Alluvial storage and the long-term stability of sediment yields

Alluvial storage and the long-termstability ofsediment yieldsJonathan Phillips

TobaccoRoadResearchTeam, Department of Geography, University of Kentucky, Lexington, Kentucky, USA

ABSTRACT

Several recent studies have shown general consistency of £uvial denudation rates over long timeperiods, or historical and contemporary sediment yields of the same general magnitude as sedimentyields or accumulation rates over geologic time.This consistency of £uvial sediment export fromsome drainage basins, despite substantial climate, hydrological, ecological, base level, and otherenvironmental changes, suggests that long-term sediment yields may be controlled by factors that areindependent of and overwhelm environmental changes (e.g. tectonics), or that the £uvial sedimentsystem is at some level dynamically stable.The latter is explored via a model based on the notion thatall debris produced by weathering within a drainage basin over any time period is either retained aspart of the regolith, transported out of the basin as solid or dissolved sediment yield, or stored asalluviumwithin the £uvial system.This system is dynamically stable if alluvium is always potentiallyavailable for transport; e.g. to be converted to yield, and if regolith development exerts a negativefeedback onweathering rates.This supports the argument that the long-term consistency of sedimentyields (where it exists)may be attributable to the storage and remobilization of alluvium,which bu¡ersthe system against environmental change. Environmental changes are manifested primarily inreorganizations within the £uvial sediment system, such as variations between net increases anddecreases in alluvial storage, and changes in the spatial locus of deposition.These ideas are illustratedand tested using data from the lowerTrinity River in southeast Texas.

INTRODUCTION

When contemporary river sediment loads are comparedwith much longer-term estimates based on sediment ac-cumulation or upland denudation rates, in some casesthere is a remarkable consistency. This phenomenonseems remarkable simply because climate, vegetation,base level, and other factors known to in£uence erosion,£ow regimes, and other aspects of the £uvial system haveundergone signi¢cant changes, and human agency hasdramatically in£uenced geomorphic processes in recentcenturies. It is widely believed,with considerable support-ing evidence, that Holocene £uxes are not the norm in ageological perspective, that climate and sea level changeshave substantially altered £uvial export, and that humanagency has greatly modi¢ed sediment £uxes in recent andhistoric times (see e.g. Jansson, 1988; Douglas, 1990; Hay,1994; Meybeck, 1994; Mulder & Syvitski, 1996; Leeder,1997; Overeem et al., 2001).Thus a few, isolated examplesof apparent consistency between contemporary and long-term sediment yields could be chalked up to coincidence,uncertainties inherent in measurement and estimationmethods, or particular situations where some overridingfactor such as rapid tectonic uplift overwhelms other en-

vironmental controls of sedimentyields.However, as moreand more evidence of long-term consistency of sedimentloads is produced, the possibility of a more generalexplanation is suggested. The purpose of this paper is toexplore the idea that the long-term consistency of sedi-ment yields observed in some locations is attributable tothe storage and remobilization of alluvium, which bu¡ersthe system against environmental change.

BACKGROUND

The focus of this paper, and this background section, isnot meant to suggest that long-term consistency in denu-dation rates is globally ubiquitous. However, there issu⁄cient evidence to suggest that such consistency is notan isolated phenomenon. This is not a general review ofdenudation rates; it is an e¡ort to show that evidencefor general long-term consistency of denudation orriver-borne export is available from several studies inseveral locations and settings. It should also be recognizedthat indicators of mass export from drainage basins varywithin and between the studies considered here, andinclude measurements or estimates of surface loweringand river incision, £uvial sediment yield, and accumula-tion in sediment sinks.

Erosion rates averaged over 10^40 kyr were estimatedfrom cosmogenic radionuclides by Schaller et al. (2001)

Correspondence: Jonathan Phillips, Tobacco Road ResearchTeam, Department of Geography, University of Kentucky, Lex-ington, Kentucky 40506, USA. E-mail: [email protected]

BasinResearch (2003) 15, 153–163

r 2003 Blackwell Publishing Ltd 153

for middle European rivers with drainage areas of 100^105 km2. These rates agree broadly with the rates of rockuplift, incision and exhumation for the same rivers, aswellas with the rates of historic soil erosion, and erosion ratescalculated from contemporary and historic sediment loadmeasurements. Schaller et al. (2002) obtained generally si-milar results for some, but not all, European drainage ba-sins where long-term erosion rates estimated fromcosmogenic nuclides were compared with modern ratesestimated from river loads. Lave¤ & Avouac (2001) esti-mated £uvial incision rates in the Himalayas from thestudy of strath terraces, extrapolating these results to theentire range and comparing results with sediment vo-lumes accumulated in the Ganga plain and Bengal fan.They found a good average correlation between short-termmean incision rates and long-term rates derived fromsedimentary volumes.

In theSantaMonica mountains,California, denudationrates based on river sediment yields averaged over 70 yearswere found to be similar to river incision rates over the last100 kyr by Meigs et al. (1999). Cosmogenic isotope datingof river sands was used by Granger et al. (1996) to deduceaverage denudation rates in two mountain basins in north-eastern California over periods on the order of 104 years,which corresponded closely to sediment accumulation insink areas. In the San Gabriel mountains, Burbank et al.(1998) also found agreement between denudation rates atdi¡erent time-scales.

