Alberto Bellin

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Microgravity observa3ons and hydrological modelling e-‐mail: [email protected]

The value of aggregated measurements of state variables in hydrological modeling

Alberto Bellin Department of Civil, Environmental and

Mechanical Engineering

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RESEARCH ARTICLE10.1002/2015WR016994

On the use of spatially distributed, time-lapse microgravitysurveys to inform hydrological modelingSebastiano Piccolroaz1, Bruno Majone1, Francesco Palmieri2, Giorgio Cassiani3, and Alberto Bellin1

1Department of Civil, Environmental, and Mechanical Engineering, University of Trento, Trento, Italy, 2Istituto Nazionale diOceanografia e di Geofisica Sperimentale, Trieste, Italy, 3Department of Geosciences, University of Padova, Padova, Italy

Abstract In the last decades significant technological advances together with improved modeling capa-bilities fostered a rapid development of geophysical monitoring techniques in support of hydrological mod-eling. Geophysical monitoring offers the attractive possibility to acquire spatially distributed information onstate variables. These provide complementary information about the functioning of the hydrological systemto that provided by standard hydrological measurements, which are either intrinsically local or the result ofa complex spatial averaging process. Soil water content is an example of state variable, which is relativelysimple to measure pointwise (locally) but with a vanishing constraining effect on catchment-scale modeling,while streamflow data, the typical hydrological measurement, offer limited possibility to disentangle thecontrolling processes. The objective of this work is to analyze the advantages offered by coupling traditionalhydrological data with unconventional geophysical information in inverse modeling of hydrological sys-tems. In particular, we explored how the use of time-lapse, spatially distributed microgravity measurementsmay improve the conceptual model identification of a topographically complex Alpine catchment (the Ver-migliana catchment, South-Eastern Alps, Italy). The inclusion of microgravity data resulted in a better con-straint of the inversion procedure and an improved capability to identify limitations of concurringconceptual models to a level that would be impossible relying only on streamflow data. This allowed for abetter identification of model parameters and a more reliable description of the controlling hydrologicalprocesses, with a significant reduction of uncertainty in water storage dynamics with respect to the casewhen only streamflow data are used.

1. Introduction

Building hydrological models able to accurately reproduce hydrological fluxes at a multiplicity of temporaland spatial scales, as more frequently required in applications, is still a serious challenge. The main difficultyis in the inability to adequately characterize the spatial variability of hydrological fluxes, due to the largeheterogeneity that characterizes the Earth’s subsurface [see e.g., Rubin, 2003]. Since this variability cannotbe assessed with the detail needed to represent the real, but unknown, spatial distribution of hydrologicalfluxes, simplifying hypotheses on the spatial distribution of the hydraulic parameters are typically intro-duced, which makes simulations highly uncertain. Traditionally, this difficulty has been addressed by usingsimplified conceptual models, which require the definition of lumped parameters with values determinedthrough suitable inference procedures with streamflow as the most used, and often the only, observationalvariable [see, e.g., Beven, 2011].

Since the works of Duan et al. [1992] and Gupta et al. [1998] the need to consider the inherent multiobjec-tive nature of inference and the importance of assessing, and possibly minimizing, the epistemic error asso-ciated to the conceptual model (i.e., the uncertainty that stems from a lack of knowledge about a givenphenomenon) emerged clearly together with a growing concern about the representativity of consolidatedbelieves [see e.g., Kirchner, 2006]. In particular, Efstratiadis and Koutsoyiannis [2010] and Beven and Wester-berg [2011] indicated that epistemic uncertainty may be related to the noninformativeness (i.e., limitedeffectiveness) of observational data in conditioning model parameters and structure. Furthermore, Efstratia-dis and Koutsoyiannis [2010] and Linde [2014] evidenced that, in some cases, the additional information pro-vided by the adoption of a multiobjective framework may lead to rejection of an inappropriate conceptualmodel, which would appear as proper against a single criterion (i.e., the classical comparison of observedand simulated water discharges).

Key Points:! Microgravity data constrain

subsurface water storage inhydrological models! Combining streamflow and

microgravity data rules out improperconceptual models! Indirect measures of state variables

constrain inversion of hydrologicaldata

Supporting Information:! Supporting Information S1

Correspondence to:S. Piccolroaz,[email protected]

Citation:Piccolroaz, S., B. Majone, F. Palmieri,G. Cassiani, and A. Bellin (2015), On theuse of spatially distributed, time-lapsemicrogravity surveys to informhydrological modeling, Water Resour.Res., 51, doi:10.1002/2015WR016994.

Received 30 JAN 2015Accepted 6 AUG 2015Accepted article online 11 AUG 2015

VC 2015. American Geophysical Union.All Rights Reserved.

