Sediment yield mapping in a large river basin: the Upper Yangtze ...
Sediment yield mapping in a large river basin: the Upper Yangtze ...
Sediment yield mapping in a large river basin: the Upper Yangtze ...
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Environmental Modell<strong>in</strong>g & Software 18 (2003) 339–353<br />
www.elsevier.com/locate/envsoft<br />
<strong>Sediment</strong> <strong>yield</strong> <strong>mapp<strong>in</strong>g</strong> <strong>in</strong> a <strong>large</strong> <strong>river</strong> bas<strong>in</strong>:<br />
<strong>the</strong> <strong>Upper</strong> <strong>Yangtze</strong>, Ch<strong>in</strong>a<br />
X.X. Lu a,∗ , P. Ashmore b , J. Wang b<br />
a<br />
Department of Geography, National University of S<strong>in</strong>gapore, 10 Kent Ridge Crescent, S<strong>in</strong>gapore 119260<br />
b<br />
Department of Geography, University of Western Ontario, London, Canada N6A 5C2<br />
Abstract<br />
A number of studies have mapped sediment <strong>yield</strong> at global or regional scales us<strong>in</strong>g sediment load measurements from <strong>river</strong>s.<br />
However, <strong>the</strong> suitability of <strong>the</strong> limited <strong>mapp<strong>in</strong>g</strong> methods has not been fully addressed, particularly for <strong>large</strong> <strong>river</strong> bas<strong>in</strong>s where <strong>the</strong><br />
sediment load data were obta<strong>in</strong>ed from a hierarchical <strong>river</strong> network. This study exam<strong>in</strong>es some of <strong>the</strong> issues related to <strong>the</strong> <strong>mapp<strong>in</strong>g</strong><br />
approaches us<strong>in</strong>g long-term sediment load data obta<strong>in</strong>ed <strong>in</strong> <strong>the</strong> <strong>Upper</strong> <strong>Yangtze</strong> bas<strong>in</strong>, Ch<strong>in</strong>a. The sediment <strong>yield</strong> data are treated<br />
as po<strong>in</strong>t values and <strong>in</strong>terpolated us<strong>in</strong>g <strong>the</strong> krig<strong>in</strong>g function <strong>in</strong> Arc/Info GIS. Barriers have been <strong>in</strong>corporated <strong>in</strong>to <strong>the</strong> <strong>in</strong>terpolation<br />
procedure to conf<strong>in</strong>e <strong>the</strong> <strong>in</strong>terpolation po<strong>in</strong>ts to <strong>the</strong> same major flow systems. The <strong>in</strong>corporation of barriers causes sharp changes<br />
of <strong>the</strong> <strong>in</strong>terpolated values along <strong>the</strong> barrier l<strong>in</strong>es, and significantly <strong>in</strong>creases <strong>in</strong>terpolation time. Scal<strong>in</strong>g ratios relative to a standard<br />
size of dra<strong>in</strong>age area have been developed for major dra<strong>in</strong>age bas<strong>in</strong>s to remove effects of dra<strong>in</strong>age sizes on sediment <strong>yield</strong>. By<br />
<strong>in</strong>corporat<strong>in</strong>g <strong>the</strong> scal<strong>in</strong>g ratios <strong>the</strong> sediment load data from various sizes of dra<strong>in</strong>age areas can be adjusted to what <strong>the</strong>y would be<br />
if <strong>the</strong> dra<strong>in</strong>age areas were <strong>the</strong> same and a less biased sediment <strong>yield</strong> map can be obta<strong>in</strong>ed as compared to us<strong>in</strong>g <strong>the</strong> orig<strong>in</strong>al dataset.<br />
© 2003 Elsevier Science Ltd. All rights reserved.<br />
Keywords: <strong>Sediment</strong> <strong>yield</strong>; Krig<strong>in</strong>g; Interpolation; Scal<strong>in</strong>g ratio; The <strong>Upper</strong> <strong>Yangtze</strong>; Ch<strong>in</strong>a<br />
1. Introduction<br />
<strong>Sediment</strong> <strong>yield</strong> is a ‘watershed wide’ measurement of<br />
soil erosion, transport and deposition (Lane et al., 1997)<br />
obta<strong>in</strong>ed by estimation of po<strong>in</strong>t loads at <strong>the</strong> outlet of <strong>the</strong><br />
bas<strong>in</strong>. <strong>Sediment</strong> <strong>yield</strong> maps can be used to <strong>in</strong>dicate <strong>the</strong><br />
regional variability of sediment sources with<strong>in</strong> a dra<strong>in</strong>age<br />
bas<strong>in</strong> and <strong>the</strong> temporal changes <strong>in</strong> <strong>the</strong> relative contributions<br />
of parts of <strong>the</strong> catchment (Lu and Higgitt,<br />
1998a,b). A number of authors have mapped sediment<br />
<strong>yield</strong> us<strong>in</strong>g sediment load data at global (Fournier, 1960;<br />
Strakhov, 1967; Milliman and Meade, 1983; Wall<strong>in</strong>g<br />
and Webb, 1983; Jansson, 1988; Ludwig and Probst,<br />
1998) or regional scales (Neil and Mazari, 1993; Stone<br />
and Saunderson, 1996). However, <strong>the</strong> suitability and<br />
comparability of <strong>mapp<strong>in</strong>g</strong> methods have not been fully<br />
addressed. Problems arise for two ma<strong>in</strong> reasons. First,<br />
sediment <strong>yield</strong> maps are areal representations of po<strong>in</strong>t<br />
∗<br />
Correspond<strong>in</strong>g author. Tel.: +1-65-6874-6135; fax: +1-65-6777-<br />
3091.<br />
E-mail address: geoluxx@nus.edu.sg (X.X. Lu).<br />
data that <strong>in</strong>tegrate <strong>the</strong> net upstream erosion effects—<br />
which raises <strong>the</strong> question of to what area should <strong>the</strong><br />
po<strong>in</strong>t value be attributed? Second, <strong>the</strong> relationship<br />
between upland erosion and downstream sediment <strong>yield</strong><br />
is complicated due to changes <strong>in</strong> sediment storage<br />
(Trimble, 1981) and variation <strong>in</strong> sediment delivery ratios<br />
(Wall<strong>in</strong>g, 1983) that often correlate with dra<strong>in</strong>age bas<strong>in</strong><br />
area. The significance of this effect of dra<strong>in</strong>age area on<br />
specific sediment <strong>yield</strong> lead Milliman and Syvitski<br />
(1992) to conclude that it is not possible to accurately<br />
map sediment <strong>yield</strong>.<br />
Certa<strong>in</strong>ly, <strong>the</strong>re is no generally agreed procedure for<br />
<strong>mapp<strong>in</strong>g</strong> and <strong>in</strong>terpret<strong>in</strong>g sediment <strong>yield</strong> data from a series<br />
of nested catchments. Lu and Higgitt (1998a) exam<strong>in</strong>ed<br />
three methods for sediment <strong>yield</strong> <strong>mapp<strong>in</strong>g</strong> <strong>in</strong> a <strong>large</strong><br />
<strong>river</strong> bas<strong>in</strong>: polygon attribution, multiple regression<br />
model<strong>in</strong>g and po<strong>in</strong>t <strong>in</strong>terpolation procedure. The previous<br />
methods used for sediment <strong>yield</strong> <strong>mapp<strong>in</strong>g</strong> at global<br />
and regional scales are classified us<strong>in</strong>g <strong>the</strong> three categories<br />
(Table 1). Each of <strong>the</strong> three methods has advantages<br />
and limitations (Lu and Higgitt, 1998a). Polygon attribution<br />
uses real values, but requires digitized boundaries<br />
for automated <strong>mapp<strong>in</strong>g</strong> and gives uniform values over<br />
1364-8152/03/$ - see front matter © 2003 Elsevier Science Ltd. All rights reserved.<br />
doi:10.1016/S1364-8152(02)00107-X
340 X.X. Lu et al. / Environmental Modell<strong>in</strong>g & Software 18 (2003) 339–353<br />
Table 1<br />
A summary of <strong>the</strong> previous sediment <strong>yield</strong> <strong>mapp<strong>in</strong>g</strong> methods<br />
Authors Number of Mapp<strong>in</strong>g area Mapp<strong>in</strong>g methods Notes<br />
stations<br />
Fournier (1960) 96 Global Polygon attribution<br />
Strakhov (1967) 60 Global Polygon attribution<br />
Milliman and Meade (1983) 65(?) Global Polygon attribution<br />
Wall<strong>in</strong>g and Webb (1983) 1500 Global Polygon attribution Only <strong>the</strong> data from 1000–10,000 km 2 used<br />
Jansson (1988) 2000 Global Polygon attribution 300–10,000 km 2 <strong>in</strong> dra<strong>in</strong>age area, and 2 years<br />