Summer¢eld & Hulton (1994) compiled estimates ofmodern denudation for large (4105 km2) basins drainingto the oceans. Although direct comparisons could not bemade with geological estimates of denudation from ther-mochronologic techniques and sediment volumes, Sum-mer¢eld & Hulton (1994) did note general agreement.They concluded that denudation rates derived from pre-sent-day mass £uxes did not di¡er greatly from long-termrates. As variables related to basin relief accounted formost of the variation in denudation rates in the moderndata, the implication is that this control is also paramountat longer time-scales.

In the south Indian shield region,Gunnell (1998) foundthat denudation rates inferred from ¢ssion track data overB100Ma agreed well with contemporary denudationrates based on river loads. Both were within the range ofdenudation rates predicted by Ahnert’s (1970) model offunctional relationships between uplift, denudation, andrelief in mountain ranges. Gunnell (1998) suggested thatrelief and uplift provide critical ¢rst-order controls of me-chanical denudation, thus establishing a ‘metabolic’ rate oferosion. Upward deviations from this rate are likely to oc-cur only in relatively short bursts, so that the metabolicrate dominates over long periods.

Me¤ tivier &Gaudemar (1999) compared the present so-lid-phase sediment discharge of large rivers in Asia to theaverage discharge estimated from mass accumulated insedimentary basins during the Quaternary. They found astrong correlation, particularly for the largest rivers,suggesting constant average sediment discharges during

the Quaternary for at least the very large rivers (drainagearea on the order of 105^106 km2). They inferred thatstrong tectonic controls on erosion, in combination withthe bu¡ering capacity of alluvial £oodplains, accountfor the consistency. In particular, Me¤ tivier & Gaudemar(1999) suggest that the characteristic reaction time-scaleof the £oodplains is longer than the time-scales of Qua-ternary climate and sea level oscillations.

The results of several studies indicating similarity oroverlap in long-term and modern erosion, denudation, or£uvial sediment transport rates are summarized inTable1.

This is not to deny the often considerable temporalvariability in £uvial sediment transport and storage. Evenwhen average annual loads are considered, substantialyear-to-year variability is typically evident. Extremeevents such as £oods or landslides introduce much varia-bility in £uvial systems. The concern here is with thegeneral relationship between recent (Holocene to contem-porary) and long-term (Quaternary or longer) average se-diment output of river systems, recognizing thatsediment transport over any time-scale is likely to be vari-able and episodic. And again, of course, it is recognizedthat long-term consistency in denudation rates or massexport is clearly not the case everywhere.

ROLE OF SEDIMENT STORAGE

Within the time-scales considered in the studies above,the tectonic and relief settings are negligibly variable, inthe sense that the time spans do not encompass episodescharacterized by wholly di¡erent ¢rst-order landforms. Ina general study of the relative importance of various con-trols on geologically contemporary £uvial erosion rates,Phillips (1990) found relief (as a surrogate for slope) to bethe most important control at the regional to global scale.This basic ¢nding has been reported in other studies aswell (Milliman & Meade, 1983; Jansson, 1988; Ludwig &Probst, 1998; Milliman & Syvitski, 1992; Summer¢eld &Hulton, 1994). Over geological time-scales the role of tec-tonic uplift in driving erosion is also well established.Thissupports the argument that relief and tectonics may (atleast in some regions) exert overwhelming control in denu-dation; so as long as the fundamental tectonic/relief re-gime is in e¡ect, denudation rates may vary little.

The other general alternative explanation of consis-tency in denudation is alluvial sediment storage. If storageis large relative to £uvial sediment yield, then large in-creases or pulses in upland sediment production may bebu¡ered at the river mouth. Further, the availability of astore of transportable debris in stream valleys allowsstreams to maintain sediment loads when sediment deliv-ery from uplands is reduced.

The purpose of this study is not to evaluate the relativemerits of these alternatives as competing explanations.Rather, the aim is to determine whether alluvial sedimentstorage is a feasible and plausible general explanation,alone or in concert with other factors, capable of explain-

r 2003 Blackwell Publishing Ltd,Basin Research, 15, 153^163154

J. Phillips

Tab

le1.Examples

ofstud

iesshowingagreem

entorsub

stantialoverlapbetweenshorter-andlonger-termratesoferosion,denu

dation

,or£u

vialsedimentyield.N

otethattheexam

ples

areselected

toillustratetheidea

thatlonger-andshorter-term

ratesaresometim

essimilar,andthus

exclud

eexam

pleswheretheresultsw

ereotherw

ise.

Location,ph

enom

enon

Long-term

rate,tim

efram

eLon

g-term

metho

dsSh

ort-term

rate,tim

efram

eSh

ort-term

metho

dsSou

rce

Him

alaya,centralN

epal,river

incision

4^15mmyr

�1 ,Quaternary

River

terracestratigraphy

anddating

5^15mmyr

�1 ,mod

ern

Riversedimentyields,

channelgeometry

Lave¤&Av

ouac

(2001)

GangesR

iver,£uvialsedim

entyield

1.402�10

9tyr

�1 ,Quaternary

Accum

ulationin

sedimentary

basins

1.285�10

9tyr�

1 ,mod

ern

Riversedimentloads

Me¤ tivier&

Gaudemar(1999)

Indu

sRiver,£uvialsedim

entyield

3.85

�10

8tyr�

1 ,Quaternary

Accum

ulationin

sedimentary

basins

4.75�10

8tyr�

1 ,mod

ern

Riversedimentloads

Me¤ tivier&

Gaudemar(1999)

