Transmission of climate, sea-level, and tectonic singals across river systems

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PROEFSCH RIFT

ter verkrijging van d e graad van d octor aan d e Technische Universiteit Delft,

op gezag van d e Rector Magnificu s Prof. ir. K. C. A. M. Lu yben, voorzitter van het College voor Prom oties,

in het op enbaar te verd ed igen op 11-03-2015 om 12.30 u u r d oor

And rea FORZON I

Master of Science, Earth Sciences VU Am sterd am geboren te Pistoia, Italië.

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Dit p roefschrift is goed gekeu rd d oor d e p rom otor en: Prof. Dr. S.M. Lu thi.

Dr. J.E.A. Storm s

Sam enstelling p rom otiecom m issie:

Rector Mangificu s voorzitter

Prof. Dr. S.M. Lu thi Delft University of Tech nology, p rom otor Dr. J.E.A. Storm s Delft University of Tech nology, co-p rom otor Prof. Dr. Tom Cou lthard University of H u ll

Prof. Dr. William H elland -H ansen University of Bergen

Prof. Dr. Ir. Marcel Stive Delft University of Tech nology Prof. Dr. Jakob Wallinga University of Wageningen Prof. Dr. Ronald van Balen Vrije Universiteit Am sterd am Prof. Dr. Giovanni Bertotti Delft University of Tech nology

This research w as financed by ALW -N WO (Du tch organization for scientific research, VIDI grant nu m ber 864.09.004 to Joep Storm s).

ISBN : 978-94-6295-108-2

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CH APTER 1

Introd u ction

1.1. Relevance

H ow are clim atic, sea-level, and tectonic histories transm itted across a river system and how are they record ed in the stratigrap hic record ? What is the im p act of the changing bou nd ary cond itions on flu vio-d eltaic stratigrap hy? These are still ou tstand ing qu estions in the field s of geom orp hology and stratigrap hy and have both a scientific and a com m ercial relevance. Investigating and qu antifying sed im ent erosion, transp ort and d ep osition p rocesses in p resent d ay river system s and sed im entary basins is the key, in actu alistic term s, for reconstru cting clim atic, tectonic, and sea-level histories of the p ast, w hich are w ritten in the stratigrap hic record . Fu rtherm ore, by m od elling river system s resp onse to forcing, w e can better p red ict the im p act of clim atic ch anges and sea-level rise on the hyd rologic and sed im entary evolu tion of river d eltas, and on hu m an infrastru ctu res and activities. Finally, u nd erstand ing the evolu tion of river system s is cru cial for p red icting the stratal architectu re and the p rop erties of sed im entary basins in the su b -su rface, w hich is one of the key challenges in the hyd rocarbon and shallow and d eep su bsu rface engineering ind u stries.

1.2. Background and open questions

River system s are the key m otor in d elivering w ater and sed im ent s to the ocean. Sed im ents are m ainly p rod u ced in the u p land p art of river system s, w here chem ical and m ech anical p rocesses d egrad e and erod e rocks. The fresh sed im ents are transp orted tow ard s rivers, w hich carry them d ow nstream either in su sp ension, solu tion or as bed load . Sed im ents can get transp orted , accu m u lated and again rem obilized several tim es d u ring their years-to-m illennia d ow nstream jou rney, on hillslop es, w ithin ch annels, in flood p lains, and in river d eltas, before reach ing their final sink in a d eep m arine environm ent. The m ajor natu ral controls on this jou rney, called sou rce-to-sink, are tectonics, clim ate, and sea-level. Tectonic p rocesses creates top ograp hy and allow s gravitational p rocesses to op erate. C lim ate fu rnishes the energy (w ater and heat) to m od ify and d egrad e top ograp hy , p rod u ce and transp ort

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2 Introduction

sed im ents. Base-level is the m ain control on accom m od ation, w hich is the am ou nt of sp ace available for sed im ents to be accu m u lated . At the end of the jou rney to the sink, the p attern in w hich sed im ents are d istribu ted and accu m u lated in river d eltas is controlled by accom m od ation, a fu nction of sea-level and su bsid ence, sed im ent su p p ly from rivers, and m arine p rocesses, i.e. w aves and tid es.

The im p act of external forcing on river system s has been extensively investigated by geom orp hologists and stratigrap hers d u ring the last d ecad es, by interp reting field d ata (Bu sschers et al., 2007; Vis et al., 2008; Whittaker et al., 2009), and sim u lating natu ral p rocesses w ith nu m erical and analogu e m od els (Tu cker and Slingerland , 1997; Mu to and Steel, 2004; Syvitski and Millim an, 2007). Althou gh su rface p rocesses are qu alitatively w ell u nd erstood , it is still d ifficu lt to qu antify them , w ith a reasonable level of u ncertainty, on a geological tim e scale. River system s are often called com p lex system s becau se of their non -linear resp onse to forcing (Cou lthard and Van De Wiel, 2007; Jerolm ack and Paola, 2010). First, the non -linearity is cau sed by the fact that it takes tim es for p ertu rbations to be transm itted across the river system (Gau d em er and Metivier, 1999; Allen, 2008). These p ertu rbations are either the u p stream m igration of tectonic-ind u ced incision, or the d ow nstream m igration of a clim ate-ind u ced high sed im ent p u lse. Consequ ently the resp onse of the system is d elayed and bu ffered (Fig. 2). Second , the system is affected by threshold s or tip p ing p oin ts, beyond w hich the system resp onse is no longer p rop ortional to the p ertu rbation, su ch as the threshold for bed rock incision on channel bed s (Wiel and Cou lthard , 2010). Third , a large am ou nt of the variability in sed im ent flu x from river system s is cau sed by au togenic p rocesses, su ch as avu lsions and bed arm ou ring. Consequ ently, in ord er to p red ict the sed im ent flu x to river d eltas and to better read the external forcing history from the stratigrap hic record it is im p ortant to incorp orate the non -linear resp onse of river system s to forcing into both concep tu al and nu m erical m od els. At the sam e tim e, it is equ ally im p ortant to w ork w ith m od els of red u ced com p lexity. This becom es fu nd am ental the farther w e m ove back in the geological p ast, becau se it is often very d ifficu lt to constrain p ast bou nd ary cond itions (clim ate, tectonics, base-level). Mod els shou ld be sim p le, or better, sim p le enou gh to sim u late only the first ord er p rocesses w ith a reasonable p rocessing tim e, and the level of ou tp u t p recision shou ld be com p arable to the level of u ncertainty of the requ ired inp u t.

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Introduction 3

1.3. Objective and approach

The objectives of this PhD p roject are (i) to d evelop and ap p ly a nu m erical catch m ent m od el to sim u late the transient land scap e and sed im ent flu x resp onse of river system s to external forcing, and (ii) to investigate and d isentangle sea level and sed im ent su p p ly histories in flu vio-d eltaic stratigrap hy. First, a catchm ent m od el, PaCMod , w as d evelop ed and tested on three river system s: the Waip aoa (N ew Zealand ), the Meu se (the N etherland s) and the Celano, (Italy). PaCMod w as then ap p lied to reconstru ct the sed im entary history of a w ell-stu d ied , Late Qu aternary river system , the Golo (Corsica, France). Mod elling resu lts w ere com p ared to new sed im ent ages, and top ograp hic, sed im entological, and geop hysical d ata acqu ired in the field , to investigate the im p act of clim ate, sea -level, and tectonic forcing on the geom orp hic and stratigrap hic evolu tion of the Golo river system . Finally, the architectu re and the heterogeneities of a Cretaceou s river d elta, the Panther Tongu e (Utah, USA) w ere stu d ied by m eans of ou tcrop observations, stratigrap hic logs correlation, and p etrological analysis of rock sam p les. These stratigrap hic d ata on the Panther Tongu e form the basis for cu rrent and fu tu re w ork w ith forw ard and inverse stratigrap hic m od el to qu antify the im p act of sed im ent su p p ly and sea -level change on stratigrap hic architectu re.