measurement <strong>in</strong>cluded<br />
Neil and Mazari (1993) 14 136 km 2 , Australia Multiple regression Investigated 14 reservoirs, and regression equation<br />
used for <strong>mapp<strong>in</strong>g</strong> a 136 km 2 catchment<br />
Stone and Saunderson (1996) 97 Laurentian Great Po<strong>in</strong>t <strong>in</strong>terpolation Only 37 stations used as a basis for <strong>in</strong>terpolation<br />
Lakes area of<br />
us<strong>in</strong>g multi-quadric <strong>in</strong>terpolation<br />
Canada<br />
Ludwig and Probst (1998) 62 Global Comb. of multiple Modeled po<strong>in</strong>ts <strong>in</strong> a 0.5×0.5° longitude/latitude grid<br />
regression and corrected by 62 observations<br />
<strong>in</strong>terpolation<br />
Church et al. (1999) 151 Canada (exclud<strong>in</strong>g Po<strong>in</strong>t <strong>in</strong>terpolation A common scal<strong>in</strong>g used. Maps presented for <strong>the</strong><br />
<strong>the</strong> Shield) standard scales of 1, 10×10, 100×100 km 2<br />
<strong>in</strong>terpolated us<strong>in</strong>g krig<strong>in</strong>g<br />
<strong>the</strong> sub-catchment unit. Multiple regression model<strong>in</strong>g is<br />
attractive, because it avoids <strong>the</strong> need for digitized boundaries<br />
and <strong>the</strong>re is scope to extend <strong>the</strong> approach to physically<br />
based model<strong>in</strong>g. However, <strong>the</strong> quality of <strong>the</strong> map<br />
output is dependent on <strong>the</strong> accuracy of <strong>the</strong> model. The<br />
third approach, po<strong>in</strong>t <strong>in</strong>terpolation, can be undertaken<br />
more efficiently because <strong>the</strong>re is less work <strong>in</strong>volved than<br />
o<strong>the</strong>r approaches. The three methods can also be used as<br />
a supplementary way. For example, Ludwig and Probst<br />
(1998) <strong>in</strong>vestigated empirical relationships between sediment<br />
<strong>yield</strong> data obta<strong>in</strong>ed from 60 major world <strong>river</strong> bas<strong>in</strong>s<br />
and a <strong>large</strong> number of parameters extracted from<br />
available hydroclimatic, biological, and geomorphological<br />
datasets at a global scale, and subsequently comb<strong>in</strong>ed<br />
<strong>the</strong> results of multiple regressions with <strong>the</strong> <strong>in</strong>terpolation<br />
of <strong>the</strong> 60 po<strong>in</strong>ts to produce a global sediment<br />
<strong>yield</strong> map with a 2.5°×2.5° longitude/latitude grid resolution.<br />
Comparison between this map and o<strong>the</strong>r global<br />
maps (Wall<strong>in</strong>g and Webb, 1983; Jansson, 1988) shows<br />
great differences, <strong>in</strong>dicat<strong>in</strong>g that <strong>the</strong>re is need for<br />
fur<strong>the</strong>r improvements.<br />
One significant problem of <strong>mapp<strong>in</strong>g</strong> sediment <strong>yield</strong>s<br />
is <strong>the</strong> necessity of hav<strong>in</strong>g a consistent dra<strong>in</strong>age area.<br />
Church et al. (1999) attempted to solve this problem by<br />
empirical adjustment of specific sediment <strong>yield</strong> to a common<br />
bas<strong>in</strong> area. This was done by develop<strong>in</strong>g regional<br />
scal<strong>in</strong>g relations for <strong>the</strong> variation of suspended sediment<br />
load with dra<strong>in</strong>age bas<strong>in</strong> area. Mapp<strong>in</strong>g was <strong>the</strong>n done<br />
by spatial <strong>in</strong>terpolation (krig<strong>in</strong>g) of <strong>the</strong> adjusted po<strong>in</strong>t<br />
data. The issue of sediment storage and delivery is particularly<br />
obvious for <strong>large</strong> <strong>river</strong> bas<strong>in</strong>s such as <strong>the</strong> <strong>Upper</strong><br />
<strong>Yangtze</strong>, where <strong>the</strong> sub-catchments represented by po<strong>in</strong>t<br />
data are highly hierarchical. This study attempts to<br />
address <strong>mapp<strong>in</strong>g</strong> suitability and scal<strong>in</strong>g issues aris<strong>in</strong>g<br />
from <strong>the</strong> use of sediment load data for <strong>mapp<strong>in</strong>g</strong> purposes<br />
for a s<strong>in</strong>gle, <strong>large</strong> <strong>river</strong> system us<strong>in</strong>g <strong>the</strong> sediment load<br />
data for <strong>the</strong> <strong>Upper</strong> <strong>Yangtze</strong> bas<strong>in</strong> as an example. The<br />
aims are to (1) exam<strong>in</strong>e <strong>the</strong> suitability of methods for<br />
<strong>mapp<strong>in</strong>g</strong> sediment <strong>yield</strong> for <strong>large</strong> <strong>river</strong> bas<strong>in</strong>s where<br />
sediment load is measured from a series of overlapp<strong>in</strong>g<br />
catchments; (2) improve <strong>the</strong> <strong>in</strong>terpolation results by conf<strong>in</strong><strong>in</strong>g<br />
<strong>the</strong> <strong>in</strong>terpolation procedure with<strong>in</strong> similar<br />
hydrological units, i.e. dra<strong>in</strong>age bas<strong>in</strong>s; and (3) attempt<br />
to remove effects of dra<strong>in</strong>age size on sediment <strong>yield</strong> by<br />
develop<strong>in</strong>g a scal<strong>in</strong>g ratio to normalize to a standard<br />
dra<strong>in</strong>age area. On <strong>the</strong> basis of <strong>the</strong> maps produced, it is<br />
possible to discuss <strong>the</strong> major sources of sediment <strong>in</strong> <strong>the</strong><br />
area. An understand<strong>in</strong>g of <strong>the</strong> l<strong>in</strong>ks between soil erosion<br />
and sediment <strong>yield</strong> and sediment transmission to <strong>the</strong><br />
fluvial system is an important component of environmental<br />
management <strong>in</strong> <strong>the</strong> bas<strong>in</strong> <strong>in</strong> <strong>the</strong> context of <strong>the</strong><br />
Three Gorges project.<br />
2. <strong>Sediment</strong> load and sediment <strong>yield</strong><br />
<strong>Sediment</strong> load (SL, t yr 1 ) from a watershed (or catchment<br />
or dra<strong>in</strong>age bas<strong>in</strong>) is <strong>the</strong> total quantity of sediment<br />
mov<strong>in</strong>g out of <strong>the</strong> watershed <strong>in</strong> a given time <strong>in</strong>terval,<br />
while sediment <strong>yield</strong> (SY, t km 2 yr 1 ) is <strong>the</strong> total quantity<br />
of sediment from a watershed relative to <strong>the</strong> watershed<br />
area. SL should <strong>in</strong>clude bed load as well as suspended<br />
load, but usually only suspended load is<br />
measured due to <strong>the</strong> difficulty of measur<strong>in</strong>g bed load.<br />
Bed load is often assumed to be of m<strong>in</strong>or importance<br />
even though <strong>in</strong> extreme cases it can reach 60% (Lane<br />
and Borland, 1951). The calculation for SY is not<br />
straightforward for a <strong>large</strong> <strong>river</strong> bas<strong>in</strong> consist<strong>in</strong>g of a
X.X. Lu et al. / Environmental Modell<strong>in</strong>g & Software 18 (2003) 339–353<br />
341<br />
series of hierarchical sub-catchments. There are two<br />
alternatives for calculat<strong>in</strong>g SY for such hierarchical subcatchments.<br />
Jansson (1988), Lajczak and Jansson (1993),<br />
and Ozturk (1996) calculated SY by deduct<strong>in</strong>g <strong>the</strong> sediment<br />
load at <strong>the</strong> neighbor<strong>in</strong>g upstream station from <strong>the</strong><br />
load at <strong>the</strong> gaug<strong>in</strong>g station which is <strong>the</strong>n divided by <strong>the</strong><br />
<strong>in</strong>cremental catchment area (Fig. 1). This may give a<br />
negative value, especially <strong>in</strong> downstream stretches of a<br />
<strong>large</strong> <strong>river</strong>, if part of sediment is deposited <strong>in</strong> <strong>the</strong> channel<br />
or on <strong>the</strong> floodpla<strong>in</strong>. SY may be looked upon as net erosion,<br />
