d; and the groundwater level zgw, not shown here) have slightlydecreased. In Norrström, θuz has decreased in summer and increased in winter (Fig.3.3a), due mainly to an increase of ET in summer [Destouni et al., 2013]. A similarpattern is observed regarding the changes in θz in Norrström (soil water content averagedover 2.5m, see Fig. 3.3b: and correspondingly also in zgw, not shown here). Inter-annualvariability has increased for θuz in both catchments (Fig. 3.3a and 3.3c). This has alsoincreased in Norrström for θz (Fig. 3.3b and 3.3d), due to an increase in the inter-annualvariability of R and zgw, and is also consistent with the increase of dry θuz events reported

13


in Paper I. Inter-annual variability of θz has slightly decreased in Piteälven (Fig. 3.3band 3.3d), in consistency with the decrease in the frequency of rare zgw events.

Overall, intra-annual variations are smaller in Piteälven than in Norrström. The snowdynamics, which is more marked in the former, leads to a more even release of snowmeltthrough the spring in the northern catchment than in the southern one. In Norrström,there is less snowmelt after the winter and, as a consequence, the soil dries out moreduring spring and summer.

Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug0.22

0.24

0.26

0.28

0.3

Vo

lum

etr

ic w

ate

r co

nte

nt

θuz

Norrström,1950−1969


Piteälven,1950−1969


(a)

Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug0.25

0.3

0.35

0.4

Vo

lum

etr

ic w

ate

r co

nte

nt

θz





(b)

0.22

0.24

0.26

0.28

Nor

r.,19

50−1

969

Nor

r.,19

90−2

009

Pite.,1

950−

1969

Pite.,1

990−

2009

Volu

metr

ic w

ate

r conte

nt θ

uz

(c)

0.28

0.3

0.32

0.34

0.36

0.38

Nor

r.,19

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969

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r.,19

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009

Pite.,1

950−

1969

Pite.,1

990−

2009

Volu

metr

ic w

ate

r conte

nt θ

z

(d)

Figure 3.3. Average intra-annual distribution of monthly average water content θuz andmonthly average water content θz over the depth z =−2.5m (panels (a) and (b) respec-tively), for an initial value of the groundwater table zgw−0 =−1m, in clay loam. Resultsare shown for two different time-periods and for the two study basins. Dashed lines showone standard deviation from average values. (c), (d) Boxplots of monthly values of θuz

(c) and θz (d). The gray squares represent the 1st and 99th percentiles

14

Lucile Verrot

Paper III

This study compares model results with data. We compare the results from the modelwith (a) the only large-scale distributed dataset that gives values of change in waterstorage (from GRACE satellites) and (b) the relative temporal fluctuations of locallymeasured soil moisture and groundwater level.

(a) Comparison of model results with changes in large-scale soil water storage ∆SWS(Fig. 3.4). GRACE measures the anomaly in the total water storage. From it, we derivethe changes in soil water storage ∆SWS and compare with corresponding model results,obtained by adding the water stored in the saturated zone (∆SWSuz) and the water storedin the saturated zone (∆SWSsz). The thickness of the unsaturated zone is given by thedepth of the groundwater level zgw−0, which is calibrated by a Monte-Carlo process,for each catchment. The factor γ is calibrated in the same way. The calibrated modelperformance is assessed by use of the Nash-Sutcliffe (NS) coefficient. Results based onNS value for the entire time series of water storage change in each catchment show thatthe calibrated model performs overall well (Fig. 3.4b, blue markers), and NS values arehigher in the model-data comparison for annual average values (orange markers). Themain fluctuation patterns are well reproduced, although the minimum and maximumvalues are not fully captured. Modeled values have smaller standard deviation than theobserved data. Furthermore, the model performs overall better in catchments with alarger variability range (Fig. 3.4b). Spatial patterns of calibrated values of the γ factorin South-America, where most of the study catchments are, show a decreasing west-to-east trend, while the values in North America and Australia are overall lower than inAfrica and South America. The calibrated values of zgw−0 could be compared to modeledgroundwater table levels in other studies, but no global study provides flow coefficientvalues for direct γ comparison.