1.4. Background on numerical modelling

The sim p lest ap p roach to sim u late river system s p rocesses is rep resented by sp atially lu m p ed m od els, w hich are based on sp atially averaged p aram eters rep resenting the behaviou r of the system in tim e (e.g., Bogaart and van Balen, 2000; Syvitski and Millim an, 2007). A m ore ad vanced and com p lex ap p roach is a tw o-d im ensional lano-d scap e evolu tion or cellu lar m oo-d el (e.g., Tu cker ano-d Slinger lano-d , 1997; Cou lthard et al., 200), w here all variables are fu nctions of tim e and sp atial coord inates. H ow ever, the generally p oor control on p alaeo-clim ate and catch m ent m orp hology ham p ers the ap p licability of cellu lar m od els, as they requ ire a high level of inp u t d etail, w hich is u su ally u navailable the fu rther w e m ove back in tim e. In contrast, red u ced com p lexity m od els, w ith one or zer o sp atial d im ensions, are m ore p arsim oniou s w ith the requ ired inp u t, com p u tation, and ou tp u t resolu tion, and they p rod u ce resu lts that have the sam e resolu tion as the inp u t bou nd ary cond itions. Lu m p ed and one-d im ensional m od els u su ally focu s on a single set of geom orp hic p rocesses, su ch as the evolu tion of a flu vial longitu d inal p rofile (Kirby and Whip p le, 2001), and they r ely on im p ortant assu m p tions, su ch that they m ay not fu lly rep licate the internal d ynam ics of the system that w e know to be im p ortant

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4 Introduction

(cf. Arm itage et al., 2011; Rohais et al., 2012). N evertheless, they are u sefu l tools to investigate catch m ent evolu tion a nd sed im ent flu x in ancient settings, w here p aram eters have a high d egree of u ncertainty, or w here long tim escales are consid ered (105_–107

a).

By d evelop ing PaCMod , an attem p t w as m ad e to brid ge the gap betw een cellu lar and sp atially-lu m p ed ap p roaches, by u sing the m axim u m level of sim p licity necessary for p alaeo-ap p lications, and by a p rocess-resp onse ap p roach to sim u late the transient resp onse of land scap e m orp hology to external forcing. PaCMod calcu lates long tim e series of w ater and sed im ent flu x from any given catchm ent. The key asp ects of the first version of the m od el is the p aram eterization of sed im ent rou ting and storage in the catchm ent (Chap ter 2). The three-d im ensional m orp hology of a real catchm ent w as collap sed into fou r sp atial d om ains, w here d ifferent p rocesses occu r and sed im ent is rou ted and tem p orar ily stored : hillslop es, flu vial netw ork, catchm ent low er reaches, and catchm ent ou tlet. In the second version of the m od el the m od el w as im p lem ented w ith new rou tines to sim u late the evolu tion of land scap e m orp hology and erosion rates u nd er tectonic a nd clim atic forcing (Chap ter 3).

1.5. Background on the Golo River System

The Golo river system (Corsica, France) w as ch osen as m od ern system to ap p ly and test PaCMod . Becau se of its sm all size, the w ell constrained coastal and offshore sed im entary archives, and the lim ited storage area w ithin the catch m ent, the Golo River system is an excellent laboratory to investigate the transm ission of clim atic and eu static sea level flu ctu ations across a flu vial system . The Golo has received significant attention from acad em ia and ind u stry d u ring the last d ecad e. Research has focu sed m ainly on the geom etries of the d eep -m arine basin floor fans, the final

Figure 1.1: Conceptu al mod el of

d elayed and bu ffered resp onse of a catchm ent to an external p ertu rbation (from Metivier and Gau d em er, 1999)

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Introduction 5

sink of the system . More recently the w hole sou rce -to-sink system w as investigated to u nd erstand the p attern of sed im ent d isp ersal and the m ech anism s controlling allu vial and m arine stratigrap hy (Som m e et al., 2011; Calves et al., 2013).

The Golo River is the m ain flu vial system on the island of Corsica. The p resent d ay ru gged relief of the catchm ent is a resu lt of the recent p hase of regional u p lift (Plio -Qu aternary), w hich reju venated the Miocene low -relief land scap e (Fellin et al., 2005). Terraced rem nants of ancient flood p lains and allu vial fans are p reserved in the Marana Plain, the allu vial-coastal p lain bord ering the Tyrrhenian Sea (Som m e et al., 2011). H ere, the Golo River accu m u lated thick conglom eratic w ed ges d u ring the Late Pleistocene (Conchon, 1972; Skyles, 2003) and rep eated ly incised into these d ep osits, as a resu lt of tectonic u p lift, clim atic and sea-level ch anges (Som m e et al., 2011). These coarse braid p lain d ep osits are organized in a cu t -and -fill p attern, w ith the you nger u nits located at p rogressively low er top ograp hic levels.

The Marana Plain w as the area of tw o field w ork cam p aigns, in collaboration w ith colleagu es from the TU Delft, IFREMER, Brest, and the N etherland s Center for Lu m inescence d ating N CL (Wageningen ). The field d ata inclu d ed geop hysical d ata (S-w ave reflection seism ics, seism ic interferom etry, electro-m agnetic p rofiles), sed im entological observations (ou tcrop s, cores), and sed im ent d ating (op tical stim u lated lu m inescence OSL and rad iocarbon 14C). The 4D m od el of the Marana Plain, constru cted integrating all the d ata, w as com p are d to nu m erical sim u lations w ith PaCMod , in ord er to investigate the relative im p act of clim ate and sea -level changes on the Golo flu vial system (Chap ter 4). This 4D m od el form s a good cond itioning d ataset for the ongoing and fu tu re w ork w ith stratigrap hic m od eling. 1.6. Background on the Panther Tongue, Utah, USA

After d evelop ing PaCMod and stu d ying a relatively w ell-constrained flu vial system , the Golo, the focu s of the research p roject sw itched to the sed im ent sink, and in p articu lar, to an ancient d eltaic system w ith p oorly-constrained bou nd ary cond itions, the Panther Tongu e d elta on the Wasatch Plateau (Utah, USA). The Panther Tongu e w as ch osen becau se its continu ou s exp osu res, su b -p arallel to the regional d ep ositional strike of d eltaic shorelines, allow reco nstru cting the stratigrap hic architectu re and the along -strike variability of the d eltaic system .

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6 Introduction

Figure 1.2: Tw o exam p les of field techniqu es u sed in th e field w ork cam p aign in Corsica. (A) S-w ave

seism ics u sing a 96 m length array of geop hones as reveivers and a m anually op erated active sou rce. (B) Sed im ent cored u sing the Van d er Staay corer and d escribed in the field .

Based on d etailed ou tcrop stu d ies in the northern Wasatch Plateau , the Panther Tongu e is consid ered a typ ical flu vial-d om inated river d elta, w hich is u sed as a p otential analogu e for hyd rocarbon reservoir s. Althou gh it is interp reted to record forced regression (Posam entier and Morris, 2000; H w ang and H eller, 2002), the architectu re of the Panther Tongu e as a coastal system and the heterogeneities on the sp atial scale of the w hole Wasatch Plateau are still p oorly u nd erstoo d . In the final p art of this research p roject, the 3D architectu re of the Panther Tongu e d eltaic system w as ch aracterized , w ith sp ecial em p hasis on the connection betw een the d ifferent sed im entary environm ents w ithin the stratigrap hic u nits . Du ring a tw o- w eeks field w ork cam p aign stratigrap hic logs w ere record ed and rock sam p les w ere collected . The stratigrap hic logs w ere correlated w ith p reviou s literatu re and w ireline log, and the sam p les w ere analysed w ith thin sections, CT-scans and XRF (X-ray flu orescence). The stratigrap hic architectu re and the lithological p rop erties of the Panther Tongu e are the basis for cu rrent and fu tu re research w ith forw ard and inverse nu m erical m od elling.