MekongRiver,£uvialsedim

entyield

1.5�10

8tyr�

1 ,Quaternary

Accum

ulationin

sedimentary

basins

0.75�10

8tyr

�1 ,mod

ern

Riversedimentloads

Me¤ tivier&

Gaudemar(1999)

Huang

HeRiver,£uvial

sedimentyield

1.0�10

8tyr�

1 ,Quaternary

Accum

ulationin

sedimentary

basins

0.94

�10

8tyr�

1 ,mod

ern

Riversedimentloads

Me¤ tivier&

Gaudemar(1999)

Western

Dharw

arCraton,S.Indian

shield,denud

ation

30^60

mMa�

1 ,B100Ma

Apatite¢ssion

trackdating

27^56mMa�

1 ,mod

ern

Riversedimentloads

Gun

nell(1998)

CatchmentA

,Ft.Sage

Mtns,CA,

USA

,erosion

rate

5.8(7

1.4)cm

ka�1 ,B16

kaAllu

vialfandepo

sition

6.0(7

1.4)cm

ka�1 ,B10

kaCosmogenicnu

clides

Grang

eretal.(1996)

SantaMon

icaMou

ntains,C

A,U

SA,

upliftand

dend

udationrates

Uplift

0.24^0.5mmyr

�1 ,

10ka

to1M

aGeologiccross-sections,

publishedrates

0.5mm

yr�1 ,mod

ern

Riversedimentloads,

age-reliefrelations

Meigs

etal.(1999)

MeuseRiver,E

urop

e,erosionrate

12^68

mmka

�1 ,B

30ka

Cosmogenicnu

clides

11^57mmka

�1 ,mod

ern

Riversedimentloads

Schalleretal.(2001)

AllierRiverFrance,erosion

rate

A:30^

65mmyr

�1 ,10

to30

ka,

B:41^70

mmyr

�1 ,o5^

30ka

A:river

terracedating

and

stratigraphy,

B:cosmogenicnu

clides

40^75mm

yr�1 ,mod

ern

Riversedimentloads

Schalleretal.(2002)

r 2003 Blackwell Publishing Ltd,Basin Research, 15, 153^163 155

Alluvial storage and the long-term stability of sediment yields

ing the long-term consistency of denudation.This will beaccomplished in three parts. First, the stability of the drai-nage basin denudation systemwill be assessed, as stabilitymust exist to maintain consistency in £uvial sediment out-put. Second, the concept of the channel delivery ratio isintroduced to explore the relationship between alluvialstorage and basin area. Finally, empirical data from theTrinity River, Texas, will be assessed for consistency withthe theoretical analyses.

DRAINAGE BASIN DENUDATIONSYSTEM

If weathering is de¢ned broadly to include all processesthat convert bedrock to transportable debris, then for anydrainage basin a gross mass balance is given by

W ¼ Y þ Aþ R: ð1Þ

W indicates the mass of debris (including solutes) pro-duced by weathering in a given time period.Y, for yield,signi¢es all material (solid and dissolved) transported outof the basin; A represents the mass stored as alluvium inchannels or £oodplains; and R represents weatheredmaterial stored as regolith on the uplands (e.g. exclusiveof alluvial storage). Equation (1) assumes that all weather-ing products either remain within the drainage basin, orare exported by river £ow in solid or dissolved form.Thusgaseous or biological losses from the drainage basin are ig-nored, based on an assumption that these are negligiblecompared to the components included in Eqn. (1). Exportout of the basin by aeolian, glacial, or other non£uvial pro-cesses is also neglected.

The rates and quantities of W, Y, A, and R arenotoriously di⁄cult to measure, particularly over largeareas, and likely to vary substantially over all time-scales.However, the qualitative relationships can be speci¢edin the sense of what e¡ect an increase or decrease in anycomponent would have on the other components. Theseare depicted graphically in Fig.1 and discussed below.

Weathering has direct e¡ects on regolith and yield (i.e.an increase or decrease in the production of weathereddebris would, other things being equal, lead to a corre-sponding increase or decrease in regolith mass or sedi-ment yield). There is a direct link from weathering toyield to account for solutional denudation and bedrock in-cision, and to regolith because upland regolith is typicallyprimarily derived from in situ weathering. Because allu-vium is, by de¢nition, deposited by £owing water, weath-ering e¡ects on alluvial storage are indirect.Weathering isitself in£uenced chie£y by external (to the mass balancesystem) forcings and constraints such as climate and biota.The exception is regolith, which may have positive or ne-gative in£uences on weathering rates. Typically regolithdevelopment enhances weathering in early stages, or inareas of thin regolith cover, by facilitating moisture storageand biological activity. Later, or with thicker regoliths,

when moisture storage and biotic e¡ects are not limiting,thicker regoliths inhibit weathering by isolating theweathering front from the surface environment.Weather-ing is also self-limiting via depletion of weatherableminerals; thus the negative self-e¡ect shown in Fig.1.