(b) Comparison of model results and local measurements of θuz and zgw (Fig. 3.5).Comparison of large-scale model results with locally observed datasets for θuz and zgw in10 catchments in the United States show that the model reproduces most of the temporalfluctuation patterns and the occurrence frequency of most of the main events aroundthe respective long-term mean value in each catchment. It is an expected result thatthe large-scale average model underestimates rather than exaggerates the magnitudesof local observation fluctuations. To focus on the main relative variations around thelong-term mean, the longest available observation time series are also processed througha Fast-Fourier Transform, with a low-pass filter set at 1 yr−1. The main intra-annualfluctuations of frequency 1 yr−1 are well reproduced by the model, for both θuz and zgw.However, for the groundwater level zgw, the longer-term fluctuations, with frequenciessmaller than 1 yr−1, are not so well reproduced by the model, with an underestimatedcleaned seasonal signal compared to the data.

Overall, the relatively simple first-order model developed in this thesis shows rela-tively good agreement with the available large-scale observation dataset for changes insoil water storage provided by the GRACE satellite. Comparing the large-scale modelresults with local measurements of θuz and zgw also shows that the model reproduces themain intra-annual fluctuations in θuz and zgw, but underestimates the relative magnitudeof inter-annual fluctuations .

15


(a)

0 50 100 150 200 250 300 350 400 450 500−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Range of the data ∆ SWS (mm)

NS

(−

) b

etw

ee

n m

od

el a

nd

da

ta f

or

∆ S

WS

Entire time serie

Monthly values of average year

(b)

Figure 3.4. Location of the 26 catchments used for the comparison of the changes insoil water storage (∆S) obtained from the model and from GRACE satellite dataset (a).Panel (b) shows the Nash-Sutcliffe (NS) coefficient for the model-data comparison withGRACE satellite dataset, against the range of the data. The blue markers indicate thatthe NS coefficient was derived from the model-data comparison based on the entire time-serie available for each catchment. The orange markers indicate that the NS was derivedfrom the model-data comparison based on the average-year monthly values.

16

Lucile Verrot

"

"" """

"""

"

"

""

Soil moisture measurements

" Wells

Watershed 4119440 (12 years dataset)





Watershed 4123063 (1 year dataset)



Watershed 4115282 (1 year dataset)


Countries

States

Elevation above sea6168 m

-86 m

±

0 1,000 2,000500 Kilometers

Figure 1

(a)

0 10 20 30 40 50 60 70 80

−2

−1

0

1

2

Unsaturated water content − 4119440

Time [months]

Orig

ina

l sig

na

l

model

data

(b)

0 1 2 3 4 5 60

0.5

1

Frequency (year−1

)

Po

we

r a

mp

litu

de

(c)

0 10 20 30 40 50 60 70 80

−2

−1

0

1

2

Time [months]

Cle

an

ed

sig

na

l

(d)

Figure 3.5. Location of the catchments used for the comparison of the model with pointmeasurements of soil moisture and groundwater level (a). Results of the fast Fouriertransform for the catchment 41119440 and for the depth-averaged soil moisture overthe unsaturated zone (b), (c) and (d). The dotted red line represents the model, and thesolid blue line represents the data.

17


Paper IV

In this study, we apply the developed modeling framework to identify changes in unsat-urated soil moisture (θuz) from the current climatic period (2006-2025) to the end of the21st century (2080-2099), based on projections from the Coupled Model Intercompari-son Project Phase 5 (CMIP5) regarding runoff (Reff) for two contrasting representativeconcentration pathways (RCP) scenarios: RCP 2.6 and RCP 8.5. RCP 2.6 representsclimatic conditions consistent with the aims to limit the increase of global mean tem-perature to less than 2◦C, while RCP 8.5 is a scenario of continued comparatively highgreenhouse gas emissions. Results are calculated for 81 study catchments spread world-wide (Fig. 3.6) and for 14 climate models in CMIP5 providing relevant Reff values asoutput.

We first show that average-year results for temporal soil-moisture CV (relative tem-poral variability) around the long-term mean, as well as for dry and wet season startwithin the year are similar across the various climate models. This justifies the focus inthis study on use of the ensemble mean output of the multiple considered climate modelsrather than on a model-by-model analysis.The study further investigates projected changes in mean monthly soil water content(Fig. 3.6a) and temporal CV (Fig. 3.6b) of θuz in the dry and wet season of each catch-ment, as well as changes in the occurrence frequency of rare wet and dry events (Fig.3.7). The two seasons are defined from CMIP5 multi-model output of precipitation dur-ing the first climatic period (2006-2025), for which some observation data are availablefor direct comparison with the climate model output. The rare wet and dry events, arefurther here determined as the values of θuz that exceed (are less than) the 95% (5%)percentile values of the first period (Fig. 3.4).