PICCOLROAZ ET AL. MICROGRAVITY AND HYDROLOGICAL MODELING 1

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Two concurring hydrological models (M1 and M2) having the same high efficiency when calibrated using only streamflow data (single objec>ve)…

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… show remarkable differences when adding geophysical informa>on (mul> objec>ve): the shape of the Pareto fronts provide useful hints to iden>fy model limita>ons, and indicate the value of including geophysical data to beGer constraint of the inversion procedure.

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Introduc3on

Microgravimetry may provide useful data on water storage in the earth’s subsurface • relevant in the evalua3on/quan3fica3on of groundwater resources (e.g. GRACE at large scale); • a promising support in hydrological modeling. Are microgravimetry data useful to inform hydrological models? We are interested in coupling tradi3onal hydrological data (inherently global) and geophysical informa3on (spa>ally distributed).

Time-‐lapse, rela3ve microgravimetry is a geophysical technique which allows to obtain an indirect es>mate of surface and subsurface water storage varia3ons (i.e., soil water content, groundwater and snowpack) Basic concept: the temporal varia>on of the gravita>onal aGrac>on is propor>onal to the hydrological storage changes (once all other contribu>ons are corrected).

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Study site: the Vermigliana catchment, located in the South-‐Eastern Alps (Italy).

Main characteris3cs: •  contribu>ng area: 104 km2; •  the main creek has a length of 4 km and an

average slope of 1%; •  eleva>on ranging from 950 to 3558 m a.s.l.; •  very steep slopes and a narrow valley

boGom (U-‐shaped profile); •  nivo-‐glacial regime; •  almost pris>ne condi>ons.

Microgravity campaign

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Fieldwork and data acquisi3on1: •  6 field campaigns between June 2009 and May 2011; •  extensive point gravity measurements on a network of 53 sta3ons; •  the Vermigliana catchment has been monitored through 8 sta3ons; •  streamflow data are available at the Vermiglio stream gauging sta>on.

1 Equipment: LaCoste-‐Romberg mod D-‐018 equipped with a Zero Length Spring feedback.

Microgravity campaign

Reference measurement

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Modeling approach

Hydrological model: a modified version of GEOTRANSF (Majone et al., 2012, WATER RESOUR RES), a distributed hydrological model characterized by 1.  subdividing the catchment into slope and valley boGom areas (assuming they are governed

by inherently different processes); 2.  explicitly coupling vadose-‐zone and groundwater dynamics.

The valley boGom is iden>fied considering thresholds on slope and eleva>on (≈ 1.8 km2, 2% of the catchment area)

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Valley bottom

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Valley bottom

Sub-basin entirely confined in the hillslope unit

coupled hydrological and water resources management model, submitted to Environmental Modelling &Software, 2015) was adopted for simulating the hydrological cycle of the Vermigliana catchment. GEO-TRANSF is built around two geomorphological units: the subcatchment and the channel. The former unitidentifies a portion of the catchment where hillslope processes dominate. The latter is the base elementcomposing the river network that connects the selected subcatchments to the control section, wherestreamflow is simulated. A mass balance equation is written for each subcatchment under the assumptionthat streamflow at its outlet depends nonlinearly upon water storage [Kirchner, 2009; Majone et al., 2010].

In order to make the model sensitive to water redistribution within the drainage area, the catchment hasbeen subdivided into two interconnected elements, the hillslope and the valley bottom, roughly corre-sponding to convex and concave areas, respectively (see Figure 3a). In this way, the conceptual model iden-tifies two storing mechanisms related to identifiable morphological characteristics [Winter, 2001; Savenije,2010; Gharari et al., 2011; Nobre et al., 2011; Gao et al., 2014]. Hillslope is identified as the area with highaverage slope where runoff is dominated by shallow subsurface flow and groundwater storage is small tonegligible. On the other hand, the valley bottom area, which in the work of Savenije [2010] is included inthe broader ‘‘wetland’’ landscape classification, is the area where water storage occurs chiefly as ground-water. Note that, in general, a subcatchment is not necessarily formed of both landscape units (see theschematic in Figure 3).

In the present study, landscape classification was performed by using the following mixed criterion. The cellsbelonging to the hillslope unit were first identified as those characterized by slope and elevation higher than

Figure 1. Map of the catchment monitored during the microgravity campaigns with indicated the locations belonging to the microgravitynetwork. The boundaries of the Vermigliana catchment are drawn, together with the subdivision in 13 subcatchments (grey lines), and theposition of the stream gauging station (blue triangle). The inset shows the location of the Vermigliana catchment within the Italianterritory.