Regolith is shown with positive links to both alluviumand yield, as the availability of weathered debris withinthe basin (or the lack thereof) will tend to increase (ordecrease) both stream loads and alluvial storage. In weath-ering-limited areas where the transport capacity oferosional agents exceeds the availability of transportabledebris there would ultimately be removal of all regolithproduced. In transport-limited systems, regolith produc-tion must keep pace with transport capacity to maintainthe transport-limited state. In some landscapes very thickweathering mantles suggests that weathering rates maygreatly exceed erosional removal for long periods. Reversalof this situation (stripping or net removal of regolith)would reverse the sign of the links from regolith toalluvium and yield for the case of declining regolith(decreasing regolith results in increasing yield and/oralluvial storage). This, however, would have no e¡ect onstability, as discussed below.

In the context of the drainage basin mass balance,whereyield is de¢ned as material removed from the basin, allu-vial storage and yield may be conceptualized as competi-tive in the sense that any material delivered to the £uvialsystem and carried from the basin cannot be stored asalluvium, while a decline in yield relative to a givensediment supply must result in an increase in alluvialstorage. This accounts for the negative link from yield toalluvium (Fig.1).

A key link in the model is from alluvium to yield. Insome senses this may be viewed as a competitive, negativerelationship. That is, a given quantity of sediment deliv-ered to channels must either be stored as alluvium or

Fig.1. Interactions betweenweathering rates and the allocationofweathering products among regolith, alluvial storage, andsediment yield.


J. Phillips

transported downstream ^ thus the more the alluvial sto-rage, the less the yield, or vice versa.While the negative re-lationship is appropriate at the reach scale, or with respectto a particular event or episode, at the basin scale and overlong time periods a positive link may be more likely.Where there is an ample supply of transportable materialin or adjacent to the channel, sediment transport is en-hanced during base £ow periods or where sediment inputfrom uplands is limited. Likewise, a shortage of alluvialmaterial available for mobilization may limit long-termyield. As we will see below, the sign of the alluvium to yieldlink is critical.

The qualitative stability of the model in Fig. 1 may beanalysed using the Routh^Hurwitz criteria (Cesari, 1971).The ¢gure shows ‘external forcings’, recognizing that cli-mate, biota, tectonics, and other factors have important in-£uences on all components of the mass balance. However,to the extent that these external forcings are independentof the system components (i.e. there are no arrows fromsystem components to these external factors), they haveno e¡ect on system stability. Factors such as climate, iso-stasy, and biota, for instance, are not independent ofweathering, regolith production, alluvial storage, and sedi-ment yield in the grand scheme of things. However, inmost instances, the feedbacks from system componentsto external factors (e.g. e¡ects of weathering on climate orof denudation on isostatic responses) operate on time-scales several orders of magnitude longer than the interac-tions included within the model. It has been shown thatfactors which vary over time-scales that di¡er by orders ofmagnitude are independent with respect to e¡ects on sys-tem stability (Scha¡er, 1981; Phillips, 1986a). Further, bytreating external forcings as independent the stability ofthe mass balance in response to small perturbations in ex-ternal forcings can be assessed.

The de¢nition of a ‘small’ perturbation is, of course, farmore problematic geologically than mathematically. Op-erational de¢nitions in the application of qualitative stabi-lity analysis in geomorphology have been based on thenotion of changes which are not su⁄cient to obliterateany system component, create new components, or tochange the rules (presence/absence or signs of the arrows)by which the system operates (see Puccia & Levins (1985)for a full mathematical development; Phillips, 1999).

The system shown inFig.1was translated into the inter-action matrix of Table 2, which shows the positive and ne-gative of negligible in£uences of the system componentson each other.The characteristic equation can be writtenin terms of feedback, as demonstrated by Puccia & Levins(1985). Feedback at levelk (Fk) signi¢es themutual in£uencesof system components on each other for all loops with kcomponents. Only disjunct loops ^ sequences of one ormore aij with no common component i or j ^ are included.

Fk ¼ �ð�1Þmþ1Zðm; kÞ: ð2Þ

Z(m, k) is the product of m disjunct loops with k compo-nents. F05 � 1 by convention. The characteristic

equation is

F0ln þ F1l

n�1 þ F2ln�2 þ � � � þ Fn�1lþ Fn ¼ 0: ð3Þ

The Routh^Hurwitz criteria give the necessary andsu⁄cient conditions for all real parts of all eigenvalues tobe negative (and thus for all Lyapunov exponents to benegative).These are:

� Fio0, for all i.� Successive Hurwitz determinants are positive.

Only alternative determinants have to be tested, and thesecond condition for n5 3 or n5 4 is

F1F2 þ F340: ð4Þ

For the system of Table 2 and Fig.1,

F1 ¼ �a11 ð5Þ

F2 ¼ a12ð�a21Þ þ ð�a34Þ ð�a43Þ ð6Þ

F3 ¼ �½ð�a43Þ ð�a34Þ ð�a11Þ� ð7Þ

F4 ¼ �½a12ð�a21Þ þ ð�a34Þ ð�a43Þ�: ð8Þ

Note that the links from regolith to alluvium and yield(a23, a24) do not appear in Eqns. (5)^(8). Changing the signof the links to account for episodes of stripping of thickregolith covers would not change the outcome of thestability analysis.

The ¢rst Routh^Hurwitz criterion can be satis¢ed ifa21o0 and a3440. If a34 is negative, then F340 and theRouth^Hurwitz criterion is violated. Ifa34 is positive, thena21 must be negative for F4 to be negative. If these condi-tions are obtained F2o0 also; otherwise, F2 is positive orcontingent on the relative strength of the two terms. It isclear that under these conditions the secondRouth^Hurwitzcriterion will also be met.