Overall, the high radiative-forcing scenario RCP 8.5 leads to greater changes thanRCP 2.6 for both wet and dry soil moisture conditions. However, the pattern is more vis-ible regarding both the mean values and the temporal CV of θuz during the dry season,where 86% of the catchments display a greater change (positive of negative) under RCP8.5 conditions than under RCP 2.6 conditions. The greatest relative changes emerge forthe frequency of wet and dry events (Fig. 3.6), with 70% and 77% of the catchments,respectively, displaying greater changes under RCP 8.5 than under RCP 2.6 conditions.The only region with consistent agreement between the two scenarios is the northernlatitude region including mainly Russia and Canada, displaying a general trend of wetterfuture soil conditions (more rare wet events and higher mean θuz for both seasons). Inmost of the other parts of the world, there is no consistent regional pattern and relativelylow regional agreement between the two RCP scenarios in term of direction as well asmagnitude of change. Overall, scenario RCP 8.5 leads to more spatially heterogeneouspattern of soil moisture changes over the world than the low forcing-scenario RCP 2.6.Relatively large change also emerges for southern India and western Africa regardingthe inter-annual variability of the mean value of θuz during the dry season (increases of100%-120% and 180%-200%, respectively).

18

Lucile Verrot

(a)

(b)

Figure 3.6. Map of the relative changes of mean soil moisture (a) and its temporalvariability (b) during the dry season. The results are presented for the climate projectionunder RCP 2.6 scenario.

19


(a)

(b)

(c)

(d)

Figure 3.7. Map of the relative changes of frequency of rare dry events under RCP 2.6scenario (a) and RCP 8.5 scenario (b), and changes of frequency of rare wet eventsunder RCP 2.6 scenario (c) and RCP 8.5 scenario (d).

20

4 Discussion

In the following, the study results and their implications are synthesized and discussedin relation to the three main thesis objectives.

Objective A: To develop a relatively simple, yet still physically based, modelingframework for quantifying variability and change of large-scale soil water content andgroundwater table level over long (climatic) time periods and with applicability over awide range of climatic and soil conditions (Papers I-II).

The present work has developed a new modeling framework, which falls in the broadcategory of lumped physically-based models and aims at long-term catchment-scalescreening of changes in soil moisture (θuz and zgw). To investigate the model usefulness,it was in Papers I-II applied to the quantification of variability and change in θuz andzgw over as long climatic periods as possible based on input data availability in differenthydrological study basins. The model applicability has also been studied in this thesis bydirect comparison of model results with observation data that test the underlying modelassumptions and simplifications, as discussed further under objective B.

The application of the developed modeling framework in Papers I-II made use of ob-served hydroclimatic and soil data in openly accessible datasets. Historic Swedish datafor P, ET and R were then used to study past changes in θuz and zgw in two hydroclimati-cally different Swedish basins. For the Norrström study basin, the results for the longestpossible climatic study period (the 20th century) in Paper I showed increased risk ofdrought and flood events over the course of this period, in agreement with hydroclimaticchanges reported for this basin in previous studies [Jaramillo et al., 2013]. Specifically,greater increase in ET than in P led to decreased R, along with increased temporal vari-ability in R, which together explain the found increased number of particularly dry days(and months) by a factor 30 (10) in this basin (Fig. 3a and 3b in Paper I).

Paper II focused on investigating the effects of snow dynamics on the variability pat-terns and changes in soil moisture and groundwater level, for which daily hydroclimaticdata were required. This requirement narrowed the possible study period to only thesecond half of the 20th century, making the results in Paper II for the Norrström basinnot directly comparable with those for the longer study period in Paper I. Due to the dif-ferent hydroclimate, and particularly the different snow dynamics characteristics, of thetwo studied basins in Paper II, the temporal intra- and inter- annual variability patternsof θuz and zgw are also different between the basins. The cold northern basin of Piteälvendisplays a more marked seasonality in its average annual variability pattern of effectiveprecipitation Peff than the warmer southern Norrström basin, while the inter-annual vari-ability is similar in both basins. Moreover, the two basins have experienced differentchanges in their hydroclimate over the study period, which is then also reflected in thetemporal changes of θuz and zgw. Specifically, both basins have experienced an increasein average temperature (by around 1◦) and an increase in P, but ET has increased andR has decreased in Norrström, while Piteälven has experienced opposite changes of a

21


lesser magnitude. With regard to groundwater level zgw, mean values have not changedmuch in any of the basins, but the overall variability has increased in Norrström with thegreatest change (decrease in zgw) occurring in spring, whereas the greatest change in thePiteälven basin occurred in autumn and winter (decrease in zgw).