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Introduction 7

1.7. Thesis outline

The stru ctu re of this thesis follow s three p arallel p aths throu gh sp ace and tim e. First, the stru ctu re rep resents the chronological ord er of the PhD p roject w orkflow . Second , it follow s a sp atial shift in focu s, m igrating from the u p stream p art of the catch m ent, the sed im ent sou rce, tow ard s the river d elta, the sed im ent sink. Third , it form s a p ath back in tim e, from H olocene river system s w ith a w ell-constrained evolu tion, to Pleistocene and then Cretaceou s river system s, w hose evolu tion is p oorly constrained .

In chap ter 2 the nu m erical m od el PaCMod and its te sting on the p resent-d ay Waip aoa and the Meu se River are d escribed . The integration of PaCMod w ith new rou tines for catchm ent transient resp onse to clim ate and tectonics and the ap p lication of the m od el to the tectonically -p ertu rbed Celano catch m ent, are t he focu s of chap ter 3. Chap ter 4 p resents field d ata and m od elling w ork on the Golo River system . Chap ter 5 d escribes the arch itectu re and the heterogeneities of the Cretaceou s Panther Tongu e coastal system . Finally, in ch ap ter 6, a synthesis is m ad e of the find ings from the p reviou s chap ters, and lines for p otential fu tu re research are p resented .

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8 Introduction

Figure 1.4: Thesis ou tline conceptu al schem e show ing the relation betw een the d ifferent chap ters to

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CH APTER 2

PaCMod : a sp atially lu m p ed m od el to investigate

d ow nstream sed im ent flu x p rop agation w ithin a flu vial

catchm ent

Abstract. A sp atially lu m p ed p r ocess-resp onse m od el, PaCMod , is p resented , w hich calcu lates long tim e series (thou sand s to m illion years) of flu vial w ater d ischarge and sed im ent load at the river catch m ent ou tlet, based on clim atic d ata, d rainage basin characteristics and u ser -d efined p aram eters. Key asp ects of the m od el are (i) the lu m p ed ap p roach, allow ing for fast sim u lations and p reserving the sam e resolu tion from p alaeoclim atic cond itions and geom orp hological reconstru ctions ; (ii) the p aram eterization of sed im ent rou ting and storage w ithin the catchm ent. PaCMod w as su ccessfu lly tested on observed d ata from three p resent -d ay flu vial system s: the Meu se, the Waip aoa, and the Po Rivers. Moreover, the sim u lated sed im ent flu x for the Meu se and for the Waip aoa Rivers in the late Qu aternary is in agreem ent w ith p u blished field and m od eling w ork. PaCMod exp erim ents show how the d ow nstream p rop agation of the original clim atic signal is ham p ered by sed im ent rou ting and storage w ithin the catchm ent.

Chap er 2 is based on: Forzoni A., d e Jag er G., Stom s J.E.A. (2013). A sp atially lu m p ed m od el to investigate d ow nstream sed im ent flu x p rop agation w ithin a flu vial catchm ent. Geomorp hology 193, 65 -80

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10 Introduction

2.1 Introduction

Und erstand ing the effects of p alaeoclim ate forcing on catch m ent sed im ent yield and on basin stratigrap hy is still an ou tstand ing research objective in sed im entary geology. N u m erical sim u lations have show n that Qu aternary clim atic changes p rod u ced clear sed im ent flu x p u lses (e.g., Tu cker and Slingerland , 1997; Tebbens et al., 2000a; Kettner et al., 2009; van Balen et al., 2010). Sed im ent bu d geting w orks have ind icated that, for certain sou rce-to-sink system s, the sed im ent flu x signal is p reserved in the stratigrap hic record (e.g., Bu sschers et al., 2007; Vis et al., 2008; Som m e et al., 2011), w hile for other system s it is lacking or strongly bu ffered (e.g., Trim ble, 1977; Metivier and Gau d em er, 1999; Phillip s, 2003; Brom m er et al., 2009). The role of sed im ent su p p ly in basin stratigrap hy has received m ore and m ore attention in the last d ecad es becau se u nd erstand ing the p alaeo sed im ent su p p ly flu xes can p rovid e a better interp retation of the available core and seism ic d ata and can help interp retation at the p arasequ ence and event -bed scale (Blu m and Törnqvist, 2000; H am p son and Storm s, 2003; Blu m and Aslan, 2006; H elland -H ansen and -H am p son, 2009; Charvin et al., 2011; -H olbrook and Bhattach arya, 2012). N u m erical sim u lations of flu viod eltaic and shoreface -shelf system s have clearly show n a relation betw een sed im ent su p p ly and stratal resp onse (H a m p son and Storm s, 2003; Storm s and Sw ift, 2003; Ku bo et al., 2006; Charvin et al., 2011). This im p lies that w e are able to d etect a clim atic signal in m arine stratigrap hy, bu t w e still p oorly u nd erstand the m od ification of su ch signal d u ring its d ow nstream p rop agation tow ard the m arine d om ain.

The sim p lest ap p roach to sim u late catchm ent p rocesses is a sp atially lu m p ed m od el, w hich is based on sp atially averaged p aram eters rep resenting the behavior of the system in tim e (e.g. Weltje et al., 1998; Bogaart and van Balen, 2000; Bogaart et al., 2003; Syvitski and Millim an, 2007; Kettner and Syvitski, 2008). A m ore ad vanced and com p lex ap p roach is a tw o-d im ensional land scap e evolu tion m od el (e.g., Tu cker and Slingerland , 1997; Whip p le and Tu cker, 1999; Cou lthar d et al., 2002; Arm itage et al., 2011) w here all d ep end ent variables are fu nctions of tim e and sp atial coord inates. These m od els inclu d e internal catch m ent d ynam ics, su ch as land scap e threshold s, sed im entation and erosion w aves p rop agation that contribu te to the generation as w ell as intra catchm ent m od ification and d am p ening of a clim atic or tectonic signal (Walling, 1982; Phillip s and Slattery, 2006; Cou lthard and Van De Wiel, 2007; Whittaker et al., 2010; Arm itage et al., 2011).

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PaCMod 11

The generally p oor control on p alaeoclim ate and catchm ent m orp hology ham p ers the ap p licability of tw o-d im ensional m od els, as they requ ire a high level of inp u t d etail, w hich is u su ally u navailable the fu rther w e m ove back in tim e. Sp atially lu m p ed m od els p rod u ce resu lts that hav e the sam e resolu tion as the inp u t bou nd ary cond itions instead . As su ch, they cou ld be u sed for p alaeo settings for w hich catchm ent p rop erties and clim ate reconstru ctions are p oorly know n. H ow ever, becau se of the sp atial lu m p ing, they d o not sim u late catch m ent m em ory, i.e. the inheritance of p reviou s clim atic and m orp hologic cond itions, w hich is enhanced by sed im ent rou ting and storage.

We have d evelop ed a sp atially lu m p ed m od el, PaCMod , that sim u lates tim e series of flu vial w ater d ischarge and sed im ent lo ad from any given catch m ent. It com bines new m od eling algorithm s and p aram eterizations for environm ental resp onse to clim atic ch anges, sed im ent rou ting, and storage (catchm ent m em ory) w ith existing and m od ified rou tines from H yd rotrend (Syvitski et al., 1998; Kettner and Syvitski, 2008) and PALAEOFLOW (Bogaart et al., 2003a). The aim s of this p ap er are (i) to d escribe the new m od eling techniqu e, its p otential and lim itations; (ii) to test the m od el on real-w orld p resent-d ay and late Pleistocene—H olocene cases, and (iii) to investigate how the sed im ent flu x signal is generated , transm itted , and bu ffered in a river d rainage system .

2.2. PaCModoutline

A schem atic overview of the PaCMod m od eling ap p roach is show n in Fig. 2.1. The m ain inp u ts are clim atic cond itions and catchm ent p rop erties. We d efine the catch m ent as the u p land , m ainly erosional p art of a d rainage basin in w hich sed im entation occu rs only tem p orarily, as allu vial fans, confined flood p lains, and channel d ep osits. PaCMod consists of three connected rou tines op erating at d ifferent tim escales: the long-term rou tine, the ep ochs rou tine, and the yearly rou tine.