Water Resources Research 10.1002/2015WR016994

PICCOLROAZ ET AL. MICROGRAVITY AND HYDROLOGICAL MODELING 4

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Valley bottom

Sub-basin partitioned between hillslope and valley bottom

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Modeling approach

Calibra3on procedure: par>cle swarm algorithm to solve a mul>-‐objec>ve op>miza>on problem

(see e.g., Robinson and Rahmat-‐Samii, 2004, IEEE T ANTENN PROPAG)

Objec3ve func3on: the following expression has been used as model performance criterion

KGE = Kling–Gupta efficiency index (Gupta et al., 2009, J HYDROL)

� =µs

µ0� =

�s

�0

r =covSO

(�S �0)

KGE = 1�q(� � 1)2 + (� � 1)2 + (r � 1)2

KGEtot

= (1� ↵)KGEhydro

+ ↵KGEgrav

, ↵ = 0÷ 1

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Modeling approach

Gravity model: the domain is divided into n prisms for which the individual contribu>on to the hydrology-‐induced gravity varia>ons is evaluated according to

The following approximated solu>on has been applied for distances larger than a given threshold from the gravimeter

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Domain discre3za3on: carried out at two levels

• Horizontal plane based on the 10x10 m resolu>on DEM available for the catchment

• Ver3cal direc3on considering the same layers of the hydrological model, including snowpack

Modeling approach

Main water storage components: soil moisture in the rizosphere and in the vadose zone, groundwater and snowpack.

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Model M1 Model M2

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Two concurring hydrological models (M1 and M2) having the same high efficiency when calibrated using only streamflow data (single objec>ve)…

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… show remarkable differences when adding geophysical informa>on (mul> objec>ve): the shape of the Pareto fronts provide useful hints to iden>fy model limita>ons, and indicate the value of including geophysical data to beGer constraint of the inversion procedure.

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Uncertainty assessment

Results

Comparison among parameters and model output uncertainty (model M1) for two significant cases: • only streamflow data are available for model calibra>on (α=0) • both streamflow and microgravity data are used for parameters inference with a balanced aggregated objec>ve func>on (α=0.5)

Among the solu>ons obtained during the explora>on of the parameters space, only those with KGEtot differing less the 1% from the maximum value (colored squares in the previous slide) have been retained for the uncertainty analysis. The analysis has been focused on the 100% confidence bands resul>ng from the retained solu>ons.

To address the c l u s t e r i n g effect of PSO.

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Model parameters

Results

The values of the parameters are normalized with respect to their range

Confidence bands are: • 45% smaller for α=0.5 than for α=0 • well distributed between 0 and 1 (proper choice of their prior range of varia>on)

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Results

Water storage

When including microgravity data, confidence bands reduce by • 26% in the hillslope • 95% in the valley boGom

The accumula>on of water in the valley boGom (due to a par>cularly wet summer in 2010) is observed only for α=0.5

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Results

Water table fluctua3on

When including microgravity data, confidence bands reduce by •  39% in the hillslope •  93% in the valley

boGom

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Results

Streamflow

The averaged confidence band reduces from 0.95 m3/s to 0.78 m3/s when microgravity data are included

microgravity data not only allow for a beGer representa>on of subsurface storage, but they also reduce uncertainty of streamflow.

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Results

Gravity change (for α=0.5)

Valley boGom sta>ons (green) show a good agreement between simulated and observed data, while hillslope sta>ons (blue) show larger devia>ons. In general, seasonal varia>ons are well reproduced.

Errors are likely due to the simplifica>on, dictated by the lack of detailed stra>graphic data, of assuming the water table moving parallel to the ground surface.

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Conclusions

Conclusions Coupled approach tradi3onal streamflow data + >me-‐lapse, spa>ally distributed microgravity measurements

Main results •  significant reduc3on of the uncertainty associated with the es>ma>on of the >me

varia>ons of the main hydrological state variables (e.g., total water volume, water table eleva>on)

•  the major effects can be observed in the valley boaom area → higher density of gravimetric sta>ons

•  uncertainty on simulated streamflow decreases as well •  gravimetric data allowed for a beaer iden>fica>on of the hydrological conceptual model

including the defini>on of the valley boGom region

Thank you

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Pareto front

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HydroSCAPE: a multi-scale framework for streamflow routing in large-scale hydrological models

Leno River at Rovereto

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Open un3l 30 October 2015

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Large scale hydrological model •  Rainfall-‐runoff model aimed at simula>ng the occurrence of floods at the large scale

(i.e., catchments with an extension ranging from 1000 km2 up to the con>nental scale). Par>cular emphasis is given to extreme events.

•  Possible extensions include the applica>on to several water resources issues: aquifer recharge, storage dynamics, water resources availability, interac>ons with river ecosystems etc.