In a comparison between basins, like that in Paper II, the differences in soil moisture(θuz and zgw) changes found between the basins do not just depend on the geographicbasin locations along a climatic gradient. The soil moisture changes are also affectedby the different history of, for example, land- and water-use changes occurring in eachbasin. In the Norrström basin example, agricultural land- and water-use changes haveled to the ET increase and associated R decrease [Destouni, 1993] that in turn deter-mined the θuz and zgw changes found in that basin.

Objective B: To test the applicability of the developed modeling framework againstrelevant available observation data for different parts of the world (Paper III).

The approximations of gravity-driven flow and unit gradient used in the presentmodel development have also been used and found support from field [Graham et al.,1998] and numerical [Destouni, 1991] experimentation. Also in the present thesis theapplicability of these approximations have been tested by the direct comparison of modelresults with available datasets of field and remotely sensed (GRACE) observations invarious parts of the world (Paper III).

In consistency with the present model use of observed catchment-scale hydroclimaticdata as inputs, previous studies have also reported that catchment-scale soil moisture isstrongly correlated with area-normalized runoff [Koster et al., 2010; Bales et al., 2011]and precipitation [Yin et al., 2014]. With such hydroclimatic input requirements, the in-put data availability is the major restriction for model application to catchments aroundthe world, with good-quality hydroclimatic data being necessary for this application. InPaper III, we found for example that the available daily P dataset [NCEP, 2004]) exhib-ited a temporal trend that was neither reflected in the corresponding ET and R datasetsnor in an independent monthly P data set for the same region [CPC US, 2015]. The dailyP data trend was therefore likely unrealistic and required bias correction, which couldhere be done based on the parallel monthly P data set.

The model comparison with field data in Paper III showed that the model couldreasonably well reproduce the relative variability of locally measured soil moisture andgroundwater level around their respective long-term average values. The input data ofP and ET used in the modeling were then monthly, with the typically coarse spatialresolution that commonly applies for the availability of such data (0.25◦ for P and 0.05◦

for ET ). A daily resolution for P, R and temperature data would further be necessaryfor catchments were snow dynamics need to be accounted for [Koster et al., 2004]. Withregard to R, datasets are available for some rivers across the globe, and for periods ofvarying length, but finding matching temporal periods for P, R, ET and T datasets is amajor restriction for the model application if daily values are needed.

Comparison of large-scale model results with local field measurements is a chal-lenging issue. The full spatial variability of soil moisture and its drivers is commonlyunknown over a whole catchment. Direct field measurements yield local data only (orsome linear transects in the case of geophysical electromagnetic methods) over variousdepths. Upscaling from such local measurements to catchment-scale average soil mois-ture is a subject of a number of studies, based on geostatistics [Western et al., 1999;Teuling, 2005], Monte-Carlo analysis [Foussereau et al., 2000] or stochastic modeling[Destouni, 1993]. Multiple local measurements over a single field may exist but are thencommonly limited in time, for example up to a few months, and with matching R and ETvalues typically not monitored in parallel. The Paper III model-data comparison shows