because eroded soil and sediment may have been<br />
deposited many times before it reaches <strong>the</strong> <strong>river</strong>, where<br />
fur<strong>the</strong>r deposition may occur on flood pla<strong>in</strong>s, <strong>in</strong> lakes or<br />
<strong>in</strong> broad <strong>river</strong> sections upstream of <strong>the</strong> gaug<strong>in</strong>g stations<br />
(Jansson, 1988). This budget method is effective for dist<strong>in</strong>guish<strong>in</strong>g<br />
sediment generation or deposition for a certa<strong>in</strong><br />
<strong>river</strong> section. The alternative is to express SY as <strong>the</strong><br />
total load divided by <strong>the</strong> total catchment area upstream<br />
of <strong>the</strong> station. This means that problems of spatial averag<strong>in</strong>g<br />
<strong>in</strong>crease <strong>in</strong> significance downstream and <strong>in</strong> hierarchical<br />
catchments (or <strong>the</strong> nested sub-catchments),<br />
which requires methods to reduce <strong>the</strong> impact of <strong>the</strong> spatial<br />
averag<strong>in</strong>g.<br />
3. Data and methods<br />
3.1. The <strong>Upper</strong> Yangzte<br />
The <strong>Upper</strong> <strong>Yangtze</strong> <strong>in</strong> general refers to <strong>the</strong> area<br />
upstream of Yichang <strong>in</strong> Hubei Prov<strong>in</strong>ce (Fig. 2a). Ris<strong>in</strong>g<br />
from Q<strong>in</strong>ghai-Tibet plateau and descend<strong>in</strong>g <strong>in</strong>to <strong>the</strong><br />
Sichuan Bas<strong>in</strong>, <strong>the</strong> <strong>Upper</strong> <strong>Yangtze</strong> bas<strong>in</strong> <strong>in</strong>cludes a<br />
diverse range of environments. The climate <strong>in</strong> <strong>the</strong> <strong>Upper</strong><br />
<strong>Yangtze</strong> is ma<strong>in</strong>ly controlled by elevation, due to <strong>the</strong><br />
effect of Q<strong>in</strong>ghai-Tibet Plateau on atmospheric circulation<br />
(Ruddiman et al., 1989). The plateau constra<strong>in</strong>s<br />
<strong>the</strong> penetration of <strong>the</strong> monsoon, result<strong>in</strong>g <strong>in</strong> a complex<br />
pattern of precipitation with<strong>in</strong> <strong>the</strong> bas<strong>in</strong>, rang<strong>in</strong>g from<br />
arid <strong>in</strong> <strong>the</strong> extreme northwest to subtropical monsoon<br />
climates <strong>in</strong> <strong>the</strong> south. With an area of over 1 million km 2 ,<br />
<strong>the</strong> <strong>Upper</strong> <strong>Yangtze</strong> bas<strong>in</strong> conta<strong>in</strong>s <strong>the</strong> follow<strong>in</strong>g major<br />
tributaries: <strong>the</strong> J<strong>in</strong>sha, <strong>the</strong> Yalong, <strong>the</strong> Dadu-M<strong>in</strong>, <strong>the</strong><br />
Tuo, <strong>the</strong> Jial<strong>in</strong> and <strong>the</strong> Wu. The <strong>Upper</strong> J<strong>in</strong>sha, <strong>the</strong><br />
Yalong, <strong>the</strong> Dadu- M<strong>in</strong> pr<strong>in</strong>cipally dra<strong>in</strong> <strong>the</strong> mounta<strong>in</strong>ous<br />
areas to <strong>the</strong> west of <strong>the</strong> bas<strong>in</strong>, while <strong>the</strong> Tuo and<br />
<strong>the</strong> Jial<strong>in</strong> flow through areas of high population density<br />
and agricultural activity. The Wu, <strong>the</strong> only significant<br />
right bank tributary, is <strong>large</strong>ly agricultural but dra<strong>in</strong>s <strong>the</strong><br />
karst upland of Guizhou Prov<strong>in</strong>ce.<br />
3.2. Hydrological data<br />
Fig. 1. Schematic map show<strong>in</strong>g hierarchical sub-catchments. SY:<br />
sediment <strong>yield</strong> (t km 2 yr 1 ), SL: sediment load (t yr 1 ), and DA:<br />
dra<strong>in</strong>age area (km 2 ).<br />
A hydrological measurement network <strong>in</strong> <strong>the</strong> <strong>Upper</strong><br />
<strong>Yangtze</strong> bas<strong>in</strong> has been ma<strong>in</strong>ta<strong>in</strong>ed s<strong>in</strong>ce <strong>the</strong> 1950s.<br />
There are over 255 stations with both water discharge<br />
and sediment load measurements (Fig. 2b). The numbers<br />
of stations by dra<strong>in</strong>age area for <strong>the</strong> tributaries and <strong>the</strong><br />
ma<strong>in</strong> <strong>river</strong> are summarized <strong>in</strong> Table 2. The available data<br />
cover <strong>the</strong> period 1957–1987. The data after 1987 are no<br />
longer available <strong>in</strong> <strong>the</strong> public doma<strong>in</strong>. The length of record<br />
is varied: 187 stations have a length of record of 5<br />
years or over and 56 stations 25 years or over. Seven<br />
out of <strong>the</strong> 255 stations have no locations <strong>in</strong> latitude and<br />
longitude and were excluded from <strong>the</strong> analysis. The<br />
hydrological data set <strong>in</strong>cludes dra<strong>in</strong>age area upstream,<br />
monthly water discharge (m 3 s 1 ) and suspended sediment<br />
load (kg s 1 ), maximum and m<strong>in</strong>imum daily water<br />
discharge and suspended sediment transport plus <strong>the</strong><br />
dates of <strong>the</strong>ir occurrences. Details about <strong>the</strong> data set have<br />
been described elsewhere (Higgitt and Lu, 1996; Lu and<br />
Higgitt, 1998a,b). There are some <strong>in</strong>consistencies <strong>in</strong> <strong>the</strong><br />
orig<strong>in</strong>al data set; it took considerable time to correct<br />
those errors dur<strong>in</strong>g <strong>the</strong> conversion from paper to digital<br />
format. The dra<strong>in</strong>age areas and locations for many stations<br />
are not consistent throughout <strong>the</strong> time series. This<br />
may reflect correction of previous measurement of dra<strong>in</strong>age<br />
area or a slight change of station location. The names<br />
of some stations are also not consistent throughout <strong>the</strong><br />
measurement years. Limited data are available for bed<br />
load transport <strong>in</strong> <strong>the</strong> <strong>Upper</strong> <strong>Yangtze</strong> bas<strong>in</strong>. Dam eng<strong>in</strong>-
342 X.X. Lu et al. / Environmental Modell<strong>in</strong>g & Software 18 (2003) 339–353<br />
Fig. 2.<br />
The <strong>Upper</strong> <strong>Yangtze</strong> bas<strong>in</strong>: (a) major tributaries, and (b) hydrological stations and <strong>the</strong> <strong>in</strong>terpolation barriers.<br />
Table 2<br />
Numbers of hydrological stations for ma<strong>in</strong> tributaries <strong>in</strong> <strong>the</strong> <strong>Upper</strong> <strong>Yangtze</strong> bas<strong>in</strong><br />
Dra<strong>in</strong>age area (km 2 ) J<strong>in</strong>sha--Yalong Dadu-M<strong>in</strong> Jial<strong>in</strong> Wu Ma<strong>in</strong> <strong>Yangtze</strong> Total<br />
100 1 0 0 0 0 1<br />
100–1000 29 7 13 5 6 60<br />
1000–10,000 29 22 42 15 12 120<br />
10,000–100,000 11 19 14 6 1 51<br />
100,000–1,000,000 14 2 1 0 5 22<br />
1,000,000 0 0 0 0 1 1<br />
Total 84 50 70 26 25 255
X.X. Lu et al. / Environmental Modell<strong>in</strong>g & Software 18 (2003) 339–353<br />
343<br />
eers for <strong>the</strong> Three Gorges Project estimated bed load as<br />
0.05% of sediment load, but measurements at Yichang<br />
suggest a bed load contribution of 1.5–2% (Higgitt and<br />
Lu, 1996). This may be particularly significant <strong>in</strong> <strong>the</strong><br />
lower J<strong>in</strong>sha, <strong>the</strong> upper Jial<strong>in</strong> and <strong>the</strong> Three Gorges area,<br />
where landslides frequently occur. The underestimates<br />
of bed load transport will result <strong>in</strong> a higher risk for <strong>the</strong><br />
potential sedimentation of <strong>the</strong> reservoir.<br />
3.3. Krig<strong>in</strong>g<br />
The po<strong>in</strong>t data are <strong>in</strong>terpolated us<strong>in</strong>g <strong>the</strong> krig<strong>in</strong>g command<br />
<strong>in</strong> Arc/Info GIS. Krig<strong>in</strong>g, an advanced geostatistical<br />