This means that the stability of the system is contingenton two situations. First, regolith must exert a negative in-£uence onweathering rates.This has been found to be thecase when a threshold regolith mass or thickness isachieved (Carson & Kirkby, 1972; Heimsath et al., 2000;Braun et al., 2001). Second, there must be a positive linkfrom alluvium to yield, indicating that alluvial storage isreadily available for transport, thus augmenting sediment

Table2. Interaction matrix derived from Fig.1.

W R A Y

Weathering (W) � a11 a12 0 a14Regolith (R) 7a21 0 a23 a24Alluvium (A ) 0 0 0 7a34Yield (Y) 0 0 � a43 0



yields when sediment supply from uplands is less thanconveyance capacity.

CHANNEL DELIVERY RATIOS

The £uvial denudation problem can also be considered interms of the channel delivery ratio, de¢ned as the sedi-ment exported from the mouth of the basin dividedby the total amount of sediment delivered to the channelsystem. For the solid phase, it is assumed that sedimenttransport capacity is a function of stream power, de¢nedby Bagnold (1977) as the energy available in water £owingdownstream. Cross-sectional stream power is given by

O ¼ gQS ð9Þ

where g is the speci¢c gravity of water, Q is the discharge,and S is the energy grade slope.Where sediment supplyexceeds transport capacity, export from a drainage basinis controlled by cross-sectional stream power at the basinmouth.

Total stream power for a channel reach is given by

P ¼ gQSL ð10Þ

where L is the length of the reach and it is assumed thatwater mass is conserved over the reach and there are nonew inputs. For a networkwith i51, 2,y,m reaches,

Pn ¼Xm

i¼1

Pi ð11Þ

where Pn is the total stream power of the network and Pithe stream power of reach i. It follows thatSLi5Ln, and

Pn ¼ �OOLn ð12Þ

where �OO is the mean cross-sectional stream power aver-aged over the network.

On an instantaneous basis the channel delivery ratio(Dc) would be given by

Dc ¼ Oo=Pn ¼ ðgQo SoÞ=ðgQSLnÞ ð13Þ

where the subscript o indicates the basin mouth or outlet.Again, this assumes that sediment in transport is di-

rectly proportional to stream power. Rewriting,

Dc ¼ ðgQo SoÞ=ðgQSÞL�rn ð14Þ

with r51 for instantaneous conditions. Over longer peri-ods, r51 is unrealistic, as thresholds of sediment entrain-ment and deposition will be transgressed. Depositionalthresholds are less than entrainment thresholds (Hjul-str˛m, 1935; Knighton, 1998), meaning that once en-trained, sediment has a greater chance of being movedthan r51 implies. Thus ro1, with a theoretical value ofr5 0.4^0.5 under kinematic assumptions (Moore &Burch, 1986; Phillips, 1989).

Speci¢c gravity is constant or negligibly variable andtreated as constant in most cases, so Dc is in£uenced by

the ratioQoSo /QS. Ignoring caseswhere there are extraor-dinary transmission, diversion, or evaporative losses,Qo4Q. In a typical stream system, however, SooS. As abroad generalization it has typically been found that theproduct QS increases downstream in large river systems.This implies that the ratio QoSo /QS41 in most cases.However, an r value of 0.4, and in fact any value appreciablygreater than zero, quickly overwhelms a positive ratio,producingDc values of less than unity.

For a transport-limited system, then,Dc5 f (Ln� r ), ro1.

As the total channel length (and associated drainage area)increases, the channel delivery ratio must decrease, indi-cating that a greater proportion of sediment supplied tothe system must be stored as channel or £oodplain allu-vium.This suggests that at the scale of large basins, allu-vial storage must be large relative to sediment delivered tothe £uvial system, indicating that e¡ects of changes in hill-slope sediment production on denudation at the basinmouth are bu¡ered by alluvial storage.This is fully consis-tent with the stability model presented above. Addition-ally, just as the stability conditions are not applicable in aweathering-limited (as opposed to transport-limited)system, the development above holds only where theavailability of transportable sediment is greater than orequal to conveyance capacity.

TRINITY RIVER,TEXAS, USA

The principles discussed above can be illustrated based ona case study of Trinity River,Texas (Fig. 2).TheTrinity is a46100 km2 drainage basin, with the headwaters in northTexas, west of Fort Worth. The river drains to theTrinity

Fig. 2.TheTrinity River Basin,Texas, showing Lake Livingston,Galveston Bay, and the location of US Geological Survey gagingstations in the lower basin.


J. Phillips

Bay, part of the Galveston Bay system on the Gulf ofMexico.The climate is generally humid subtropical.Thereis a well-developed soil and regolith cover over essentiallythe entire basin, and the Trinity has well-developed£oodplains and alluvial storage along much of its length.Thus the Trinity River Basin should meet the stabilitycriteria outlined above.