22

Lucile Verrot

that the catchment-scale model does not capture the full temporal variability range ofthe locally measured soil moisture and groundwater level. This is physically reason-able, both because the local water content is only measured over a fraction of the wholeunsaturated zone, and because the measurement is also local in the horizontal extent(as measured by TDR sensors) while the model results represent depth- and catchment-average values [Destouni, 1991, 1992; Li and Islam, 1999]. Relating this finding to thedrought and flood risk estimates in Paper II indicates that the modeled variability of θuz

and zgw likely under- rather over-estimates the risks.In contrast to local field measurements, satellite measures represent large areal ob-

servations but for only the top few centimeters of the soil. The GRACE satellite productprovides then large-scale observations of changes in soil water storage. GRACE waslaunched in 2002, thus providing 14 years of data so far. There are three main limitationsin the comparison of this dataset with the results of the present model. First, GRACEvalues represent monthly anomalies of total water storage, not distinguishing changesin the water volume associated with lakes, rivers, or the unsaturated and saturated zoneof the soil. In Paper III, direct observations of water volume changes associated withmajor lakes were subtracted from the GRACE values of total change in water storage inorder to determine the subsurface change component (equation 5 in Paper III). Second,reliable statistics for the frequency of rare dry and wet events (as calculated in Papers I,II and IV for data series of 50-100 years) could not be calculated for the only 15 yearsof data provided by GRACE. Third, the GRACE satellite observations are snapshots intime, determined by the satellite orbital speed and period of revolution, which do notcapture changes occurring between two measurements.

Nevertheless, despite those three main limitations, the anomalies in total water stor-age observed by GRACE can be related modeled changes in subsurface water storage asdescribed in Paper III. The model-data comparison shows overall good agreement be-tween the temporal variation patterns and the range of values agree of the model and theobservations. The large-scale temporal fluctuations are captured by the model across theentire observation time series, and for the average year (Fig. 2a and Fig. S3 in Paper III).The inter-annual variability is slightly underestimated in most study catchments (Fig. 2band Fig. S4 in Paper III), indicating again that results in Papers I and II are not likely toexaggerate the frequency of dry and wet events over the 20th century.

Objective C: To use the developed and tested modeling framework for investigatingthe implications of projected long-term scenarios of hydro-climatic change for possiblefuture variability and change of large-scale soil water content and groundwater tablelevel in different parts of the world (Paper IV).

The present model cannot be used with zero average R values, and neither theSwedish basins studied in Papers I and II, nor the U.S. basins studied in Paper III dis-played such zero R values at the daily-monthly averaging scales used in those modelapplications. However, in some large catchments studied for the GRACE comparisonin Paper III, R data values were sometimes equal to 0. The θuz value was then approxi-mated to be θir, i.e., the irreducible water content value. In the future projection PaperIV, the subsurface runoff component Reff was directly available from the CMIP5 modeloutput of the "total runoff" minus the "landsurface runoff" component for each grid cellof each climate model. For a few catchments, the resulting Reff became then negativeover the whole catchment scale (over all grid cells in the catchment), implying an up-ward water flux from the soil to the atmosphere in addition to the separately evaluatedevapotranspiration flux in the same climate model. Besides such an additional negativewater flux not being realistic, it is also incompatible with the present approach to soilmoisture modeling. Consequently, catchments with negative monthly value of Reff and

23


climate models yielding systematically more negative monthly Reff values than the otherclimate models were discarded from the Paper IV analysis.

Model projections of climate values may be unrealistic at various scales. However,the approach of the study presented in Paper IV, which is focused on quantification of rel-ative rather than absolute changes, is less affected by inter-model variance, and therebyby individual models biases, than corresponding analysis of absolute changes projectedby the various CMIP5 models; see supplementary Fig. S3 to Paper IV, with nearly allmodels almost fully agreeing on the relative variability of monthly unsaturated soil watercontent being less or much less than 0.5, in comparison with the very large inter-modelvariability reported by Bring et al. [2015] for net water balance in the landscape im-plied by the absolute hydroclimatic outputs of different CMIP5 models. Nevertheless,many previous studies have even directly used absolute CMIP5 hydroclimatic outputs,even though their inter-model variability is high and individual model bias effects arethereby large for these direct absolute outputs [Bring et al., 2015]; for example, Kumaret al. [2014] focused on P and ET outputs, while Wu et al. [2015] studied directly soilmoisture values provided by CMIP5 models. Some CMIP5 models thus do provide ownsoil water content values, but these represent varying soil depths across various models,and the thickness of the considered unsaturated zone is not specified. Therefore, the soilwater content values provided by some CMIP5 models may not be directly comparable,with each other or with the results for various possible soil depths, with or without someincluded saturated zone part, that can be provided by the present modeling approach.