procedure that generates an estimated surface from<br />
a scattered set of po<strong>in</strong>ts, <strong>in</strong>volves an <strong>in</strong>teractive <strong>in</strong>vestigation<br />
of <strong>the</strong> spatial behavior of <strong>the</strong> phenomenon, so that<br />
<strong>the</strong> best estimation method for generat<strong>in</strong>g <strong>the</strong> output surface<br />
can be made (ESRI, 1994). Krig<strong>in</strong>g is based on <strong>the</strong><br />
regionalized variable <strong>the</strong>ory that assumes that <strong>the</strong> spatial<br />
variation <strong>in</strong> <strong>the</strong> phenomenon is statistically homogeneous<br />
throughout <strong>the</strong> surface. The spatial variation of<br />
a variable is quantified by a semi-variogram that can be<br />
modeled by fitt<strong>in</strong>g a <strong>the</strong>oretical function to <strong>the</strong> sample<br />
semi-variogram:<br />
g∗(h) [2N(h)] 1[z(x)z(x h)] 2 (1)<br />
where g∗(h) is <strong>the</strong> experimental variogram as a function<br />
of distance h, z(h) and z(x + h) are measurements of a<br />
given variable at locations x and x + h, separated by <strong>the</strong><br />
directional distance h, and N(h) is <strong>the</strong> number of pairs<br />
of sampl<strong>in</strong>g units <strong>in</strong> <strong>the</strong> given distance class. The variogram<br />
is derived us<strong>in</strong>g one of a number of suitable variogram<br />
models. Arc/Info provides two types of surface estimators:<br />
ord<strong>in</strong>ary krig<strong>in</strong>g and universal krig<strong>in</strong>g. Ord<strong>in</strong>ary<br />
krig<strong>in</strong>g, which assumes that <strong>the</strong> variation of <strong>the</strong> variable<br />
is free of any structural component (drift), uses <strong>the</strong><br />
spherical, circular, exponential, Gaussian and l<strong>in</strong>ear<br />
methods. Universal krig<strong>in</strong>g, represented by <strong>the</strong> universal<br />
1 (l<strong>in</strong>ear function) and universal 2 (quadratic equation)<br />
methods, assumes that <strong>the</strong> spatial variation across <strong>the</strong><br />
surface has a structural component (drift), i.e. a systematic<br />
change <strong>in</strong> a particular direction. The spatial variation<br />
of a variable for universal krig<strong>in</strong>g is <strong>the</strong> sum of three<br />
components: a structural component (drift), a random but<br />
spatially correlated component, and random noise represent<strong>in</strong>g<br />
<strong>the</strong> residual error (ESRI, 1994).<br />
The procedures outl<strong>in</strong>ed by ESRI (1994) are followed<br />
to generate <strong>the</strong> best results. The universal 1 (l<strong>in</strong>ear<br />
function) method is chosen because <strong>the</strong> sediment <strong>yield</strong>s<br />
show a clear <strong>in</strong>crease from west to east (Fig. 2b). The<br />
grid resolution has a substantial effect on <strong>the</strong> modeled<br />
semi-variogram. The 10 km grid resolution was selected,<br />
which gives a 100 km 2 of cell size and is close to <strong>the</strong><br />
size of <strong>the</strong> smallest catchment (Table 2). The grid resolution<br />
is also close to <strong>the</strong> resolutions of most environmental<br />
databases such as GTOPO30 and global land cover,<br />
which were used <strong>in</strong> a sediment <strong>yield</strong> study by Lu and<br />
Higgitt (1999) and Higgitt and Lu (1999). Under <strong>the</strong><br />
fixed grid resolution, <strong>the</strong> sample size and search radius<br />
should be based on <strong>the</strong> distance (range) with<strong>in</strong> which<br />
<strong>the</strong> observed po<strong>in</strong>t values are spatially correlated. The<br />
default value of sampl<strong>in</strong>g po<strong>in</strong>ts for Arc/Info is 12. To<br />
m<strong>in</strong>imize <strong>the</strong> possibility of us<strong>in</strong>g trans-boundary po<strong>in</strong>ts<br />
dur<strong>in</strong>g <strong>the</strong> <strong>in</strong>terpolation procedure, <strong>the</strong> number of <strong>the</strong><br />
sampl<strong>in</strong>g po<strong>in</strong>ts was reduced to 6. The reduction <strong>in</strong> <strong>the</strong><br />
sampl<strong>in</strong>g po<strong>in</strong>ts permits local variations to be prom<strong>in</strong>ent.<br />
We left <strong>the</strong> maximum search radius (<strong>the</strong> diagonal extent<br />
of <strong>the</strong> <strong>in</strong>put sample) as <strong>the</strong> default. If <strong>the</strong> number of<br />
sampl<strong>in</strong>g po<strong>in</strong>ts cannot be satisfied with<strong>in</strong> <strong>the</strong> maximum<br />
search radius, a smaller number of po<strong>in</strong>ts will be used.<br />
4. Results and discussion<br />
The orig<strong>in</strong>al sediment load dataset was first <strong>in</strong>terpolated<br />
us<strong>in</strong>g krig<strong>in</strong>g. Subsequently, attempts were made<br />
to improve <strong>the</strong> <strong>in</strong>terpolation by (i) controll<strong>in</strong>g <strong>the</strong> <strong>in</strong>terpolation<br />
processes with<strong>in</strong> a similar hydrological unit, and<br />
(ii) remov<strong>in</strong>g <strong>the</strong> dra<strong>in</strong>age area effects on sediment <strong>yield</strong><br />
by develop<strong>in</strong>g a scal<strong>in</strong>g ratio us<strong>in</strong>g <strong>the</strong> relationship<br />
between sediment load and dra<strong>in</strong>age area. Some of <strong>the</strong><br />
issues associated with <strong>the</strong>se modifications are discussed<br />
<strong>in</strong> <strong>the</strong> follow<strong>in</strong>g sections.<br />
4.1. Data <strong>in</strong>terpolation<br />
The orig<strong>in</strong>al sediment load data were <strong>in</strong>terpolated follow<strong>in</strong>g<br />
<strong>the</strong> procedures outl<strong>in</strong>ed above. The contour l<strong>in</strong>es<br />
<strong>in</strong>dicate <strong>the</strong> four classes, 0–250, 250–500, 500–1000 and<br />
1000 t km 2 yr 1 (Fig. 3a), which are <strong>the</strong> standard<br />
categories of soil erosion classes used <strong>in</strong> Ch<strong>in</strong>a. The<br />
mean value of <strong>the</strong> sediment <strong>yield</strong> throughout <strong>the</strong> bas<strong>in</strong><br />
is 497 t km 2 yr 1 with a standard deviation of 519 t<br />
km 2 yr 1 . The upper Jial<strong>in</strong> and <strong>the</strong> lower J<strong>in</strong>sha tributaries<br />
have <strong>the</strong> highest sediment <strong>yield</strong>s (1000 t km 2<br />
yr 1 ), and <strong>the</strong> upper J<strong>in</strong>sha and Yalong tributaries <strong>the</strong><br />
lowest (250 t km –2 yr 1 ). The highest sediment <strong>yield</strong><br />
<strong>in</strong> <strong>the</strong> upper Jial<strong>in</strong> and <strong>the</strong> lower J<strong>in</strong>sha is associated<br />
with landslides, debris flows and a cover of loess<br />
materials (Yu et al., 1991; Higgitt and Lu, 1999). In contrast,<br />
<strong>the</strong> upper J<strong>in</strong>sha-Yalong and <strong>the</strong> upper Dadu-M<strong>in</strong><br />
are tundra areas with lower population density and lower<br />
sediment <strong>yield</strong>. <strong>Sediment</strong> <strong>yield</strong> is also higher <strong>in</strong> <strong>the</strong><br />
Sichuan bas<strong>in</strong> (ma<strong>in</strong>ly <strong>the</strong> Jial<strong>in</strong> and <strong>the</strong> Tuo tributaries),<br />
reflect<strong>in</strong>g an area dom<strong>in</strong>ated by agricultural lands with<br />
some of <strong>the</strong> highest population densities <strong>in</strong> Ch<strong>in</strong>a. Purple<br />
soil, one of <strong>the</strong> most erodible soils (Lu and Shi, 1992),<br />
is <strong>the</strong> dom<strong>in</strong>ant soil type <strong>in</strong> this area. When<br />
implement<strong>in</strong>g soil and water conservation measures,<br />
attention should be paid to those areas with higher sediment<br />
<strong>yield</strong>.