In the long-term rou tine, the long-term clim atic and environm ental bou nd ary cond itions are d efined . We consid er the long -term clim ate as a series of d iscrete p oints in tim e, w hich w e call ep ochs. The sp acing betw een ep ochs (typ ically 500-1000 years) is based on the d iscreteness of the p alaeoclim atic p roxies d ata and on com p u tational d em and . For each ep och (ep ochs rou tine), PaCMod p erform s short sim u lations (10-30 years) at a d aily tim escale, p rod u cing d aily w eather cond itions (weather module) and river d isch arge valu es (hydrological module). In ad d ition, erosion rates, long-term su sp end ed load , and ch annel p attern are calcu lated for each ep och

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12 PaCMod outline

based on average environm ental cond itions (erosion module and channel pattern module).

Figure 2.1: Schem atic overview of PaCMod mod eling ap p roach. The three-d im ensional morp hology of a

real catchm ent is collap sed into fou r sp atial d omains w here d ifferent p roce sses occu r and sed im ent is rou ted and tem porary stored . The p rocesses occu rring in the catchm ent op erate sim u ltaneou sly bu t at d ifferent tim e scales (e.g., d ecennia to m illennia for hillslop e erosion and d ays for flu vial transport). Therefore the m od el stru ctu re is com p osed of three d ifferent rou tines w orking at d ifferent tim escales.

Finally, the yearly rou tine interp olates the d aily valu es obtained from the ep ochs rou tine over the w hole sim u lation tim esp an on a yearly scale. A long tim e series of flu vial w ater d ischarge is generated , and the bed load transp ort cap acity is calcu lated for each tim e step (discharge and transport capacity module). The sed im ent su p p ly from hillslop es, the su sp end ed sed im ent load , and the bed load transp ort cap acity are eventu ally balanced in a global sed im ent transp ort m od u le (sediment balance module).

2.2.1 Long-term routine

In the long-term rou tine, the clim atic bou nd ary cond itions (tem p eratu re and p recip itation), d erived from p alaeoclim ate p roxies, are related to three

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PaCMod 13

environm ental p aram eters: vegetation cover V eg, soil hold ing cap acity H_c, and ru noff/ infiltration coefficient R/I. We d efine V eg as the area of the catchm ent covered by arboreal sp ecies (0-1); H_c is d efined as the am ou nt of w ater that can be held by soils (m m ); and R/I is d efined as the ratio (0-1) betw een overland flow and w ater that infiltrates u nd er the su rface (Bogaart et al, 2003a). The relation betw een total annu al p recip itation Pa (m m / y) and V eg is m od eled as a logarithm ic fu nction,

w ith the constant of p rop ortion ality set by the coefficient v1. The relation betw een m ean annu al tem p eratu re T_a (°C) and V eg is treated as a Gau ssian fu nction (Eq. 2.1), sim ilar to Weltje et al. (1998), w ith a therm al op tim u m set by the coefficient v2 (Fig. 2.2A).

𝑉𝑒𝑔 = (− 1

𝑒(𝑣1∙𝑃𝑎)+ 1) ∙ (

𝑒−(𝑇𝑎−𝑣2)2

2 ∙ 𝑣32 ) (2.1)

Figure 2.2: (A) Vegetation cover as

a fu nction of tem p eratu re (°C) and annual p recip itation (m m / y); (B)

R/I coefficient as a fu nction of

tem p eratu re and vegetation cover (0-1). The valu es of the u ser-d efined coefficients are: v1 (0.001), v2 (20),

v3 (20), x1 (0.5), x2 (0.2), x3 (0.01),

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14 PaCMod outline

H_c is assu m ed to be d irectly related to vegetation cover (Weltje et al., 1998) w ith a range of 0-100 m m (Bogaart et al., 2003a). The R/I is m od eled as inversely p rop ortional to vegetation cover (Eq. 2.2) and d irectly p rop ortional to tem p eratu re, w hen T_a > 0°C. For T_a < 0°C w e assu m ed a valu e of 0.9 for R/I based on Bogaart (2003a). In this w ay w e sim u late the effect of p erm afrost (or soil frost), w hich inhibits the infiltration cap acity (Fig. 2.2B) (Cou tu re and Pollard , 2007).

𝑅/𝐼 = 𝑥1 − 𝑉𝑒𝑔𝑥2_{+ 𝑥3}𝑥4∙𝑇_𝑎

for Ta > 0°C

(2.2)

w here v3, x1, x2, x3, and x4 are u ser-d efined coefficients. 2.2.2. Epochs routine

Weather module and hydrological module

Valu es of d aily tem p eratu re, p recip itation, vegetation cover, soil storage cap acity, and R/I ratio cond itions are created by a w eather m od u le that ad d s seasonal and synop tic variations to the average clim atic signal (Bogaart and van Balen, 2000; Bogaart et al, 2003a) (see ap p end ix A). Precip itation m ay be w ater or snow , d ep end ing on elevation and tem p eratu re. In the m od el, the p recip itation that infiltrates u nd er the su rface can contribu te to the soil w ater reservoir. The soil w ater reservoir can lose w ater by evap otransp iration and by infiltration to a d eep grou nd w ater reservoir. The actu al evap otransp iration is a fu nction of the availability of w ater in the soil w ater reservoir and of the p otential evap oration. The flu vial w ater d ischarge at the ou tlet of the river catchm ent is calcu lated as the d aily su m of su p erficial ru noff, snow m elt and base flow from the grou nd w ater. A flow d iagram of the hyd rological m od u le is show n in Fig. 2.3.

The algorithm s u sed in the w eath er and hyd rological m od u le are based on Bogaart and van Balen (2000). Yet, w e m od ified them in ord er to consid er hyp som etry and for nonu niform d istribu tion of p recip itation, w hich are m ajor controls on volu m es and tim ing of w ater d ischarge p u lses, p articu larly for high relief catchm ents. Becau se p alaeotem p eratu re reconstru ctions u su ally refer to sea level, w e need to accou nt for elevation to obtain rep resentative tem p eratu re valu es for the w hole catch m ent. PaCMod calcu lates d aily tem p eratu re, p recip itation , and ratio betw een snow and rain for 10 hyp som etric classes (see Ap p end ix B).

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PaCMod 15

Precip itation d ata is based on p resent -d ay observations from w eather stations, w hich are generally located at low altitu d es. H ow ever, m ost of the p recip itation occu rs at higher altitu d es. To correct for this, w e calcu late an extra am ou nt of p recip itation (EP) for every hyp som etric class as a fu nction of p recip itation grad ient Pg (m m d

-1

m-1), i.e. the increase of p recip itation w ith altitu d e H (m ) (Eq. 2.3):

𝐸𝑃 = 𝑃𝑔∙ 𝐻 (2.3)

The P_g can be calibrated on p resent-d ay p recip itation d ata. Daily p otential evap oration PET (m m d-1

) is calcu lated follow ing the Linacre m ethod (Eq. 8 in Linacre, 1977). The d elay of the p eak d ischarge w ith resp ect to a p recip itatio n event is calcu lated u sing the u ser -d efined d irect flow bu ffer p aram eter, w hich can be calibrated u sing real-w orld p recip itation and d isch arge d ata. Finally, PaCMod calcu lates the river bankfu ll d ischarge (m3

s-1

) Q_pas the average p eak d ischarge for each ep och.