•  Specific aGen>on is given to the flow rou3ng algorithm, which has been indicated as an aspect of LSM and global hydrological models needing some improvement (Clark et al, WRR 2015)

REVIEW ARTICLE10.1002/2015WR017096

Improving the representation of hydrologic processes in EarthSystem ModelsMartyn P. Clark1, Ying Fan2, David M. Lawrence1, Jennifer C. Adam3, Diogo Bolster4, David J. Gochis1,Richard P. Hooper5, Mukesh Kumar6, L. Ruby Leung7, D. Scott Mackay8, Reed M. Maxwell9,Chaopeng Shen10, Sean C. Swenson1, and Xubin Zeng11

1National Center for Atmospheric Research, Boulder, Colorado, USA, 2Department of Earth and Planetary Sciences,Rutgers University, New Brunswick, New Jersey, USA, 3Department of Civil and Environmental Engineering, WashingtonState University, Pullman, Washington, USA, 4Department of Civil & Environmental Engineering and Earth Sciences,University of Notre Dame, South Bend, Indiana, USA, 5The Consortium of Universities for the Advancement of HydrologicScience, Inc., 6Nichols Schools of Environment, Duke University, Durham, North Carolina, USA, 7Pacific Northwest NationalLaboratory, Richland, Washington, USA, 8Department of Geography, University at Buffalo, State University of New York,Buffalo, New York, USA, 9Department of Geology and Geological Engineering, Colorado School of Mines, Golden,Colorado, USA, 10Department of Civil and Environmental Engineering, Pennsylvania State University, State College,Pennsylvania, USA, 11Department of Atmospheric Sciences, University of Arizona, Tucson, Arizona, USA

Abstract Many of the scientific and societal challenges in understanding and preparing for global envi-ronmental change rest upon our ability to understand and predict the water cycle change at large riverbasin, continent, and global scales. However, current large-scale land models (as a component of Earth Sys-tem Models, or ESMs) do not yet reflect the best hydrologic process understanding or utilize the largeamount of hydrologic observations for model testing. This paper discusses the opportunities and key chal-lenges to improve hydrologic process representations and benchmarking in ESM land models, suggestingthat (1) land model development can benefit from recent advances in hydrology, both through incorporat-ing key processes (e.g., groundwater-surface water interactions) and new approaches to describe multiscalespatial variability and hydrologic connectivity; (2) accelerating model advances requires comprehensivehydrologic benchmarking in order to systematically evaluate competing alternatives, understand modelweaknesses, and prioritize model development needs, and (3) stronger collaboration is needed betweenthe hydrology and ESM modeling communities, both through greater engagement of hydrologists in ESMland model development, and through rigorous evaluation of ESM hydrology performance in researchwatersheds or Critical Zone Observatories. Such coordinated efforts in advancing hydrology in ESMs havethe potential to substantially impact energy, carbon, and nutrient cycle prediction capabilities through thefundamental role hydrologic processes play in regulating these cycles.

1. Introduction

The stores and fluxes of water near the land surface modulate nearly all processes at the land-atmosphereinterface. For example, evapotranspiration affects weather and climate through its influence on boundarylayer dynamics and thermal dynamics. The stores and fluxes of water on land also influence ecosystemstructure and functioning, carbon, nutrient, and other biogeochemical cycles, and dictate freshwater avail-ability for societies. Many of the scientific and societal challenges to understand and prepare for global envi-ronmental change rest upon our ability to understand and predict water cycle changes at large river basin,continent, and global scales [Eagleson, 1986].

Simulations of global environmental change are now performed using Earth System Models (ESMs), whichare designed to capture the key interactions among the components of the Earth System including theatmosphere, ocean, land, and sea ice [Flato, 2011; Dunne et al., 2012; Hurrell et al., 2013]. ESMs build onglobal climate model platforms but substantially extend their capabilities by representing a diverse set ofphysical, chemical, and biological interactions across multiple space and time scales [Hurrell et al., 2013].Here we focus on the hydrologic processes in the so-called ‘‘land models’’—the land component of ESMs.Because terrestrial water stores and fluxes are strong modulators of energy and biogeochemical stores on

Special Section:The 50th Anniversary of WaterResources Research

Key Points:! Land model development can

benefit from recent advances inhydrology! Accelerating modeling advances

requires comprehensivebenchmarking activities! Stronger collaboration is needed

between the hydrology and ESMmodeling communities

Correspondence to:M. P. Clark,[email protected]

Citation:Clark, M. P., Y. Fan, D. M. Lawrence,J. C. Adam, D. Bolster, D. J. Gochis,R. P. Hooper, M. Kumar, L. R. Leung,D. S. Mackay, R. M. Maxwell, C. Shen,S. C. Swenson, and X. Zeng (2015),Improving the representation ofhydrologic processes in Earth SystemModels, Water Resour. Res., 51,doi:10.1002/2015WR017096.