It is not known whether theTrinity is characterized bylong-term stability of sediment yields.The Colorado Riv-er, Texas, may have experienced a major decline in sedi-ment yields, based on a comparison of dated Quaternarydeltaic accumulations o¡shore and contemporary and his-torical sediment yields (Blum & Price, 1994). Estimates oflong-term sediment budgets and yields for coastal plainrivers such as theTrinity and Colorado are di⁄cult, how-ever, because of the migration of depocentres up anddownstream as sea level varies.There are £uvial and deltaicdeposits associated with theTrinity River well o¡shore ofthe current coastline, and evidence that sea level rise mayhave in£uenced aggradation up to 130 km upstream of thehighstand shoreline (Thomas&Anderson,1994).Thus the‘mouth’of the river mayhave varied in location by as muchas 200 km in the upstream^downstream direction, consid-erably complicating e¡orts to de¢ne an accumulationbasin. Even now, it is 60 km from the point, near Liberty,where the channel bed is below sea level to the mouth oftheTrinity at Trinity Bay.

The alluvial morphology and stratigraphy of the lowerTrinity (and the nearby and similar Sabine River), and thedeposits and paleochannels now submerged inTrinity andGalveston Bays and the Gulf of Mexico unquestionablypreserve evidence of climate, sea level, and upstream sedi-ment delivery changes (Anderson et al., 1992; Thomas &Anderson, 1994; Blum et al., 1995; Anderson & Rodriguez,2000; Rodriguez &Anderson, 2000; Rodriguez et al., 2001;Phillips, 2003; Phillips & Musselman, 2003). If these areinterpreted as representing variations in alluvial storageand remobilization, is it possible that alluvial bu¡ering intheTrinity is su⁄cient to minimize long-term variation inexport to the ocean?

TheTrinityhas also experienced recent changes in sedi-ment delivery to the lower river as a consequence of LakeLivingston and Livingston Dam, completed in 1967. Thelake is an e⁄cient sediment trap, and channel scour andremobilization immediately downstream of the dam is ap-parent.There has been an apparent reduction in sedimentloads at Romayor, approximately 50 km downstream (Soliset al., 1994). If the model described above applies to theTrinity, these disruptions should not be readily apparentat the basin mouth about 175 km downstream of the dam,due to the storage bottlenecks and the ready availability ofremobilizable alluvium downstream of the dam.

Estimates of sediment delivery to streams are available,based on reservoir surveys conducted by theTexas WaterDevelopment Board (TWDB). The surveys documentchanges in reservoir capacity, which are assumed to bedue to sedimentation. Dividing the capacity change bythe number of years between surveys gives a volume of

sediment accumulation per year.This is further adjustedfor drainage areas to produce a virtual rate in m3 km^

2 yr�1. The bulk densities of newly deposited lake sedi-ments in Texas range from 0.5 to 0.9 t m� 3, and those ofolder, more compacted lake sediments are typically 1.1^1.3(Welborn, 1967;Williams, 1991).Thus, assuming a densityof 1t m� 3 is a conservative estimate, and follows the prac-tice of Smith etal. (2002). Datawere averaged for 21 lakes ineast and central Texas, in the same land resource areas asthose encompassing theTrinity drainage basin.

Daily suspended sediment measurements were takenfor several stations by the TWDB for the period 1964^1989. These are point samples using the ‘Texas sampler’(Welborn, 1967) rather than the depth-integrated samplestaken using standard US Geological Survey methods.Comparison of same-day samples for the Romayor, Texasstation shows that the sediment loads indicated by thedepth-integrated samples are consistently twice or morethose suggested by theTexas sampler, with a mean ratio of2.378.TheTWDBnumbers were used to compute an aver-age daily sediment load, whichwas then mutltiplied by the2.378 correction factor.Thiswas used to compute sedimentyield in tonnes per square kilometre of drainage area peryear. A similar correction factor was used by Solis et al.(1994). Data were used from theTrinity River stations atLiberty,Romayor, andCrockett. Liberty is the downstream^ most station where sediment data are available, and is atthe approximate head of tide for the lowerTrinity (the gagedatum is about 0.7mbelow sea level). Romayor is upstreamof Liberty, but downstream of the Lake Livingston damand reservoir.Time series show some evidence that sedi-ment yields at Romayor are reduced by the lake, whichwas completed in 1967.There is no evidence of any trend,downward or otherwise, at Liberty.The Crockett station isupstream of Lake Livingston and not in£uenced by theimpoundment. Data were also examined for Long KingCreek, aTrinity River tributary that enters downstream ofLake Livingston (Fig. 2).

The sediment yields (Table 3) clearly show the impor-tance of alluvial sediment storage in the contemporaryTri-nity River. The lake surveys and Long King Creek datasuggest that about 275^400 t km� 2 yr�1 of sediment isbeing delivered to channels, no more than a third of whichis transported into the lowerTrinity. The sediment yieldsfor LongKingCreek, the surveyed lakes, and at theCrock-

Table3. Sediment delivery and yields in the lowerTrinity RiverBasin. Sediment data from theTexasWater Development Board,adjusted as described in the text.

Location or data sourceDrainagearea (km2)

Yield(t km� 2 yr�1)

Lake surveys 8196 (mean) 276Long King Creek 365 425Trinity at Crockett 36 029 129Trinity at Romayor 44512 69Trinity at Liberty 45242 1.4



ett, Romayor, and Liberty stations illustrate the increasingsediment storage and declining channel delivery ratiowithtotal stream length and basin area.While sediment loads atRomayor are apparently reduced byLakeLivingston, thereis no evidence of a dam-related change in sediment yieldsat Liberty.