344 X.X. Lu et al. / Environmental Modell<strong>in</strong>g & Software 18 (2003) 339–353<br />
Fig. 3. Interpolated SY maps: (a) without barrier control, (b) with barrier control, (c) scaled to 100 km 2 , (d) scaled to 1000 km 2 , and (e) scaled to 10,000 km 2 .
X.X. Lu et al. / Environmental Modell<strong>in</strong>g & Software 18 (2003) 339–353<br />
345<br />
Fig. 3. Cont<strong>in</strong>ued
346 X.X. Lu et al. / Environmental Modell<strong>in</strong>g & Software 18 (2003) 339–353<br />
Fig. 3. Cont<strong>in</strong>ued
X.X. Lu et al. / Environmental Modell<strong>in</strong>g & Software 18 (2003) 339–353<br />
347<br />
Fig. 3. Cont<strong>in</strong>ued
348 X.X. Lu et al. / Environmental Modell<strong>in</strong>g & Software 18 (2003) 339–353<br />
Fig. 3. Cont<strong>in</strong>ued
X.X. Lu et al. / Environmental Modell<strong>in</strong>g & Software 18 (2003) 339–353<br />
349<br />
4.2. Data <strong>in</strong>terpolation with controls<br />
The above <strong>in</strong>terpolation uses adjo<strong>in</strong><strong>in</strong>g po<strong>in</strong>ts regardless<br />
of whe<strong>the</strong>r <strong>the</strong>y are <strong>in</strong> <strong>the</strong> same flow system. In<br />
order to conf<strong>in</strong>e <strong>the</strong> <strong>in</strong>terpolation processes with<strong>in</strong> relatively<br />
uniform environmental conditions, a barrier option<br />
is <strong>in</strong>corporated <strong>in</strong>to <strong>the</strong> <strong>in</strong>terpolation procedures. The<br />
bas<strong>in</strong> can be divided <strong>in</strong>to <strong>the</strong> six hydrological units: <strong>the</strong><br />
upper J<strong>in</strong>sha-Yalong, <strong>the</strong> lower J<strong>in</strong>sha, <strong>the</strong> Dadu-M<strong>in</strong>,<br />
<strong>the</strong> Jial<strong>in</strong>, <strong>the</strong> Wu and Ma<strong>in</strong> River (Fig. 2), based upon<br />
<strong>the</strong> major tributaries and environmental variables such<br />
as elevation, land cover and population density (Lu and<br />
Higgitt, 1999). Ma<strong>in</strong> River here refers to <strong>the</strong> rest of <strong>the</strong><br />
area which does not fall <strong>in</strong> any of <strong>the</strong> tributaries and<br />
ma<strong>in</strong>ly <strong>in</strong>cludes <strong>the</strong> Three Gorges area. Each of <strong>the</strong> six<br />
units has unique characteristics <strong>in</strong> terms of expla<strong>in</strong><strong>in</strong>g<br />
sediment <strong>yield</strong> variability (Lu and Higgitt, 1999). The<br />
division us<strong>in</strong>g <strong>the</strong> watershed boundaries as major <strong>in</strong>terpolation<br />
units is also relevant for watershed-based natural<br />
resource management and soil erosion control. The alternative<br />
is to put <strong>in</strong> barriers related to particular physiographic<br />
boundaries that cut across a bas<strong>in</strong> (e.g. a geological<br />
boundary), but allow <strong>in</strong>terpolation across watershed<br />
boundaries provided <strong>the</strong>y have similar physiography.<br />
This may be better than use of <strong>the</strong> dra<strong>in</strong>age bas<strong>in</strong>s <strong>in</strong><br />
terms of <strong>the</strong> controls on erosion rate, but it is difficult<br />
to obta<strong>in</strong> such boundaries without fur<strong>the</strong>r data.<br />
The orig<strong>in</strong>al data are <strong>in</strong>terpolated with <strong>the</strong> <strong>in</strong>corporation<br />
of <strong>the</strong> dra<strong>in</strong>age divides (Fig. 2b) as barriers us<strong>in</strong>g<br />
<strong>the</strong> krig<strong>in</strong>g barrier function <strong>in</strong> Arc/Info, and shaded<br />
us<strong>in</strong>g <strong>the</strong> same sediment <strong>yield</strong> classes <strong>in</strong>troduced above<br />
(Fig. 3b). The mean sediment <strong>yield</strong> for <strong>the</strong> entire bas<strong>in</strong><br />
is 493 t km 2 yr 1 with a standard deviation of 559 t<br />
km 2 yr 1 , which is very close to <strong>the</strong> <strong>in</strong>terpolation without<br />
any barriers. Us<strong>in</strong>g major bas<strong>in</strong> boundaries does<br />
allow step changes <strong>in</strong> <strong>yield</strong> that cannot occur with <strong>the</strong><br />
polygon attribution method (one of <strong>the</strong> <strong>mapp<strong>in</strong>g</strong> methods<br />
listed <strong>in</strong> Table 1). In o<strong>the</strong>r words us<strong>in</strong>g major dra<strong>in</strong>age<br />
bas<strong>in</strong> boundaries resembles polygon attribution but<br />
allows for variation with<strong>in</strong> polygons (i.e. <strong>the</strong> dra<strong>in</strong>age<br />
bas<strong>in</strong>s). If <strong>the</strong> barriers are set for each po<strong>in</strong>t, <strong>the</strong>n <strong>the</strong><br />
barriers become <strong>the</strong> boundary of each watershed and <strong>the</strong><br />
po<strong>in</strong>t <strong>in</strong>terpolation becomes polygon attribution, as<br />
described by Lu and Higgitt (1998a). However, <strong>the</strong> <strong>in</strong>troduction<br />
of barriers causes sharp changes along <strong>the</strong> barrier<br />
l<strong>in</strong>es (Fig. 3b). The effects of <strong>the</strong> barriers on <strong>in</strong>terpolation<br />
values are exam<strong>in</strong>ed us<strong>in</strong>g <strong>the</strong> three l<strong>in</strong>es across<br />
<strong>the</strong> bas<strong>in</strong> as outl<strong>in</strong>ed <strong>in</strong> Fig. 2b. The l<strong>in</strong>es of A–A1 and<br />
B–B1 cross <strong>the</strong> whole bas<strong>in</strong> approximately from west to<br />
east and north to south, while <strong>the</strong> l<strong>in</strong>e of C–C1 is <strong>the</strong><br />
l<strong>in</strong>e used as a barrier. The values <strong>in</strong>terpolated without<br />
or with barriers are very similar, except for <strong>the</strong> areas<br />
near <strong>the</strong> barrier l<strong>in</strong>es (Fig. 4). The <strong>in</strong>corporation of barriers<br />
<strong>in</strong>to <strong>the</strong> krig<strong>in</strong>g <strong>in</strong>terpolation considerably <strong>in</strong>creases<br />
<strong>the</strong> computer process<strong>in</strong>g time, and reduces <strong>the</strong> number<br />
of <strong>in</strong>terpolation po<strong>in</strong>ts which is problematic for <strong>the</strong> units<br />
with fewer data po<strong>in</strong>ts such as <strong>the</strong> ma<strong>in</strong> <strong>river</strong> unit. The<br />
effects of <strong>the</strong> barriers on <strong>the</strong> sediment <strong>yield</strong> map will<br />
also depend on <strong>the</strong> numbers of <strong>the</strong> sampl<strong>in</strong>g po<strong>in</strong>ts, e.g.<br />
<strong>the</strong> <strong>large</strong>r <strong>the</strong> number of sampl<strong>in</strong>g po<strong>in</strong>ts <strong>the</strong> stronger<br />
<strong>the</strong> barrier effect will be.<br />
4.3. <strong>Sediment</strong> <strong>yield</strong> scal<strong>in</strong>g<br />
The above <strong>in</strong>terpolation procedures treat <strong>the</strong> data as<br />
po<strong>in</strong>t values located at <strong>the</strong> sub-catchment outlets (<strong>the</strong><br />
gaug<strong>in</strong>g stations), which does not allow for a weight<strong>in</strong>g<br />
of <strong>the</strong> value accord<strong>in</strong>g to <strong>the</strong> size of sub-catchment area,<br />