Received 13 FEB 2015Accepted 19 JUL 2015Accepted article online 22 JUL 2015

VC 2015. American Geophysical Union.All Rights Reserved.

CLARK ET AL. REPRESENTING HYDROLOGIC PROCESSES IN EARTH SYSTEM MODELS 1

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•  Some key scien3fic ques3ons: •  How climate change may modify the sta>s>cs of floods occurring IN large river

basins? •  What are the consequences on the management of the hydraulic structures? •  Can we determine the uncertainty associated with the es>mate of extreme

hydrological events?

Large scale hydrological model

LETTERSPUBLISHED ONLINE: 21 OCTOBER 2012 | DOI: 10.1038/NCLIMATE1719

Hydroclimatic shifts driven by human water usefor food and energy productionGeorgia Destouni*, Fernando Jaramillo and Carmen Prieto

Hydrological change is a central part of global change1–3. Itsdrivers in the past need to be understood and quantified for ac-curate projection of disruptive future changes4. Here we anal-yse past hydro-climatic, agricultural and hydropower changesfrom twentieth century data for nine major Swedish drainagebasins, and synthesize and compare these results with otherregional5–7 and global2 assessments of hydrological change byirrigation and deforestation. Cross-regional comparison showssimilar increases of evapotranspiration by non-irrigated agri-culture and hydropower as for irrigated agriculture. In theSwedish basins, non-irrigated agriculture has also increased,whereas hydropower has decreased temporal runoff variability.A global indication of the regional results is a net total increaseof evapotranspiration that is larger than a proposed associatedplanetary boundary8. This emphasizes the need for climateand Earth system models to account for different human usesof water as anthropogenic drivers of hydro-climatic change.The present study shows how these drivers and their effectscan be distinguished and quantified for hydrological basins ondifferent scales and in different world regions. This should en-courage further exploration of greater basin variety for betterunderstanding of anthropogenic hydro-climatic change.

Drivers of freshwater changes are multiple and difficult todistinguish and quantify9–12. Global increase of evapotranspiration(ET) by irrigation and a parallel decrease by deforestation hasbeen estimated by spatial compilation of crop and forest data2.Furthermore, spatial analysis of relatively short-term (30-year)data has shown effects of large dams and their reservoirs onatmospheric variables of convective available potential energy,specific humidity and surface evaporation extending over distancesof around 100 km away from reservoir shorelines13. Such spatialresults indicate ET changes by different land and water uses,but do not reveal the actual change dynamics and timing.Moreover, global averaging hides the spatial variation of ETand its regional change drivers and further effects on waterchange (through changed water loss by ET to the atmosphere5,7,14)and climate change (through changed latent heat flux6,15 andatmospheric circulation16).

Hydrological model interpretation of consistently long,twentieth century time series of relevant hydro-climatic and land–water use data has distinguished between climate and irrigationdrivers of ET change in the drainage basins of the Aral Sea in CentralAsia5,6 and Mahanadi River in India7 (Fig. 1a). Both of these basinsrepresent areas withmajor irrigation developments that have drivenincreases of ET and associated water loss to the atmosphere. Directtemporal analysis of long-term hydro-climatic and land–water usedata, accounting for the water balance constraints of hydrologicalbasins, can thus complement spatial studies, particularly for thetwentieth century, which has seen large land–water use changes,

Department of Physical Geography and Quaternary Geology, Bert Bolin Centre for Climate Research, Stockholm University, SE-106 91 Stockholm, Sweden.*e-mail: [email protected].

while instrumental hydro-climatic data have become available fordirect analysis of their hydrological effects.

In this study, we investigate twentieth century land–water useand hydro-climatic data, and interpret them by the fundamentalwater balance quantification P�ET�R�DS= 0 (where P isprecipitation, R is runoff and DS is water storage change) fornine major Swedish drainage basins (Fig. 1a). The investigationhas three goals. First, a basin-scale distinction of hydrologicalchanges and their drivers in the Swedish basins, which amongthem represent different land–water uses (Fig. 1a, green: dominantnon-irrigated agriculture, red: dominant hydropower, blue: withessentially unregulated rivers and little agriculture) and hydro-climatic conditions in terms of surface temperature (T ; Fig. 1b)and P (Fig. 1c). Second, cross-regional result comparison acrossthe complementary Swedish, Aral and Mahanadi basins (Fig. 1a),representing an even wider range of different hydro-climaticconditions (Fig. 1b,c) and land–water uses (irrigated and non-irrigated agriculture, hydropower, unregulated). Third, cross-scale/method comparison between the extrapolation implicationsof the regional basin results and previous spatial estimates ofglobal hydrological changes and drivers2. Hydrological, and otherphysical and ecological science communities11,17,18 have identifiedfundamental needs for such synthesis and comparisons alongclimatic and other gradients.