A short distance downstream of Romayor, the Trinity£oodplain becomes wider, lower, and characterized by agreater number and size of oxbows and other depressions.The e¡ects on alluvial storage are obvious in the di¡erencein yield between Romayor and Liberty ^ in fact, alluvialstorage in the lower Trinity appears to exceed sedimentstorage in Lake Livingston.

TheTrinity valley from Livingston Dam to the head ofTrinity Bay is 174 km long.The average width of the £ood-plain is about 5 km. Channel surveys at12 locations on thelowerTrinity in 2002 indicate a typical bank height of about7m.Taking the latter as an e¡ective thickness of potentialactivation of alluvium (a reasonable assumption, as theTrinity is near bedrock at many locations below Lake Li-vingston) yields a total volume of potentially remobilizablealluvial storage of 6.0858�109m3. At a typical bulk densityof1.4 t m� 3, there are 8.52�109 t available.This represents138758 years worth of sediment yields at Liberty. Whilethese calculations are admittedly rough, since they onlyconsider alluvial storage in the lowermost reaches of theriver, they are su⁄cient to make the point that the reactiontime of the £oodplain sediment storage is substantiallylonger than the time-scales of climate and sea leveloscillations.

This is generally consistentwith studies of theQuatern-ary evolution of central and east Texas rivers (Blum &Price, 1998; Blum et al., 1995) and of southeast Texas estu-ary and delta complexes (Anderson & Rodriguez, 2000;Rodriguez et al., 2001).These studies show episodes of cutand ¢ll, and of inland-o¡shore migration of depositionalloci, but no evidence of anything approaching completeevacuation of stored alluvium.

While data are not su⁄cient to assess the consistency oflong-term mass export from theTrinity River, LivingstonDam provides an opportunity to test the idea that sedi-ment export from a £uvial system that meets the stabilitycriteria described above and which is su⁄ciently largemay be insensitive to changes in sediment productionwithin the basin. The evidence supports the notion thatalluvial storage can e¡ectively bu¡er output of the riversystem from variations in upland sediment production.The lower river is a sediment bottleneck during generallyaggradational periods or during high upland sediment£uxes. During degradational periods, the available alluvialstorage far exceeds the ability of the river to transport it tothe coastal zone.

DISCUSSION

The stability model suggests that the drainage basin denu-dation system is dynamically stable under certain circum-

stances. This stability indicates that, following smalldisturbances, feedbacks within the system will operate tomaintain or restore the predisturbance state.This in turnimplies that a drainage basin is able to maintain a dynamicequilibrium characterized by variations in sediment yield(and the other components of the system), which £uctuatearound a constant value.This condition is consistent withresults suggesting a general consistency of sediment yieldsand denudation in large drainage basins over time-scalesof 104 years and longer. Such consistency, in spite ofchanges in climate, biotic in£uences, human agency, andbase level, requires either stability of the type describedabove, or controls over sediment yields such as relief ortectonic forcings that overwhelm other in£uences.

The dynamic stability requires that there be a negativefeedback from regolith to weathering; i.e. that weatheringrates decrease as the regolith thickens.While this is typi-cally the case where soils and regoliths are relatively thickand well developed, the feedback is often positive in theearly stages of regolith evolution or where cover is thin.Maintaining the positive feedback would require regularor at least episodic partial or complete removal of regolithcover.This kind of situation is generally weathering-lim-ited, and denudation rates would be directly related toweathering rates. This is consistent with McClellan’s(1993) argument that highly weathered areas are stable,characterized as ‘equilibrium denudation regions’, and thatless weathered regions are ‘nonequilibrium denudationregions’.

Stability of the basin denudation system also requires apositive relationship linking alluvium to yield.While thisimplies that declining alluvial storage would (other thingsbeing equal) reduce yields, the more important implica-tion is that alluvium is readily available for transport andincreases in alluvial storage lead to increased sedimentyield. In this way alluvial storage provides a bu¡er between£uvial transport and variations in hillslope denudation.Me¤ tivier & Gaudemar (1999) found £oodplain bu¡ering,along with long-term tectonic control, to be the maincause for the average constancy of sediment yield in eastAsian rivers during the Quaternary. Over historic time-scales of two to three centuries or less, remobilization ofpreviously stored alluvium in rivers of the southeasternUS piedmont has maintained sediment yields even as up-land erosion rates have generally declined (Trimble, 1977;Phillips, 1986b). In the North Carolina coastal plain, allu-vial storage in the lower reaches of rivers and £uvial-es-tuarine transition zone is high and transport capacity intothe estuaries is low. Accordingly, dramatic historic changesin upland soil erosion and upstream sediment yields arebu¡ered, so that sediment delivery to the coast is little in-£uenced (Phillips1997a).

The conditions for stability are less likely to be met insmaller basins, in more inland situations, and in more re-stricted areas than they are for large externally drained ba-sins considered in the aggregate. If the conditions are notmet, the dynamical instability implies that sediment yield(and other system components) is sensitive to small


J. Phillips

changes in climate, vegetation, land use, base level, etc.This seems consistent with the weight of the evidenceshowing large and rapid responses of upland erosion and£uvial sediment yield to environmental changes (see e.g.Jansson, 1988; Douglas, 1990).

The bu¡ering of basin mass export by changes in sto-ragewithin the basin implies thatwithin the basin, at morerestricted scales, the £uvial sediment system must be un-stable. Perturbations associatedwith climate, land use, ve-getation, base level, etc. would lead to new con¢gurationswithin the system, re£ected in new system states regardingallocation of weathered debris. The general phenomenonof dynamical instability in geomorphic systems being ne-cessary to establish stability at broader scales is discussedby Huggett (1988), Phillips (1997b, 1999), Scheidegger(1987) and Tro¢mov & Phillips (1992).