Erosion module

Erosion in a catch m ent occu rs throu gh d ifferent p rocesses (e.g. rill and gu lly erosion, soil creep , m ass w asting) in d ifferent p arts of the catchm ent and w ith sp ecific rates (Tu cker and Slingerland , 1997). The sp atial d istribu tion a nd intensity

Figure 2.3: Flow d iagram of

the hyd rological m od u le

(w ithin the Ep ochs rou tine). Arrow s ind icate inp u t/ ou tp u t

relation betw een m od el

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16 PaCMod outline

of these p rocesses is p red om inantly controlled by local hillslop e angle and vegetation cover (Bogaart et al., 2003b). We ap p ly the m ethod p rop osed by Zhang (2002) to calcu late the long-term average soil erosion rate (m m y-1

) (Eq. 2.4),

𝐸 = 𝐾𝑠𝑜𝑖𝑙∙ 𝑟𝑢𝑛𝑜𝑓𝑓2_{∙ 𝑆ℎ}1.67_{+ 𝑒}7∙𝑉𝑒𝑔 _(2.4)

w here K_soilis a coefficient for soil erod ibility, runoff is the m ean long-term p red icted ru noff (m m d-1), Sh is the average hillslop e angle, and V eg is the m ean vegetation

cover. The K_soilcan be calcu lated based on soil p rop erties (USDA) or calibrated w hen all other variables in Eq. (2.4) are know n. Regolith erod ed from hillslop es is transp orted by the river d ischarge as bed load or su sp end ed load . Su sp end ed load is cou p led to flu vial d isch arge, w hile bed load is d elayed in the flu vial channel, d ep end ing on the d rainage system m orp hology and on the grain size. In PaCMod , bed load is m od eled as the balance betw een sed im ent su p p ly from hillslop es and bed load transp ort cap acity (section 2.3.2). The long-term p otential su sp end ed load is calcu lated w ith the BQART equ ation (based on Eq. 7 in Syvitski and Millim an, 2007; Kettner and Syvitski, 2008):

𝑄𝑠= 𝐵𝑄′𝐴𝑅𝑇 (2.5)

H ere, Q_s (kg s-1

) is the long-term p otential su sp end ed load , R is m axim u m relief (km ), T is the average tem p eratu re (°C), A is the catchm ent area (km2

), Q’ is the long term -average flu vial d isch arge (m3 s-1), and B is a coefficient that incorp orates the effect of glacial erosion and ou tcrop p ing lithology. Equ ation (2.4) and (2.5) assu m e u nlim ited availability of regolith on hillslop es. To accou nt for regolith availability, w e ap p ly the BQART equ ation as a p otential su sp end ed load transp ort cap acity; the long-term p otential su sp end ed load Q_s and E can be com p ared by introd u cing a term E’ (kg s-1):

𝐸′_{= 𝐸/𝑁 ∙ 𝐴 ∙ 𝜌𝑠} _(2.6)

w here N is the nu m ber of second s in one year, A is the catch m ent area, and ρ_sisthe average sed im ent d ensity that w e assu m e to be 2700 kg m-3

. The calcu lated p otential su sp end ed load Q_s can exceed E’. In su ch case, w e assu m e that Eq. (2.5) is overp red icting the su sp end ed load . The actu al long -term su sp end ed load Qfines’ is a

fraction (0.9) of E’, becau se su sp end ed load generally accou nts for m ost of of the total sed im ent load (Su m m erfield and H u lton, 1994; Bu rbank and And erson, 2008; Kettner and Syvitski, 2008). When Q_s< E’ then Qfines’ = Qs. The fraction of coarse

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PaCMod 17

sed im ent d erived from hillslop e erosion E available for bed load transp ort, Qcoarse’, is

calcu lated as the d ifference betw een total erosion from hillslop es and actu al long -term su sp end ed load (Eq. 2.7):

𝑄𝑐𝑜𝑎𝑟𝑠𝑒′ = 𝐸′− 𝑄𝑓𝑖𝑛𝑒𝑠′ (2.7)

2.2.3. Channel pattern module

For each ep och, PaCMod p red icts the river ch annel p attern in the low er reaches of the catchment u sing Millar’s (2000) approach. A braid ed channel p attern is assum ed to d evelop w hen the river grad ient exceed s a critical grad ient S_c(Eq. 2.8), and vice versa for a m eand ering p attern:

𝑆𝑐= 0.0002 ∙ 𝐵𝑆1.75_{∙ 𝐷}

500.61∙ 𝑄𝑝−0.25 (2.8)

w here Q_p is bankfu ll d ischarge (m3 s-1), D₅₀ is the average grain size (m m ), and BS is the river bank friction angle (°) that is d efined as

𝐵𝑆 = 20 + 0.5 ∙ 𝑉𝑒𝑔 ∙ 100 (2.9)

Vegetation has a stabilizing effect on river banks. The coefficients linking BS to average vegetation cover V eg w ere calibrated based on Millar (2000). We have ap p lied the low erm ost (20.1°) and the m axim u m valu e (79.1°) of bank friction angle in Millar (2000) to rep resent resp ectively 0% and 100% vegetation cover. With this ap p roach w e d id not consid er the im p act of lithology on bank friction angle.

2.2.3. Yearly routine

D ischarge and transport capacity module

In the d ischarge and transp ort cap acity m od u le, w e ap p ly an u p scaling m ethod that cap tu res long-term signal and extrem e events. For each ep och, the m ain statistics are extracted (w ater d ischarge, su sp end ed load , erosion rate, and flu vial channel p attern), and then interp olated over the w hole sim u lation p eriod . We ch ose fou r valu es to rep resent the statistical d istribu tion of w ater d isch arge: p eak d ischarge, average-low d isch arge, and their associated stand ard d eviations. We refer to p eak d isch arge as the average (ov er the ep och d u ration) yearly m axim u m d ischarge and to average-low d isch arge as the average d ischarge below the long term average (Fig. 2.4).

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18 PaCMod outline

Figure 2.4. (Left) Meu se River w ater d ischarge above (red ) and below (green) the long -term average (240

m3

/ s) for fou r years (1980-1983). Based on this d ata, the average p eak d ischarge, the average -low d ischarge, and the nu m ber of d ays w ith p eak or average-low d ischarge are calcu lated . (Right) Tw o yearly tim e step s: average-low d ischarge and p eak d ischarge tim e step . The nu m ber of d ays w ith p eak or average-low d ischarge (Fig. 2. 5A) d eterm ines the length of the tw o tim e step s.

In this w ay tw o tim e step s p er year are m od eled : the p eak and the average -low d isch arge. The average length of the tw o tim e step s is d eterm ined based on p resent-d ay m easu rem ents (Fig. 2.4A) or on the reconstru cteresent-d resent-d aily tim e series. A tim e series of yearly average, low -average, and p eak d isch arge is generated stochastically from the statistical d istribu tion of w ater d ischarge. The kind of d ist ribu tion (exp onential, norm al, logarithm ic) is u ser -d efined and can be constrained by m easu rem ent d ata. The bed load transp ort cap acity of the river TC is based on the bed shear stress (Tu cker and Slingerland , 1997) and p article critical shear stress (USACE, 2007) ap p roach (see Ap p end ix C).

Sediment balance module

We interp olate the long-term actu al su sp end ed load Qfines’, to calcu late the actu al

su sp end ed load for each tim e step Q_fines, ap p lying Morehead et al., (2003) form u la: 𝑄𝑓𝑖𝑛𝑒𝑠 𝑄𝑓𝑖𝑛𝑒𝑠′= 𝜓 ∙ ( 𝑄 𝑄′) 𝐶 (2.10)

w here Q is the w ater d ischarge p er tim e step . All u nits are in m3 s-1; Ψ and C are coefficients based on catchm ent tem p eratu re, relief, and average d ischarge (Morehead et al., 2003).

The long-term coarse fraction of the m aterial erod ed from hillslop es, Q_coarse’, is not d irectly available for transp ort in the catchm ent low er reaches, becau se it takes tim e

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PaCMod 19

(102-104 years) for coarse sed im ent to be d elivered from the hillslop es to the flu vial channel and then to the low er reaches (Tebbens and Veld kam p , 2000; Veld kam p and Tebbens, 2001; Cou lthard et al., 2002; van Balen et al., 2010). The transp ort of coarse sed im ent is a d iffu sive p rocess that bu ffers the d ow nstream p rop agation of the hillslop e erosion signal (Trim ble, 1977; Walling, 1983; Mead e, 1982; Chu rch and Slaym aker, 1989; Frostick and Jones, 2002; Cou lthard et al., 2005). The bu ffering effect is also enhanced by the m ixing of d ifferent sed im ent sou rces w ithin the catch m ent and by the slow m ovem ent of coarse sed im ents w ithin the channel itself w here transp ort is p red om inantly occu rring d u ring p eak d ischarge p eriod s.