For the Swedish basins, we calculated annual ET as ETwb =P�Rfrom available P (ref. 19) and R (ref. 20) data (SupplementaryFig. S1), assuming annual DS⇡ 0. This assumption is justifiedbecause possible alternative DS assumptions that can be made onthe basis of lake water level changes19 affect mostly the short-term fluctuations and not the long-term variation and changes ofaverage ETwb = P �R�DS that are the main focus of this study(Supplementary Fig. S2 compares ETwb calculated with differentDSassumptions). Furthermore, we compared ETwb with two different,purely climate-determined estimates (denoted ETclim) of ET byBudyko and Turc expressions21 using available data on P andT (ref. 19), and potential evapotranspiration (PET) calculatedfrom T data (Supplementary Methods). We also compared thedata-given changes in annual average R with a Budyko-basedestimate of purely climate-driven change21 (1Rclim; SupplementaryMethods), and quantified the temporal R variability and its changesin terms of the coefficient of variation of daily R, CV(R), in amoving 20-year window.

For the Mahanadi and Aral Sea basins, hydro-climatic changesfrom the beginning to the end of the twentieth century have beenreported in previous studies5–7 (summarized in SupplementaryTables S1 and S2) that calculated ETwb by distributed hydrologicalmodelling. They distinguished purely climatic (T and P) changeeffects on ETwb by comparison of realistic simulations of bothirrigation and climate change with a hypothetical scenario of

NATURE CLIMATE CHANGE | ADVANCE ONLINE PUBLICATION | www.nature.com/natureclimatechange 1

Resilience of river flow regimesGianluca Bottera, Stefano Bassoa,b, Ignacio Rodriguez-Iturbec, and Andrea Rinaldoa,d,1

aDepartment of Civil, Architectural, and Environmental Engineering, University of Padua, I-35100 Padua, Italy; bDepartment of Water Resources and DrinkingWater, Swiss Federal Institute of Aquatic Science and Technology, CH-8600 Dübendorf, Switzerland; cDepartment of Civil and Environmental Engineering,Princeton University, Princeton 08540, NJ; and dLaboratory of Ecohydrology, School of Architecture, Civil and Environmental Engineering, École PolytechniqueFédérale de Lausanne, Lausanne CH-1015, Switzerland

Contributed by Andrea Rinaldo, June 25, 2013 (sent for review March 3, 2013)

Landscape and climate alterations foreshadow global-scale shifts ofriver flow regimes. However, a theory that identifies the range offoreseen impacts on streamflows resulting from inhomogeneousforcings and sensitivity gradients across diverse regimes is lacking.Here, we derive a measurable index embedding climate andlandscape attributes (the ratio of the mean interarrival of stream-flow-producing rainfall events and the mean catchment responsetime) that discriminates erratic regimes with enhanced intraseaso-nal streamflow variability from persistent regimes endowed withregular flow patterns. Theoretical and empirical data show thaterratic hydrological regimes typical of rivers with low meandischarges are resilient in that they hold a reduced sensitivity toclimate fluctuations. The distinction between erratic and persistentregimes provides a robust framework for characterizing the hydrol-ogy of freshwater ecosystems and improving water managementstrategies in times of global change.

climate change | flow variability | hydroclimatic shift | water uses

The river flow regime identifies the streamflow temporal vari-ability at a station (1), which is the natural byproduct of the

sequence of flow pulses conveyed to the stream network from thecontributing catchment after rainfall. The flow regime is embodiedby the probability distribution function (pdf) of daily flows (2–4),which provides information on the mean water availability, theextent of discharge fluctuations (5), and the frequency of high/lowflows. Flow regimes not only constrain anthropogenic uses, such asenergy production and irrigation, but shape form and functions ofriverine ecosystems owing to the dynamic control of flow magni-tude on stream habitats (1, 4, 6–8). In the past decades, naturaland anthropogenic modifications of climate drivers (9), jointlywith landscape changes, have led to increasingly nonstationaryflow regimes (10–14). These ubiquitous and accelerating alter-ations of river flows challenge the sustainability of water uses (5,15) and the ecosystem services provided by river biomes (6, 16, 17).However, streamflow alterations are not expected to be uniform(18, 19), owing to heterogeneous climate/landscape drifts andsensitivity gradients across diverse climate zones and regime types.Here, the flow regimes of pristine rivers are analyzed using a