The results of Paper IV regarding projections of future climate-driven θuz changeshow that the changes differ among catchments and between the two studied climatescenarios RCP 2.6 and RCP 8.5 for each catchment. However, some general resultscould still be identified. First, the concentration pathway (RCP) scenario determines thedirection of changes in half of the catchments for both dry and wet conditions (changesin mean θuz, in the temporal CV of θuz, and in event frequency). Second, the relativechanges in frequency of rare events and in inter-annual variability of seasonal θuz areoverall greater than the changes in mean seasonal θuz; the relatively large increases ininter-annual variability indicate increased flood and/or drought risks for many parts ofthe world. Third, increases of mean seasonal soil moisture in the high latitudes are tosome degree correlated with increased frequency of wet events and/or decreased fre-quency of dry events. However, some catchments differ in this respect, such as catch-ments Afr3 and Eur3, which exhibit increased frequency of wet events along with de-creased average soil moisture during the wet season in the RCP 8.5 scenario. Furtherinvestigations of changes in the frequency of wet and dry events within each seasonwould be an interesting follow-up of the present work to better understand such individ-ual catchment results.

Paper IV also complements a conclusion drawn in Paper II, about the geograph-ical location of a catchment along a climatic gradient not being a good predictor ofsoil moisture change under a changing climate. Paper IV shows additionally that pro-jected hydroclimatic variables alone cannot explain the change patterns of soil moisture.Specifically, the P, ET and Reff output data from the CMIP5 models correlate poorlywith the resulting θuz (Pearson coefficients of 0.39, 0.28 and 0.45 respectively), eventhough θuz depends on Reff, which in turn depends on P and ET . This is due to thenon-linear relationship between θuz and q≈ Reff (Eq. 2.2) and emphasizes the necessityof actually modeling the soil moisture dependence on both the hydroclimatic forcingand the soil hydraulic conditions in the landscape of a catchment, as done in the presentmodeling framework.

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5 Conclusion

This thesis has developed a modeling framework that allows for long-term catchment-scale screening of soil moisture and groundwater level changes. The novelty in thisdevelopment resides in the explicit link drawn between catchment-scale hydroclimaticand soil hydraulics conditions, based on the use of observed runoff data as an approx-imation of soil water flux. The extension provided by the addition of snow dynamicseffects in Paper II extends the use of the modeling framework to a wide range of cli-matic conditions, as tested further in Paper III.

Large-scale and long-term screening of variability and change in soil water contentand groundwater level is not commonly possible from direct field monitoring of thesevariables, and such monitoring is certainly impossible for projection of future variableconditions. Many developed soil moisture models are computationally costly and needextended datasets for many more variables than those included in the present modelingframework. The present framework requires only a set of few, commonly availablehydroclimatic data for many parts of the world. Both past and future relative changescan be assessed by use of this modeling framework, with future changes projected basedon common climate model outputs.

By direct model-observation comparison, the thesis has shown that the developedmodeling framework is able to reasonably reproduce the temporal variability of large-scale changes in soil water storage, as obtained from the GRACE satellites, for mostof the studied 25 large catchments around the world. Better agreement between themodel and GRACE observations is generally found for catchments with greater fluctu-ation range. Also compared with locally measured soil water content and groundwaterlevel in ten U.S. catchments, the modeling approach could reasonably well reproducerelative seasonal fluctuations around long-term average values.

Projected soil moisture changes due to global climate change for the 81 study catch-ments around the world depend heavily on the considered radiative forcing scenario(RCP). Projected changes are largest for the occurrence frequency of rare events and theoccurence frequency of dry events. Changes in the occurrence frequency of rare dry/wetevents and in the mean seasonal soil moisture follow a consistent geographic pattern,with some individual catchments deviating from that common pattern.

Overall, the climate change scenario RCP 8.5 leads to more spatially heterogenouschanges than scenario RCP 2.6, and to greater changes in mean seasonal soil moistureand in occurrence frequency of dry/wet events. For the inter-annual variability of sea-sonal soil moisture, however, the two scenarios lead to more or less equally large changesand spatial change heterogeneity. Furthermore, the change magnitude is overall higherfor the dry event frequency and the dry season than for the corresponding wet quantities,indicating increased drought risk for some parts of the world.

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6 Perspectives for future work

6.1 From lumped to semi-distributed modeling

The modeling framework developed in this thesis can be further extended to be spatiallydistributed and differentiate sub-catchments/areas within each main study catchment.Different average hydro-climate and soil texture conditions would then be consideredand quantified for the different sub-catchments/area units and the modeling frameworkwould be in the category of semi-distributed hydrological models.