We assu m e that hillslop e erosion occu rs only in the u p p er reaches of the catch m ent, and w e d efine the low er reaches as the m ost d ow nstream p ortion of the catch m ent, near the ou tlet, w here sed im ent can be stored in confined flood p lains, valley fill, and allu vial fans. In PaCMod w e u se a scaling p aram eter K_dto sim u late bed load rou ting and hence d elay in sed im ent transp ort d ow nstream (Eq. 2.11):

𝑄𝑏= 𝐾𝑑∙ 𝑄𝑐𝑜𝑎𝑟𝑠𝑒′ (2.11)

w here Q_b is the sed im ent available for bed load transp ort in the low er reaches of the catch m ent. The low er reaches of catchm ents p rovid e accom m od ation sp ace for sed im ent accu m u lation on confined flood p lains, in case sed im ent availability p revails over flu vial transp ort cap acity TC. Su ch confined flood p lains m ay becom e incised w hen erosion cap acity increases, and p reviou sly d ep osited sed im ents m ay be rew orked . In ad d ition, p atches of su ch flood p lain d ep osits m ay becom e p reserved as flu vial terraces (Merrits et al., 1994; Blu m and Törnqvist, 2000, Leigh et al., 2004; Blu m and Aslan, 2006; Leigh, 2008). In PaCMod the actu al availability of coarse-grained sed im ents for transp ort, Q_bactual, is the su m of the d elayed bed load su p p ly from hillslop es Qb, ad d ed to a p ortion of the sed im ent n1 p reviou sly stored in

a confined flood p lain reservoir R_v , in case flood p lain d ep osition has occu rred (Eq. 2.12).

𝑄𝑏𝑎𝑐𝑡𝑢𝑎𝑙= 𝑄𝑏+ 𝑛1∙ 𝑅𝑣 (2.12)

The bed load leaving the catchm ent Qbedload equ als Qbactual w hen Qbactual is exceed ed by TC.

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20 Tests

𝑤ℎ𝑒𝑛 𝑇𝐶 > 𝑄𝑏𝑎𝑐𝑡𝑢𝑎𝑙 𝑄𝑏𝑒𝑑𝑙𝑜𝑎𝑑= 𝑄𝑏𝑎𝑐𝑡𝑢𝑎𝑙 𝑅𝑣= 0 (2.13)

𝑤ℎ𝑒𝑛 𝑇𝐶 < 𝑄𝑏𝑎𝑐𝑡𝑢𝑎𝑙 𝑄𝑏𝑒𝑑𝑙𝑜𝑎𝑑= 𝑇𝐶 𝑅𝑣= 𝑄𝑏𝑎𝑐𝑡𝑢𝑎𝑙− 𝑇𝐶

In ad d ition, PaCMod accou nts for a constant fraction n₂ of the sed im ents stored in R_v that are never rew orked and becom e p art of a terrace reservoir R_t (Eq. 2.14):

𝑅𝑡= 𝑛2∙ 𝑅𝑣 (2.14)

Ou r p aram eterized ap p roach relies on som e im p ortant assu m p tion: (i) the coefficient n₁ and n₂ rem ain constant in tim e, (ii) bed load is rep resented only by D₅₀, and (iii) the flu vial ch annel grad ient, like the hillslop e angle, rem ains constant in tim e. The m od el resu lts are sensitive to these assu m p tions. Using coefficient n₁ and n2 constant in tim e im p lies that the geom etry and the d im ension of flood p lains

rem ains constant in tim e. This m ay resu lt in an overestim ation of sed im ent storage d u ring p eriod s of flu vial incision and consequ ent flood p lain narrow ing. The op p osite m ay occu r in the case of increase in accom m od ation lead ing to flood p lain w id ening and enhaced sed im ent storage. Using assu m p tion (ii) w e d id not consid er tem p oral ch anges in bed load grain size and p ossible m u ltim od al grain size d istribu tions. Finally, assu m p tion (iii) is valid in the case of catch m ent m orp hology in equ ilibriu m w ith the tectonic regim e. In ad d ition, this ap p roach neglects the changes in flu vial channel grad ient and hillslop e angle ind u ced by clim atic, tectonic, and eu static changes. The im p act of clim atic and tectonic ch anges on catch m ent m orp hology is d ealt w ith in ch ap ter 3.

2.3. Tests

2.3.1. Hydrograph

PaCMod hyd rological rou tines w ere tested on three p resent -d ay flu vial system s: the Meu se River in the N etherland s, the Po River in Italy, and the Waip aoa River in N ew Zealand . Meteorological d ata (Table 2.1) and catch m ent p hysiograp hic p rop erties (H yd ro1K d igital elevation m od el) w ere u sed as inp u t. We averaged p recip itation and tem p eratu re from tw o w eather stations in each catchm ent and corrected for altitu d e. The m od eled hyd rograp h w as com p ared to m easu red w ater d isch arge, and it w as op tim ized by tu ning the u ser -d efined p aram eters: grou nd w ater resid ence tim e, p recip itation gr ad ient, snow m elt coefficient, and d irect flow bu ffer p aram eter (Table 2.2).

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PaCMod 21

Table 2.1: inp u t d ata and sou rces of inform ation for the hyd rograp h calibration River Weather stations Gauging station Period D ata source

Meu se Maastricht (N L) Lu xem bu rg (L) Borgharen 1980-2009 KN MI Rijsw aterstaat Waip aoa Gisborne Waitangiru a Kanakanaia 1986-1991 N IWA TUTIEMPO.net Po Bologna (IT) Lu gano (CH ) Pontelagoscu ro 1950-1979 KN MI Rijsw aterstaat

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22 Tests

Figure 2.6: Monthly w ater d ischarge of the Po River d u ring 30 years (1950-1979).

Table 2.2: Calibrated p aram eters for the three analyzed catchments

Parameter Meuse Waipaoa Po Unit

Precip itation grad ient 10-4

10-7

10-4

m m d-1

m-1

Snow m elt coefficient 0,08 0,1 0,1 m m d-1

°C-1

Grou nd w ater resid ence tim e 400 90,0 1000,0 d

Direct flow bu ffer 8 2,0 15,0 d

PaCMod can be calibrated in su ch a w ay that it is able to sim u late a realistic hyd rograp h for all the analyzed rivers based on only tw o w eather stations (Figs. 2.5-2.7). The p eaks in w ater d isch arge, w hich are influ enced by su p erficial ru noff, and the general d ecreasing trend after su ch p eaks, w hich is influ enced by base flow , are w ell rep resented . The m ain d iscrep ancies betw een m od eled and m easu red d isch arge, occu rring d u ring p eriod s of very high and very low d isch arge, can be exp lained by the lack of sp atial inform ation for local storm s. The p robability and the m agnitu d e of p recip itation events can be very d ifferent from p lace to p lace across the catch m ent, and su ch heterogeneity cannot be cap tu red by a sp atially lu m p ed m od el. In ad d ition, the p resence of d am s affects the hyd rograp h by tem p oral storage and release of w ater in artificial reservoirs, w hich is not inclu d ed in the m od el.

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PaCMod 23

Figure 2.7: Average d aily w ater d ischarge above a w ater d ischarge threshold . We calcu lated the average

w ater d ischarge (vertical axis) of the d ays, w hen w ater d ischarge w as above a d efined threshold (horizontal axis), and the stand ard d eviation on the average. We u sed these statistics to comp are m easu red and mod eled w ater d ischarge for the Meu se River and for the Waip aoa River.

2.3.2. Sediment flux

We tested PaCMod p erform ance ap p lying it to the late Qu aternary flu vial d evelop m ent of tw o river system s, the Meu se River and the Waip aoa River, both w ell d ocu m ented in term s of geom orp hological evolu tion, sed im ent flu x, and p alaeoclim atic cond itions.