mechanistic analytical model in which streamflow dynamics aredriven by a catchment-scale soil–water balance forced by sto-chastic daily rainfall (2, 3). The analytical model indicates that thenature of flow regimes and their sensitivity to climate change canbe discriminated based on the frequency of effective (i.e., flow-producing) rainfall events and the time scale of the hydrologicalresponse through which these rainfall inputs are propagated acrosscatchments. This hypothesis is tested through extended climateand flow records taken from 44 US and Italian catchmentsbelonging to the US Geological Survey/National Oceanic andAtmospheric Administration and the Regional Agency for Envi-ronmental Protection of the Veneto Region monitoring networks(Table S1). To comply with the basic assumptions of the mecha-nistic model (pertaining to the features of climate forcing and thedominant mechanisms of streamflow production), the choice ofthe catchments is restricted to unregulated, small/medium water-sheds weakly influenced by snow dynamics (SI Materials andMethods). In this setting, flow-producing rainfall events result

from the censoring operated by catchment soils on daily rainfall,and they are modeled as a spatially uniform marked Poissonprocess with mean depth α [L] and mean frequency λ ½T−1". Al-though α quantifies the average daily intensity of rainfall events, λis smaller than the underlying precipitation frequency because thesoil–water deficit created by plant transpiration in the root zonemay hinder the routing of some inputs to streams (Eq. S3).Therefore, λ crucially embeds rainfall attributes; soil/vegetationproperties; and other climate variables, such as temperature, hu-midity, and wind speed.The time scale of the hydrological response, defined as the

mean water retention time in the upstream catchment, is opera-tionally identified by the inverse of the flow decay rate ðk ½T−1"Þobserved during recessions, conveniently assumed to be exponential(2, 3, 20). The term k quantifies catchment-scale morphologicaland hydrological attributes [e.g., the mean length of hydrologicalpathways and upscaled soil conductivity (3)]. High k values implylow duration of the flow pulses released from the catchment afterrainfall, typical of fast-responding catchments.When flow-producing rainfall events are relatively frequent,

such that their mean interarrival is smaller than the duration of theflow pulses delivered from the contributing catchment ðλ> kÞ, therange of streamflows observed at a station between two sub-sequent events is reduced, and a persistent supply is guaranteed tothe stream from catchment soils. Therefore, river flows are weaklyvariable around the mean (Fig. 1A, Lower) and quite predictable.This type of regime (hereafter termed persistent) is typicallyexpected during humid, cold seasons in slow-responding catch-ments (high λ, low k).When the mean interarrival between flow-producing rainfall

events is larger than the typical duration of the resulting flow pulsesðλ< kÞ, a wider range of streamflows is observed between eventsbecause the reach is allowed to dry significantly before the arrivalof a new pulse. The temporal patterns of streamflows are thusmore unpredictable (Fig. 1A, Upper), leading to erratic regimeswith significant streamflow fluctuations. Under these circum-stances, the preferential state of the system is typically lower thanthe mean. Erratic regimes are likely expected in fast-respondingcatchments during seasons with sporadic rainfall events (low λ,high k). However, this type of regime also can frequently be ob-served during hot, humid seasons (where relatively high rainfallrates are compensated by enhanced evapotranspiration).The analytical mechanistic model on which the proposed classi-

fication of hydrological regimes is grounded allows the river flowpdf to be expressed as a gamma-distribution with shape parameterλ=k and rate parameter αk (2, 3) (Materials and Methods). Theparameters α, λ, and k (which we hereafter term hydroclimaticparameters) summarize the underlying morphological and

Author contributions: G.B., I.R.-I., and A.R. designed research; G.B., S.B., and A.R. per-formed research; G.B. and S.B. analyzed data; and G.B., I.R.-I., and A.R. wrote the paper.

The authors declare no conflict of interest.

Freely available online through the PNAS open access option.1To whom correspondence should be addressed. E-mail: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1311920110/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1311920110 PNAS | August 6, 2013 | vol. 110 | no. 32 | 12925–12930

ENVIRO

NMEN

TAL

SCIENCE

S

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Characteristics of the model Macro-‐regional/con>nental hydrological model for flood assessment.

Possible applica>on to water resources problems: aquifer recharge, storage dynamics, water resources availability, interac>ons with river ecosystems etc.

Discre>za>on into large macro-‐cells: computa>onal requirements, direct coupling with climate models, focus on large scale dynamics.

Simplicity: a few parameters, possibly linked to physical proper>es for which distributed informa>on is easily available.

Linearity of the processes: in order to ensure a simple and efficient numerical paralleliza>on.

Rigorous upscaling of the spa>al distribu>on of water fluxes.

Physically based (WFIUH approach).

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Delinea>on of the catchment area.

Pre-processing

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Pre-processing

Discre3za3on of the domain into a number of macrocells.


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Pre-processing


Extrac>on of the river network from the DEM.


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Extrac>on of the river network from the DEM. Iden3fica3on of target points (hereater referred to as nodes): gauged sec>ons, residen>al areas, hydraulic structures, reservoir etc. Defini>on of the width func3on for each node-‐macrocell pair.