A major difficulty would be the equations 2.2 and 2.6 evaluation for each sub-catchment /area, requiring more data than for just one main catchment, for examplein order to describe the routing process of subsurface flow among the subunits. Quan-tification of Reff (from available R data) would then be necessary for each unit and thehorizontal flow direction among units could, for example, be determined based on a topo-graphic approximation of the flow-driving hydraulic gradient direction in the subsurface(e.g., Shibuo et al. [2007]; Jarsjö et al. [2008]; Darracq et al. [2009]). The amount ofinput data and the modeling effort that such a development would require are greaterthan for the whole-catchment applications in this thesis, but still not as great as to becontradictory to the original purpose of the modeling framework to be a large-scale andlong-term screening tool.

6.2 Identification of main drivers of large-scale long-term soilmoisture change

The developed modeling framework relates large-scale hydrological flux changes (in P,ET and R) to resulting changes in the soil moisture variables θuz and zgw and their rareevent statistics. In Papers I and II (and to a lesser extent, Paper IV) the flux changescould in turn be related to their possible drivers, including direct land-use and water-use changes in the landscape, in addition to atmospheric climate change. This relationwas possible in the present thesis mainly due to the existence of previous works thathave studied these various drivers in the same study catchments [Jaramillo et al., 2013;Destouni et al., 2013]. Future work should focus on distinguishing major change driversspecifically for soil moisture conditions in the landscape. Furthermore, as highlighted inPapers II and IV, the prevailing soil types within each catchment also plays an importantrole for the absolute soil moisture magnitude and its possible changes. The presentmodeling framework can be used for such further studies, aiming to differentiate directhuman change drivers and identify regions in the world that are particularly vulnerable tosoil moisture changes, in terms of water resource availability and drought and flood risksrelated to both human resource management and from a global climate change point ofview.

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6.3 More general perspectives on future soil moisture research

Obtaining soil moisture data at the catchment scale remains a fundamental challenge inhydrology. Satellite sensors can now provide such data for large catchments, but a gapstill exists for smaller catchments and areas. Cosmic-ray sensors could possibly fill thisgap, as they provide soil moisture values representative of 50 m to 200 m around theirimplantation. However, they require fine calibration to understand the representativity ofmeasurements over the soil profile, which varies depending on moisture content. Thereis ongoing research focusing on the specific calibration of such sensors [Franz et al.,2012, 2013], but also more generally on the scaling questions discussed in this thesis:How does the spatiotemporal variability of local measurements relate to catchment-scaleconditions and their variations? What are the main (temporally variable) drivers for soilmoisture dynamics at various scales? Can cosmic-ray sensors help address these chal-lenging issues with direct implications for hydrological modeling of the spatiotemporalvariability of soil moisture?

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7 Acknowledgements

The research in this thesis has been funded through grants from the Swedish ResearchCouncil (VR; Project Number 2009-3221), the Swedish Research Council Formas (project2012-790), and the strategic research program Ekoklim at Stockholm University.

I was able to present this work in several international conferences and to attendsummer schools thanks to grants received from the graduate research school of the BolinCenter for Climate Research and the K&A Wallenberg foundation.

I would also like to thank my advisor, Gia, for her constant support and for herincredible ability to share her knowledge and ideas. It was an immense privilege to be’launched’ into the academic world by such a researcher.

During those 4 years, I was also given the opportunity to set foot in the teachingworld. I discovered that learning by teaching is not a myth. Thank you Jerker Jarsjö,Andrew Frampton, Steve Lyon and Stefano Manzoni for showing me the way.

As someone scared of any official looking documents, I cannot thank Susanna Blånd-man enough for patiently helping me through the Swedish administration.

Printing this thesis from abroad required help from some of my Stockholmer friends:Audrey, Vincent and Romain, thank you!

Both scientifically and personally, I am indebted to Benoît, colleague and friend:despite trying, I never found the limit of his patience or understanding. I now realizethat the list of friends, colleagues and family members I would like to thank is too long:I will make sure to thank you all individually in Sweden, Switzerland, France, Greece,Slovakia, Belgium, Russia, Georgia, the U.S. and Scotland.

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modeling long-term variability and change of soil moisture

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