upon which sediment <strong>yield</strong> is dependent. The dra<strong>in</strong>age<br />
areas of <strong>the</strong> sub-catchments from which <strong>the</strong> sediment<br />
measurement data were obta<strong>in</strong>ed <strong>in</strong> <strong>the</strong> <strong>Upper</strong> <strong>Yangtze</strong><br />
range from less than 100 to over 1,000,000 km 2 (Table<br />
2). SY from bas<strong>in</strong>s of widely vary<strong>in</strong>g sizes cannot be<br />
used directly for SY comparison because of <strong>the</strong> likely<br />
relation between SY and dra<strong>in</strong>age bas<strong>in</strong> area (Lu and<br />
Higgitt, 1998a; Church et al., 1999). The classic way to<br />
exam<strong>in</strong>e sediment <strong>yield</strong> for different dra<strong>in</strong>age areas is to<br />
plot sediment <strong>yield</strong> aga<strong>in</strong>st dra<strong>in</strong>age area. Recent discussion<br />
has questioned <strong>the</strong> validity of regression<br />
between variables that have catchment area as a common<br />
term (Waythomas and Williams, 1988; De Boer and<br />
Crosby, 1996). Milliman and Syvitski (1992) plotted<br />
sediment load and dra<strong>in</strong>age area to exam<strong>in</strong>e global sediment<br />
<strong>yield</strong>. A plot of SL and DA and <strong>the</strong>ir residuals for<br />
<strong>the</strong> <strong>Upper</strong> <strong>Yangtze</strong> bas<strong>in</strong> are shown <strong>in</strong> Fig. 5. The best<br />
fit equation is:<br />
SL 849.15DA 0.9215 (n 248, r 2 0.7735) (2)<br />
Despite <strong>the</strong> significant scatters <strong>in</strong> Fig. 5b, Eq. (2) <strong>in</strong>dicates<br />
that over 77% of <strong>the</strong> variance <strong>in</strong> sediment load<br />
(SL) can be expla<strong>in</strong>ed by <strong>the</strong> size of dra<strong>in</strong>age area (DA).<br />
The exponent (hereafter referred to as b) for Eq. (2) <strong>in</strong>dicates<br />
<strong>the</strong> extent to which SL <strong>in</strong>creases <strong>in</strong> <strong>the</strong> downstream<br />
direction (Higgitt and Lu, 1999). When b 1, SL is<br />
<strong>in</strong>creas<strong>in</strong>g more slowly than bas<strong>in</strong> area, which has been<br />
reported <strong>in</strong> many agricultural environments as a consequence<br />
of sediment storage (Wall<strong>in</strong>g, 1983). When b<br />
1, SL <strong>in</strong>creases more rapidly than bas<strong>in</strong> area. This<br />
situation is generally found <strong>in</strong> mounta<strong>in</strong>ous regions as a<br />
consequence of channel processes and/or rework<strong>in</strong>g of<br />
Quaternary sediments (Ashmore and Day, 1988; Church<br />
et al., 1989; Dedkov and Moszher<strong>in</strong>, 1992). The<br />
exponent for <strong>the</strong> whole <strong>Upper</strong> <strong>Yangtze</strong> is higher than<br />
those reported by Milliman and Syvitski (1992), <strong>in</strong>dicat<strong>in</strong>g<br />
that <strong>the</strong> proportion of eroded material transferred<br />
downstream is somewhat higher than <strong>the</strong> global average<br />
(Table 3).<br />
The close relationship between SL and DA is not surpris<strong>in</strong>g<br />
due to <strong>the</strong> fact that <strong>large</strong>r areas have <strong>the</strong> potential<br />
to generate more sediment. Eq. (2) divided by DA <strong>yield</strong>s<br />
a relationship between SY and DA as:<br />
SY 849.15DA 0.0785 (3)
350 X.X. Lu et al. / Environmental Modell<strong>in</strong>g & Software 18 (2003) 339–353<br />
Fig. 4. Profiles show<strong>in</strong>g barrier effects on <strong>in</strong>terpolation (l<strong>in</strong>es: without barriers, dots: with barriers). See positions of A–A1, B–B1 and C–C1 <strong>in</strong><br />
Figure 2b.<br />
Fig. 5.<br />
SL and DA relationship and residuals for <strong>the</strong> entire <strong>Upper</strong> <strong>Yangtze</strong> bas<strong>in</strong>.<br />
An exponent of 0.0785 (close to 0) <strong>in</strong>dicates almost<br />
no effect of area on SY, so <strong>the</strong>re is no need to adjust<br />
SY for differences <strong>in</strong> <strong>the</strong> entire <strong>Upper</strong> <strong>Yangtze</strong> bas<strong>in</strong>.<br />
However, <strong>the</strong> SL–DA relation differs between <strong>the</strong> six<br />
regions (Table 3), so <strong>the</strong>re is a need to make such adjustment<br />
for most of <strong>the</strong> regions. The exponents are contrary<br />
to expectation. The predom<strong>in</strong>antly agricultural areas (i.e.<br />
<strong>the</strong> Jial<strong>in</strong> and <strong>the</strong> Wu dra<strong>in</strong>age bas<strong>in</strong>s) have values of<br />
b 1, and <strong>the</strong> units located <strong>in</strong> <strong>the</strong> west part of <strong>the</strong> bas<strong>in</strong>,<br />
notably <strong>the</strong> J<strong>in</strong>sha-Yalong and <strong>the</strong> Dadu-M<strong>in</strong> bas<strong>in</strong>s,<br />
have b 1. The results may <strong>in</strong> part be an artifact due<br />
to <strong>the</strong> geographic spac<strong>in</strong>g of gaug<strong>in</strong>g stations (Higgitt<br />
and Lu, 1999). In <strong>the</strong> Jial<strong>in</strong> and <strong>the</strong> Wu bas<strong>in</strong>s agricultural<br />
land is ma<strong>in</strong>ly located <strong>in</strong> <strong>the</strong> lower parts of <strong>the</strong><br />
bas<strong>in</strong>s that have more sediment generation than sediment<br />
deposition, whereas <strong>in</strong> <strong>the</strong> western mounta<strong>in</strong>ous regions<br />
<strong>the</strong>re is a dramatic reduction <strong>in</strong> <strong>the</strong> relief <strong>in</strong> <strong>the</strong> lower<br />
parts of <strong>the</strong> bas<strong>in</strong>s, which provides more opportunity for<br />
sediment deposition. The difference <strong>in</strong> <strong>the</strong> exponent b<br />
between <strong>the</strong> six regions <strong>in</strong>dicates that <strong>the</strong>re is no spatially<br />
consistent scal<strong>in</strong>g, as compared with <strong>the</strong> Canadian<br />
case <strong>in</strong> which <strong>the</strong> scal<strong>in</strong>g relation for SY–DA was almost<br />
<strong>the</strong> same <strong>in</strong> all regions so that a s<strong>in</strong>gle adjustment could<br />
be made for all <strong>the</strong> data (Church et al., 1999).<br />
On <strong>the</strong> basis of Eq. (3), a scal<strong>in</strong>g ratio (SR) relative<br />
to a standard dra<strong>in</strong>age area (SDA) can be developed as:<br />
SR SDA 0.0785 DA 0.0785 (4)<br />
where SR = SY/SSY, with SSY be<strong>in</strong>g <strong>the</strong> sediment<br />
<strong>yield</strong> for <strong>the</strong> standard dra<strong>in</strong>age area. Assum<strong>in</strong>g a standard<br />
dra<strong>in</strong>age area of 100, 1000 and 10,000 km 2 , Eq. (4)<br />
results <strong>in</strong> a constant a = SDA 0.0785 of 1.44, 1.72 and 2.06,<br />
respectively. Us<strong>in</strong>g <strong>the</strong> same approach as develop<strong>in</strong>g Eq.<br />
(3) and (4), scal<strong>in</strong>g ratios relative to certa<strong>in</strong> standard<br />
dra<strong>in</strong>age areas can be developed. Fig. 6 shows <strong>the</strong> scal<strong>in</strong>g<br />
ratios relative to <strong>the</strong> three standard dra<strong>in</strong>age areas<br />
for each of <strong>the</strong> six hydrological units. There are two dist<strong>in</strong>ctive<br />