Pre-processing

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Structure of the model Water balance dynamics at the hillslope scale are simulated using a simple rainfall-‐runoff model (e.g., SCS) Hillslope drains into the river network, where water is transferred towards nodes, with a given channel velocity. WFIUH approach (e.g. Rinaldo, Marani, Rigon, 1991)

The streamflow simulated at each node is given by the sum of the contribu>ons of all macrocells contribu>ng to that node.

The model is linear → the streamflow generated at each macrocell is evaluated independently from the others.

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Characteris3cs: •  Few reservoir and hydraulic structures.

•  Snow precipita>on and mel>ng is negligible.

•  Historical series (a few decades) of streamflow, rainfall and air temperature are available.

•  Surface area of the catchment equal to 4116 km2.

•  5 nodes, in correspondence to gauging sec>ons.

Example application: Upper Tiber

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3 grid sizes: 5, 10 and 50 km


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Width func>ons at Ponte Nuovo obtained aggrega>ng the original 20 m DEM to 5, 10 and 50 km: Models in which the geomorphological descrip>on of the drainage network has the same scale of the computa>onal grid, suffer from a deteriora>on of the geomorphological response of the watershed. This is not the case of the proposed formula>on, in which the width func>on maintains all the informa>on derived from the original DEM


Figure 5. Width functions of the Upper Tiber river basin at Ponte Nuovo (PN) outlet (4116 km2) derived from

DEMs obtained aggregating the original 20 m DEM to 5, 10 and 50 km (lower panels). The width function

obtained with the original 20 m DEM is also shown with a red line.

to represent the travel time distribution at the hillslope scale. In this case, rescaling may be obtained

by using a hillslope specific velocity V`

<< Vc

.

The overall streamflow generation model can be summarized as follows7 EdN:7335

Ri,j

=

⇣Pj

k=1Ji,k�t� Ia,i

⌘2

Pj

k=1Ji,k�t+ cS

Si

� Ia,i

, j = 1, ...,np

(5)

7EDNOTE: L’equazione dell’SCS che c’era nel testo non mi torna, mi sembra che avevamo detto di applicarla in

modo continuo. L’ho quindi commentata nel file tex e riscritta in modo che sa da una vostra verifica risulta che è invece

corretta si può ripristinare. C’e’ anche problema che qui t è usato come contatore, mentre prima è stato usato come

variabile tempo. L’ho quindi cambiato

13

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Rainfall-‐runoff models

Model parameters

v λ cS kH SCSLRH

✓ ✓ ✓ ✓

Data requirements

•  SCSLRH: SCS + linear reservoir for the hillslope

QUESTO E’ IL MODELLO DI PRODUZIONE USATO IN HESS, LE ALTRE SLIDE LE HO NASCOSTE

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Rainfall-‐runoff models •  none: runoff=rainfall

Model parameters

v λ cS k kH none ✓ - - - - SCS ✓ ✓ ✓ - - SCSLRI

✓ ✓ ✓ ✓ -

SCSLRH

✓ ✓ ✓ - ✓

SCSLRHI

✓ ✓ ✓ ✓ ✓

Data requirements

 

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Model parameters


✓ ✓ ✓ ✓ -

SCSLRH

✓ ✓ ✓ - ✓

SCSLRHI

✓ ✓ ✓ ✓ ✓

Data requirements

•  SCS: Soil Conserva>on Service – Curve Number Methodology

 

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Model parameters


✓ ✓ ✓ ✓ -

SCSLRH

✓ ✓ ✓ - ✓

SCSLRHI

✓ ✓ ✓ ✓ ✓

Data requirements


 

•  SCSLRI: SCS + linear reservoir for infiltra>on

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Model parameters


✓ ✓ ✓ ✓ -

SCSLRH

✓ ✓ ✓ - ✓

SCSLRHI

✓ ✓ ✓ ✓ ✓

Data requirements


•  SCSLRH: SCS + linear reservoir for the hillslope

•  SCSLRHI: SCS + linear reservoir for the hillslope + linear reservoir for infiltra>on

•  SCSLRI: SCS + linear reservoir for infiltra>on

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Calibra>on at Ponte Nuovo Example application: Upper Tiber

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Mul> site valida>on Example application: Upper Tiber

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Mul> event valida>on Example application: Upper Tiber

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Conclusions •  We proposed a routing scheme independent on

the gridding of the LSM; •  “perfect” upscaling with geomorphological

dispersion preserved; •  The scheme is computational efficient (major

computational burden in the preprocessing);

•  Routing dependent on 2 parameters.

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THANK YOU

Alberto Bellin

Science

Transcript of Alberto Bellin