Meuse River

We ran a 20-ky sim u lation from the late Pleniglacial to the p rese nt, based on p alaeoclim atic p roxies (Table 2.3; Fig. 2.8) and catch m ent m orp hology (Fig. 2.9). We ap p lied a bed load travel tim e K_d of 1 ky, based on Veld kam p and Tebbens (2001) and van Balen et al. (2010). PaCMod sim u lated high d elayed bed load su p p ly ( Q_coarse’) and hillslop es erosion rate d u ring cold p hases (Fig. 2.11A), becau se of low vegetation cover and high ru noff/ infiltration ratio. Sim u lated erosion rates varied betw een 0.005 to 0.05 m m y-1

, w hich is in the sam e range as the long -term erosion rates calcu lated w ith cosm ogenic nu clid es for the last 20 ky (van Balen et al., 2010) (0.014-0.08 m m / y). The sim u lated bed load and su sp end ed load su p p ly w ere ou t of p hase betw een 14 and 8 ky BP. Du ring the late Pleniglacial and the You nger Dryas, bed load su p p ly exceed ed su sp end ed load su p p ly, w hile the op p osite occu rred d u ring early Bølling-Allerød and H olocene.

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24 Tests

Figure 2.8: Su m mary of reconstructed late Qu aternary tem p eratu re (H u isink, 1999; Bogaart et al., 2003b),

vegetation cover (H oek, 1997; Bu sschers et al., 2007), terraces grain size trend (H u isink, 1999; Bu sschers et al., 2007), and channel p attern (H uisink, 1999; Vand enberghe et al., 1994) for the Meu se River.

Becau se fine sed im ents are generally transp orted as su sp end ed load w hile coarse sed im ent as bed load , w e consid ered the ratio bed load / su sp end ed load a p roxy for average grain size. The m od el sim u lation ind icates p red om inantly coarser m aterial being su p p lied d u ring cold –d ry p hases and finer m aterial d u ring w arm –w et p hases, w hich is in general agreem ent w ith the observations from Meu se River flu vial terraces (H u isink, 1999). Du ring p hases of high bed load su p p ly and low transp ort cap acity (Fig. 2.11B), m ost of the sed im ent w as stored in the confined flood p lain reservoir Rv (Fig. 2.12C). For this sim u lation, w e assu m ed that 90% of the sed im ents

in R_vcan be rew orked at a later stage (n₁= 0.9), and that 10 % of R_v(n₂= 0.9) is p reserved as a flu vial terrace reservoir R_t(Fig. 2.11C).

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PaCMod 25

Table 2.3: Inp u t p aram eters for the Meu se River and Waip aoa River sim u lations Parameter Meuse Waipaoa

Sh 5,0 17,0 A 31000,0 2050,0 R 710,0 1710,0 D50 3,0 3,0 Sf 0,3 12,.0 Ksoil 0,03 0,04 Kb 1000,0 100,0 n1 0,5 0,9 n2 0,9 0,9

Table 2.4: Com p arison betw een PaCMod sed im ent flu x and erosion rate p red ictions and valu es from

literatu re for the last 20 ky

PaCMod Test Unit Source

Su sp end ed load 0,3433 0,7354 km3 ky-1 Ward (2008) Bed load 0,0218 0,0500 km3 ky-1 Doom en (2008)

Total sed im ent load 0,3651 0,19-0,70 km3

ky-1

Mu rillo-N u ñoz et al., (2006) Long term erosion rate 0,005-0,05 0,014-0,08 mky-1

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26 Tests

Figure 2.9: DEM of the Meu se River catchm ent (sou rce: ASTER G-DEM), schematic map of the region

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PaCMod 27

Figure 2.10: Clim atic inp u t for PaCMod for the past 20 ky of the Meu se catchm ent. The ice core d eltaO18

signal (N GRIP, 2004) w as u sed as inp u t for all clim atic bou nd ary cond itions. Su ch signal w as calibrated based on p erm afrost stru ctu res (H u isink, 1999) and palaeoclim atic m od els (Bogaart et al., 2003b) in ord er to obtain tem p eratu re, p recip itation, and storm iness cu rves for the area of the Meu se catchm ent. Bo -Al = Bølling–Allerød ; YD=You nger Dryas.

The m od el p red icted accu m u lation of sed im ents in R_vd u ring the late Pleniglacial and from the late Bølling -Allerød to the beginning of the H olocene. Byp ass or incision occu r from the late Pleniglacial to the early Bølling -Allerød and in the H olocene. These m od el resu lts are in line w ith the observations by Vand enberghe et al. (1994) and H u isink (1999) and w ith m od el reconstru ctions by Bogaart et al. (2003b) and van Balen et al. (2010). The m od eled cu m u lative volu m e of R_tis in the ord er of 108 m3, w hich is in the sam e ord er of m agnitu d e as the sed im ent volu m es calcu lated by H u isink (1999) in the Meu se River terraces in sou thern N etherland s. Ap p lying a constant flu vial ch annel grad ient (0.2 m km-1

) and a constant average grain size (3 m m ) (Tebbens and Veld kam p , 2000; Mu rillo-N u ñoz et al., 2006), PaCMod p red icted a braid ed channel p attern d u ring cold p hases and a m eand ering channel p attern d u ring w arm p hases, sim ilarly to find ings by Vand enberghe (1994) and H u isink (1999) (Fig. 2.12A). The calcu lated vegetation cover (Fig. 2.12B) follow ed a sim ilar trend as the arboreal/ nonarboreal cu rve in the sou thern N etherland s p ollen record (H oek, 1997; Bu sschers et al. 2007).

The m od eled sed im ent flu x signal (Fig. 2.13) w as ch aracterized by high d isch arge and su sp end ed load d u ring w arm intervals and high bed load flu x d u ring stad ials. Overall, su sp end ed load and bed load sim u lated by PaCMod betw een 20 ky BP to p resent are com p arable to those calcu lated in the literatu re (Table 2.4).

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28 Tests

Figure 2.11: (A) Sim u lated d elayed bed load su p p ly Qb and su sp end ed load su p p ly Qfines’; (B) relation betw een Qb and flu vial transp ort capacity TC; (C) am ou nt of bed load m aterial stored in the confined flood p lain reservoir Rv and cu m u lative am ou nt of bed load material stored in t he flu vial terrace reservoir

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PaCMod 29

Waipaoa River

We ap p lied PaCMod to reconstru ct the sed im ent flu x history of the Waip aoa River catch m ent, N ew Zealand , from 22.5 ky BP to Present, based on catchm ent m orp hology (Fig. 2.14 and Table 2.3) and on the hyd rograp h calibration (section 3.1). We u sed the sam e p alaeoclim atic p roxies ap p lied by Up ton et al. (2012) (Fig. 2.15) and w e sim u lated the w id esp read , hu m an -ind u ced d eforestation d u ring the last 200 years (Mard en et al., 2008), w ith a 50% d ecrease of vegetation cover V eg. From 22.5 to 15 ka, the low vegetation cover and high R/I ratio (Fig. 2.16A), ind u ced high bed load su p p ly Q_b (Fig. 2.16B), high bed load Q_bactual, and su sp end ed load Q_fines (Fig. 2.17) (scenario W1). Becau se flu vial transp ort cap acity TC w as relatively low , com p ared to Q_b, a large am ou nt of coarse m aterial w as stored in R_v and R_t(Fig. 2.16C). The Qb d ecreased step w ise u ntil 14 ka, w ith the m ajor step at ca. 15 ka, w hile

TC rem ained relatively con stant throu ghou t the w hole sim u lation. As a resu lt, the volu m e of sed im ents stored in R_v and in R_td rastically d ecreased at 15 ka and rem ained at low valu es u ntil 200 BP.

Figure 2.12: (A) Relation

betw een flu vial channel

grad ient (0.2 m / km ) and critical grad ient Sc. The flu vial channel p attern is braid ed w hen the

flu vial channel grad ient is

above the critical grad ient, w hile m eand ering if below . (B) Sim u lated vegetation cover V eg.