groups: (1) <strong>the</strong> Jial<strong>in</strong> and <strong>the</strong> Wu, and (2) <strong>the</strong><br />
J<strong>in</strong>sha-Yalong, <strong>the</strong> lower J<strong>in</strong>sha, <strong>the</strong> Dadu-M<strong>in</strong>, and<br />
Ma<strong>in</strong> River. The scal<strong>in</strong>g ratio of 1 <strong>in</strong>dicates an upward<br />
shift, and 1 a downward shift.<br />
With <strong>the</strong> scal<strong>in</strong>g ratios available, <strong>the</strong> orig<strong>in</strong>al sediment<br />
<strong>yield</strong> data were scaled to <strong>the</strong> three standard areas. The<br />
scaled data were <strong>the</strong>n <strong>in</strong>terpolated and shaded us<strong>in</strong>g <strong>the</strong><br />
same procedures outl<strong>in</strong>ed above (without barriers). One<br />
of <strong>the</strong> marked features is <strong>the</strong> pattern of <strong>the</strong> sediment<br />
<strong>yield</strong> chang<strong>in</strong>g with <strong>the</strong> standard dra<strong>in</strong>age sizes <strong>in</strong> <strong>the</strong><br />
southwest corner of <strong>the</strong> bas<strong>in</strong> (Fig. 3c–e). Fig. 3e has a
X.X. Lu et al. / Environmental Modell<strong>in</strong>g & Software 18 (2003) 339–353<br />
351<br />
Table 3<br />
The relationships between SL and dra<strong>in</strong>age area (DA) for <strong>the</strong> global<br />
data set (after Milliman and Syvitski, 1992) and <strong>the</strong> <strong>Upper</strong> <strong>Yangtze</strong><br />
bas<strong>in</strong><br />
River systems<br />
SL=aDA b<br />
a b R 2 Number of<br />
stations<br />
3000 m 280 0.46 0.80 21<br />
1000–3000 m<br />
N/S America, Africa, 170 0.52 0.70 41<br />
Alp<strong>in</strong>e Europe<br />
South Asia and Oceania 65 0.56 0.74 90<br />
Non-alp<strong>in</strong>e Europe and 50 0.73 0.78 10<br />
High Arctic<br />
500–1000 m 12 0.42 0.82 55<br />
100–500 m 8 0.66 0.81 43<br />
100 m 1 0.64 0.81 15<br />
<strong>Upper</strong> <strong>Yangtze</strong> 849 0.92 0.77 248<br />
J<strong>in</strong>sha-Yalong 5606 0.65 0.65 33<br />
Lower J<strong>in</strong>sha 639 1.01 0.76 47<br />
Dadu-M<strong>in</strong> 1569 0.84 0.76 44<br />
Jial<strong>in</strong> 222 1.13 0.84 75<br />
Wu 98 1.14 0.80 25<br />
Ma<strong>in</strong> <strong>Yangtze</strong> 611 0.96 0.97 24<br />
Table 4<br />
<strong>Sediment</strong> <strong>yield</strong> relative to each standard dra<strong>in</strong>age area calculated based<br />
on SY–DA relationships for <strong>the</strong> six units<br />
Major tributary Standard dra<strong>in</strong>age areas (km 2 )<br />
100 1000 10,000 100,000<br />
J<strong>in</strong>sha-Yalong 1102 489 216 96<br />
Lower-J<strong>in</strong>sha 465 475 486 497<br />
Dadu-M<strong>in</strong> 747 516 356 245<br />
Jial<strong>in</strong> 397 531 710 950<br />
Wu 183 250 342 468<br />
Ma<strong>in</strong> <strong>Yangtze</strong> 606 564 524 487<br />
very similar pattern to Fig. 3a, but it removes <strong>the</strong> effect<br />
of dra<strong>in</strong>age size on sediment <strong>yield</strong>. The effects of <strong>the</strong><br />
scal<strong>in</strong>g ratios are clearly shown <strong>in</strong> Table 4 <strong>in</strong> which sediment<br />
<strong>yield</strong> relative to each of <strong>the</strong> standard dra<strong>in</strong>age areas<br />
is calculated for <strong>the</strong> six units. The upper J<strong>in</strong>sha-Yalong<br />
has a very high sediment <strong>yield</strong> for <strong>the</strong> smaller standard<br />
dra<strong>in</strong>age area, but rapidly dropped down when dra<strong>in</strong>age<br />
area <strong>in</strong>creases. An appropriate scal<strong>in</strong>g ratio for each of<br />
<strong>the</strong> six units can be determ<strong>in</strong>ed accord<strong>in</strong>g to <strong>the</strong> majority<br />
of dra<strong>in</strong>age bas<strong>in</strong> sizes (Table 2). The majority of dra<strong>in</strong>age<br />
areas of <strong>the</strong> entire <strong>Upper</strong> <strong>Yangtze</strong> bas<strong>in</strong> are with<strong>in</strong><br />
<strong>the</strong> range of 1000–10,000 km 2 , an appropriate standardized<br />
size <strong>the</strong>refore should fall <strong>in</strong> this range.<br />
5. Summary and conclusion<br />
Mapp<strong>in</strong>g sediment <strong>yield</strong> us<strong>in</strong>g sediment load measurements<br />
is not straightforward for a s<strong>in</strong>gle <strong>large</strong> <strong>river</strong> bas<strong>in</strong><br />
where <strong>the</strong> data set <strong>in</strong>cludes hierarchical relationships.<br />
After review<strong>in</strong>g <strong>the</strong> available sediment <strong>yield</strong> <strong>mapp<strong>in</strong>g</strong><br />
methods, this study <strong>in</strong>terpolates sediment load measurements<br />
from hydrological stations us<strong>in</strong>g krig<strong>in</strong>g. The<br />
characteristics of <strong>the</strong> <strong>in</strong>terpolated surface can be controlled<br />
by limit<strong>in</strong>g <strong>the</strong> number of po<strong>in</strong>ts used for calculat<strong>in</strong>g<br />
each <strong>in</strong>terpolated value, or by def<strong>in</strong><strong>in</strong>g <strong>the</strong> radius<br />
with<strong>in</strong> which all po<strong>in</strong>ts are used <strong>in</strong> <strong>the</strong> <strong>in</strong>terpolation. The<br />
<strong>in</strong>terpolation uses <strong>the</strong> nearest po<strong>in</strong>ts regardless of<br />
whe<strong>the</strong>r <strong>the</strong>y are from <strong>the</strong> same hydrological system;<br />
<strong>the</strong>refore, an attempt has been made to conf<strong>in</strong>e <strong>the</strong> po<strong>in</strong>ts<br />
used for <strong>in</strong>terpolation by <strong>in</strong>corporat<strong>in</strong>g major hydrological<br />
units as barriers. The <strong>in</strong>corporation of barriers causes<br />
sharp changes of <strong>the</strong> <strong>in</strong>terpolated values near <strong>the</strong> barriers,<br />
and significantly <strong>in</strong>creases <strong>in</strong>terpolation time. The<br />
control of <strong>the</strong> <strong>in</strong>terpolation might be necessary if <strong>the</strong> distribution<br />
of land surfaces undergo<strong>in</strong>g high rates of soil<br />
erosion does not co<strong>in</strong>cide with tributary boundaries.<br />
Krig<strong>in</strong>g <strong>in</strong>terpolates po<strong>in</strong>t values, which does not allow<br />
a weight<strong>in</strong>g of <strong>the</strong> value accord<strong>in</strong>g to <strong>the</strong> size of <strong>the</strong> subcatchment<br />
area. This study attempts to standardize <strong>the</strong><br />
sediment <strong>yield</strong> data by develop<strong>in</strong>g a scal<strong>in</strong>g ratio relative<br />
to <strong>the</strong> standard sizes of dra<strong>in</strong>age areas for each major<br />
hydrological unit. An appropriate standard size for scal<strong>in</strong>g<br />
is critical to obta<strong>in</strong> a less biased map.<br />
<strong>Sediment</strong> <strong>yield</strong> <strong>mapp<strong>in</strong>g</strong> through po<strong>in</strong>t <strong>in</strong>terpolation<br />
procedures treats <strong>the</strong> data as a po<strong>in</strong>t value located at <strong>the</strong><br />
sub-catchment outlet (<strong>the</strong> gaug<strong>in</strong>g station). This does not<br />
Fig. 6.<br />
Scal<strong>in</strong>g ratios as affected by dra<strong>in</strong>age areas.