The hillslope mass balance ^ re£ecting weatheringrates, erosion, deposition, and slope-elevation feedbacks^ was shown to be unstable (Tro¢mov &Moskovkin, 1984;Phillips,1993;Allison,1994).Numerical models of regoliththickness show dynamical instability when negative feed-backs of regolith thickness to weathering rates are strong(Phillips, 1993; Allison, 1994), suggesting consistency be-tween instability at the hillslope scale and stability at thedrainage basin scale.

The relationship between upland erosion, colluvial sto-rage, alluvial storage, and sediment yield in theTar River,North Carolina, was shown to be dynamically unstable(Phillips, 1987), suggesting the kind of rapid accommoda-tion necessarywithin the basin sediment system necessaryto maintain stability at the broader scale. Bourke (1994)found that complex stratigraphy in Australian £oodplainscan be explained as the chaotic outcome of a few simple de-terministic mechanisms, involving micro-, meso-, andmacroscale £ood impacts. Nanson & Erskine (1988) re-ported that coastal rivers of New South Wales, Australiashow evidence of £uctuation between two or more mor-phological states (based on the balance between channeland £oodplain erosion and deposition), rather than equili-brium behaviour, and are sensitive to small perturbationsto the erosion/deposition ratio. Knox (1985, 1993) used di-mensions of relict channels and sedimentology of pointbars to reconstruct the Holocene chronology of £oods inthe Upper Mississippi Valley, Wisconsin. He found that£uvial responses are associated with long-term episodicmobility and storage of sediment, and are disproportio-nately large compared to climate changes, indicating anunstable response. These studies, too, are indicative ofthe instability within the £uvial sediment system thatmay be necessary to maintain stability of the system as awhole.

Two general classes of explanation for the consistency ofdrainage basin export over time were put forth in the in-troduction: either some control such as relief or tectonicforcings so strongly in£uences denudation that other en-vironmental changes are not readily noticeable in termsof their e¡ects of sediment yield, or the £uvial sedimentsystem exhibits broadscale dynamical stability.This paper

has emphasized the latter explanation, but not necessarilywith the goal of arguing against the former. However, theresults here do suggest thatwhere the conditions for £uvialsediment system stability are likely to be met ^ transport-limited basinswhere alluvium is readily available for £uvialtransport ^ overriding controls are not necessary.The £u-vial system stability can lead to consistent denudation ratesover time by bu¡ering sediment yield from the e¡ects ofvariations in environmental controls and erosional distur-bances.

Gunnell’s (1998) notion of a ‘metabolic’ rate of denuda-tion that dominates the long-term trend, with superim-posed spikes of increased mass export, may provide ameans for integrating the two classes of explanation above.Climate change, human impacts, and other environmentalchanges clearly seem to produce spikes (positive or nega-tive) in erosion and mass £uxes. If uplift and relief indeedprovide strong, if not overwhelming, controls over long-term denudation, then a key question is where the e¡ectsof the spikes are manifested ^ within the interior drainagebasin, particularly in the alluvial storage compartment, orin the external basin of accumulation.

CONCLUSIONS

What are we to make of studies showing general consis-tency of £uvial denudation rates over long time periods,and historical and contemporary sediment yields of thesame magnitude as yields over longer time intervals? Thisconsistency suggests that climate, hydrological, ecological,base level, and other environmental changes are over-whelmed in terms of their in£uence on basin denudationby other controlling factors, or that the £uvial sedimentsystem is dynamically stable.This paper has explored thelatter possibility, via a general model based on the notionthat all debris produced by weathering within a drainagebasin over any given time period is either retained as partof the regolith, transported out of the basin as solid ordissolved sediment yield, or stored as alluviumwithin the£uvial system. This system is dynamically stable ifalluvium is always potentially available for transport; e.g.to be converted to yield, and if regolith development exertsa negative feedback on weathering rates. Similar conclu-sions are reached based on a consideration of channeldelivery ratios at the basin scale, which shows that as thetotal channel length in a network increases in a transport-limited system, alluvial storage must become large relativeto the amount of sediment delivered from hillslopes.

Data from the Trinity River Texas, illustrate thesepoints.There is extensive alluvial storage in the lowerTri-nity Basin, and alluvial storage rates in the lower river arelarge relative to yield.The timescale of £oodplain responseis long relative to the time-scales of major climate and sealevel £uctuations, and the channel delivery ratio is low.

The results of this study support the argument that thelong-term consistency of sedimentyields can be attributa-ble to the storage and remobilization of alluvium, which



bu¡ers the system against environmental change. E¡ectsof environmental changes are manifested primarily in re-organizations within the £uvial sediment system, such asvariations between net increases and decreases in alluvialstorage, and changes in the spatial locus of deposition.

ACKNOWLEDGEMENTS

Basil Gomez, ZachMusselman, James Syvitksi, and Stan-ley Schumm provided helpful reviews and discussions.TheTrinity River work is funded byTexasWater Develop-ment Board Contract No. 2002-483-442.

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Manuscript accepted 23 February 2003



Alluvial storage and the long-term stability of sediment yields

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