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30 Tests

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PaCMod 31

Figure 2.14: Location m ap (A and B, from Up ton et al., 2012) and d igital elevation m od el of the Waip aoa

catchm ent (C) w ith the position of the gau ging station of Kanakataia and the w eather stations of Waintangiru a and Gisborne. PBF=Poverty Bay Flats; WSS=Waip aoa sed im entary system . The core MD97-2122 w as u sed by Phillip s and Gom ez (2007) to calcu late the rate of terrigenou s mass accu m u lation in the m id d le shelf. For the hyd rograp h test, w e consid ered the Waip aoa catchm en ts as the portion of the catchm ent u p stream of Kanakataia (C), w hile for the sed im ent flu x test w e also consid ered all the Poverty Bay Flats and all its tribu taries.

Sim ilarly, Q_bactual d ecreased step w ise u ntil 15 ka and then stabilized . The Q_fines d im inished grad u ally from 15 to 10 ka, and excep t for a m inor increase betw een 5 and 3 ka, it rem ained at low valu es u ntil 200 BP. From 200 BP, becau se of d eforestation, R_v, Q_bactual, and Q_fines sharp ly increased . The ages of 15 ky BP and ca. 200 BP w ere critical not only in the m od el sim u lation bu t also accord ing to geom orp hological evid ence. The transition from flood p lain aggrad ation to incision

Figure 2.15: Inp u t tem p eratu re Ta (A) and p recip itation Pa (B) in the Waip aoa catchm ent from 22.5 ky to Present

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32 Tests

and consequ ent form ation of the Waip aoa1 terrace, u p stream of Kanakataia (Brow n, 1995; Berrym an et al., 2000) is m arked at 15 ky BP. The Waip aoa River started aggrad ing again, after ca. 200 BP, w hen Eu rop eans colonized N ew Zealand (Phillip s and Gom ez, 2007; Mard en et al., 2008). The p hases of high R_v are thu s correlated w ith p hases of flood p lain aggrad ation, w h ile low R_vw ith incision.

Philip s et al. (2007) calcu lated that, in the case of sed im ent su p p ly exceed ing transp ort cap acity (H olocene), 30-40% of allu vial d ep osits w as rem obilized in the Waip aoa flood p lain. Su ch p ercentage w as likely higher in p eriod s d o m inated by flu vial incision. We cond u cted another test (scenario W2) to evalu ate the im p act of sed im ent rou ting and sed im ent storage/ rem obilization on sed im ent flu x, setting a high Kb valu e (2000 years) and n1 = 0.3. The resu lts w ere sim ilar to scenario W 1 (Fig.

2.18). N evertheless, the higher K_b, and thu s longer sed im ent travel tim es, p rod u ced a sm oother Q_b and Q_bactual signal, characterized by a grad u al d ecrease from 15 to 5 ka. Becau se of the sm aller n₁ valu e, and thu s less sed im ent rem obilization, R_v and R_t w ere alm ost one ord er of m agnitu d e higher than in scenario W1.

Finally, w e com p ared ou r m od eled erosion rates to the sed im ent flu x reconstru ction by Kettner et al. (2009) and Up ton et al. (2012) (Fig. 2.19). We calcu lated tw o end -m e-m bers erosion rates, in ord er to accou nt for u ncertainty in average hillslop e angle S_h and soil erod ibility coefficient K_soil: a m axim u m erosion case, m axim u m E (K_soil = 0.05; Sh = 20°), and a m inim u m erosion case, m inim u m E (Ksoil = 0.03; Sh = 15°). The

long-term su sp end ed load , calcu lated w ith the BQART equ ation Q_s, increased throu ghou t the w hole sim u lation. Differently, m od eled erosion rates E d rastically d ecreased from 5-15 Mton/ y at 22.5 ky BP to 1-3 Mton/ y at 10 ky BP, and rem ained stable u ntil 200 BP, w hen they rose to 6-18 Mton/ y. This trend is com p arable to the Qs(Eh) calcu lated by Up ton et al. (2012), althou gh PaCMod p red icted higher E than Qs(Eh) u ntil 12 ky BP, w hereas the op p osite occu rred afterw ard . Du ring the last 3 ky, m od eled erosion rates w ere com p arable to the rate of terrigenou s m ass accu m u lation on the m id d le shelf at core site MD97-2122 (Phillip s and Gom ez, 2007).

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PaCMod 33

Figure 2.16: Waip aoa catchm ent geom orp hic resp onse to clim atic changes for scenario W1, w ith Kb = 100 years, and n1 = 0.9: (A) vegetation cover V eg and ru noff/ infiltration ratio R/I; (B) relation betw een d elayed bed load su p p ly Qb and flu vial transp ort capacity TCpeaks and TCaverage, and (C) amou nt of bed load m aterial stored in the confined flood p lain reservoir Rv and cu m u lative am ou nt of bed load m aterial stored in the flu vial terrace reservoir Rt.

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34 Tests

Figure 2.17: (A) Bed load p eaks Qbactualpeaks, (B) su sp end ed load p eaks Qfinespeaks, and (C) w ater d ischarge p eaks Qpeaks from the Waip aoa catchm ent. Only p eaks are show n, becau se w ater d ischar ge and sed im ent flu x d u ring average cond itions w ere too little for d isp lay.

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PaCMod 35

Figure 2.18: Waip aoa catchm ent geom orp hic resp onse to clim atic changes for scenario W2. Relation

betw een d elayed bed load su p p ly Qb and flu vial transp ort capacity TC (A); bed load material stored in Rv and cu m u lative amou nt of bed load m aterial stored in Rt (B), and bed load p eaks Qbactualpeaks (C).

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36 Sensitivity analysis

Figure 2.19: Com parison betw een PaCMod ou tp u t, H yd rotrend outp u t (Up ton et al., 2012), and rate of

terrigenou s m ass accu m u lation on the m id d le shelf at core site MD97-2122 (Phillip s and Gom ez, 2007). PaCMod ou tp u t consists of m axim u m (Maxim u m E) and m inim u m (m inim u m E) erosion rates (Zhang, 2002 ap p roach). H yd rotrend ou tpu t consists of long -term su sp end ed load Qs (BQART ap p roach, id entical in PaCMod ), and long-term su sp end ed load calcu lated accou nting for vegetation cover change and hu m an im pact Qs(Eh).

The m od eled total volu m e of sed im ents transp orted ou t of the catchm ent from 18 ky BP to Present is in the range 10-30 km3, assigning a d ry bu lk d ensity of 1400 kg m-3 (Mard en et al., 2008). In the sam e p eriod , 20 km3 of m u d accu m u lated on the continental shelf (Foster and Carter, 1997) and 6.6 km3 of gravel, sand , and m u d accu m u lated in the Poverty Bay Flats (Mard en et al., 2008). The p resent d ay m easu red m ass of su sp end ed load ou t of the catch m ent is 15 Mton y-1

(Mard en et al.. 2008). Thu s, the m od eled volu m e of sed im ent erod ed u p stream , or at least the high end of the range, is com p arable to the volu m e of m aterial accu m u lated d ow n stream and p resent d ay m easu rem ents.

2.4. Sensitivity analysis

A sensitivity analysis w as cond u cted to evalu ate the relative im p ortance of the m od el p aram eters (Table 2.5) on PaCMod ou tp u t. For each inp u t p aram eter a realistic range w as ch osen and d iscretized into a m inim u m , m ean, and m axim u m valu e, d esignated by -1, 0, and 1, resp ectively. This gave a ch oice of three inp u t valu es for each of the 28 p aram eters. We ran PaCMod 10 tim es for all p aram eter com binations in ord er to accou nt for the rand om com p onents in the m od el. For each ru n, the average su sp end ed and bed load flu x volu m es w ere calcu lated as w ell as (i) the su sp end ed load and bed load cu m u lative volu m e, (ii) the RMSE (root m ean