352 X.X. Lu et al. / Environmental Modell<strong>in</strong>g & Software 18 (2003) 339–353<br />
<strong>in</strong>corporate any locational <strong>in</strong>formation about <strong>the</strong> subcatchment<br />
position o<strong>the</strong>r than <strong>the</strong> location of <strong>the</strong> outlet<br />
<strong>in</strong>to <strong>the</strong> <strong>in</strong>terpolation procedure. Stichl<strong>in</strong>g (1973) plotted<br />
sediment concentration <strong>in</strong> <strong>the</strong> center of gravity of <strong>the</strong><br />
catchment when draw<strong>in</strong>g a map of Canada. At present<br />
<strong>the</strong>re appear to be no suitable methods for <strong>in</strong>terpolat<strong>in</strong>g<br />
values which have hierarchical relationships. It is hoped<br />
that this paper has raised attention to <strong>the</strong> lack of a uniform<br />
approach to sediment <strong>yield</strong> <strong>mapp<strong>in</strong>g</strong> at present. The<br />
maps which have been generated have some utility for<br />
macro-scale management of problems imposed by high<br />
sediment transport, particularly <strong>in</strong> <strong>the</strong> identification of<br />
sediment sources attributable to soil erosion. The<br />
<strong>in</strong>creas<strong>in</strong>g availability of high resolution environmental<br />
databases suggests that it is possible to employ physically-based<br />
models for sediment <strong>yield</strong> <strong>mapp<strong>in</strong>g</strong> at both<br />
global and regional scales.<br />
Acknowledgements<br />
The research started while <strong>the</strong> first author was <strong>in</strong><br />
receipt of a Natural Sciences and Eng<strong>in</strong>eer<strong>in</strong>g Research<br />
Council of Canada (NSERC) Postdoctoral Fellowship,<br />
and subsequently completed at National University of<br />
S<strong>in</strong>gapore (NUS). We acknowledge f<strong>in</strong>ancial support<br />
from NUS to X.X. Lu, an NSERC grant to P. Ashmore,<br />
and an Academic Development Fund to J. Wang. We<br />
are grateful to Dr I. Creed, Department of Geography,<br />
University of Western Ontario, for access<strong>in</strong>g Arc/Info<br />
GIS facilities, and Mrs Lee Li Kheng, Department of<br />
Geography, NUS, for prepar<strong>in</strong>g some of <strong>the</strong> diagrams.<br />
References<br />
Ashmore, P.E., Day, T.J., 1988. Spatial and temporal patterns of suspended-sediment<br />
<strong>yield</strong> <strong>in</strong> <strong>the</strong> Saskachewan River bas<strong>in</strong>. Canadian<br />
Journal of Earth Sciences 25, 1450–1463.<br />
Church, M., Kellerhals, R., Day, T.J., 1989. Regional clastic sediment<br />
<strong>yield</strong> <strong>in</strong> British Columbia. Canadian Journal of Earth Science 26,<br />
31–45.<br />
Church, M., Ham, D., Hassan, M., Slaymaker, O., 1999. Fluvial clastic<br />
sediment <strong>yield</strong> <strong>in</strong> Canada: scaled analysis. Canadian Journal of<br />
Earth Sciences 39, 1267–1280.<br />
De Boer, D.H., Crosby, G., 1996. Specific sediment <strong>yield</strong> and dra<strong>in</strong>age<br />
bas<strong>in</strong> scale. In: Wall<strong>in</strong>g, D.E., Webb, B.W. (Eds.), Erosion and<br />
<strong>Sediment</strong> Yield: Global and Regional Perspectives (Proceed<strong>in</strong>gs of<br />
<strong>the</strong> Exeter Symposium, July 1996). IAHS Publ. no. 236., pp.<br />
333–338.<br />
Dedkov, A.P., Moszher<strong>in</strong>, V.I., 1992. Erosion and sediment <strong>yield</strong> <strong>in</strong><br />
mounta<strong>in</strong> regions of <strong>the</strong> world. In: Wall<strong>in</strong>g, D.E., Davies, T.R.,<br />
Hasholt, B. (Eds.), Erosion, Debris Flows and Environment <strong>in</strong><br />
Mounta<strong>in</strong> Regions (Proceed<strong>in</strong>gs of <strong>the</strong> Chengdu Symposium, July).<br />
IAHS Publ. no. 209., pp. 29–36.<br />
ESRI, 1994. Cell-based modell<strong>in</strong>g with GRID, ArcDoc version 7.0.2<br />
on-l<strong>in</strong>e help.<br />
Fournier, F., 1960. Climat et Erosion. P.U.F., Paris, pp. 201<br />
Higgitt, D.L., Lu, X.X., 1996. Patterns of sediment <strong>yield</strong> <strong>in</strong> <strong>the</strong> <strong>Upper</strong><br />
<strong>Yangtze</strong> Bas<strong>in</strong>, Ch<strong>in</strong>a. In: Wall<strong>in</strong>g, D.E., Webb, B.W. (Eds.), Erosion<br />
and <strong>Sediment</strong> Yield: Global and Regional Perspectives. IAHS<br />
Publ. no. 236., pp. 205–214.<br />
Higgitt, D.L., Lu, X.X., 1999. Challenges <strong>in</strong> relat<strong>in</strong>g land use to sediment<br />
<strong>yield</strong> <strong>in</strong> <strong>the</strong> <strong>Upper</strong> <strong>Yangtze</strong>. Hydrobiologia 410, 269–277.<br />
Lajczak, A., Jansson, M.B., 1993. Suspended sediment <strong>yield</strong> <strong>in</strong> <strong>the</strong><br />
Baltic dra<strong>in</strong>age bas<strong>in</strong>. Nordic Hydrology 24, 31–52.<br />
Jansson, M.B., 1988. A global survey of sediment <strong>yield</strong>. Geogra. Ann.<br />
70A, 81–98.<br />
Lane, E.W., Borland, W.M., 1951. Estimat<strong>in</strong>g bed load. Trans. Am.<br />
Geophys. Union 32 (1).<br />
Lane, L.J., Hernandez, M., Nichols, M., 1997. Processes controll<strong>in</strong>g<br />
sediment <strong>yield</strong> from watersheds as functions of spatial scale.<br />
Environmental Modell<strong>in</strong>g & Software 12 (4), 355–369.<br />
Lu, X.X., Higgitt, D.L., 1998a. <strong>Sediment</strong> <strong>yield</strong> <strong>mapp<strong>in</strong>g</strong> us<strong>in</strong>g GIS <strong>in</strong><br />
<strong>the</strong> <strong>Upper</strong> <strong>Yangtze</strong>. In: Chao, Z.H. (Ed.), Soil, Human and Environment<br />
Interactions (Proceed<strong>in</strong>gs of International Symposium on<br />
Soil, Human and Environmental Interactions, 4–11 May 1997,<br />
Nanj<strong>in</strong>g, Ch<strong>in</strong>a). Ch<strong>in</strong>a Science & Technology Press, pp. 40–50.<br />
Lu, X.X., Higgitt, D.L., 1998b. Recent changes of sediment <strong>yield</strong> <strong>in</strong><br />
<strong>the</strong> <strong>Upper</strong> <strong>Yangtze</strong>, Ch<strong>in</strong>a. Environmental Management 22 (5),<br />
697–709.<br />
Lu, X.X., Higgitt, D.L., 1999. <strong>Sediment</strong> <strong>yield</strong>s variability <strong>in</strong> <strong>the</strong> <strong>Upper</strong><br />
<strong>Yangtze</strong>. Earth Surface Processes & Landforms 24 (11), 1077–<br />
1093.<br />
Lu, X.X., Shi, D.M., 1992. Soil erosion and revegetation <strong>in</strong> <strong>the</strong> hilly<br />
areas of South Ch<strong>in</strong>a. In: Proceed<strong>in</strong>gs of an International Symposium<br />
on Forage Development of <strong>the</strong> Red Soils of South Central<br />
Ch<strong>in</strong>a. Australian Center for International Agricultural Research,<br />
Canberra, pp. 31–34.<br />
Ludwig, W., Probst, J.L., 1998. River sediment discharge to <strong>the</strong> oceans:<br />
present-day controls and global budgets. American Journal of<br />
Science 298, 265–295.<br />
Milliman, J.D., Meade, R.H., 1983. World-wide delivery of <strong>river</strong> sediment<br />
to <strong>the</strong> oceans. Journal of Geology 91, 1–21.<br />
Milliman, J.D., Syvitski, J.P.M., 1992. Geomorphic/tectonic control of<br />
sediment discharge to <strong>the</strong> ocean: <strong>the</strong> importance of small mounta<strong>in</strong>ous<br />
<strong>river</strong>s. Journal of Geology 100, 525–544.<br />
Neil, D.T., Mazari, R.K., 1993. <strong>Sediment</strong> <strong>yield</strong> <strong>mapp<strong>in</strong>g</strong> us<strong>in</strong>g small<br />
dam sedimentation surveys, Sou<strong>the</strong>rn Tablelands, New South<br />
Wales. Catena 20, 13–25.<br />
Ozturk, F., 1996. Suspended sediment <strong>yield</strong>s of <strong>river</strong>s <strong>in</strong> Turkey. In:<br />
Wall<strong>in</strong>g, D.E., Webb, B.W. (Eds.), Erosion and <strong>Sediment</strong> Yield:<br />
Global and Regional Perspectives (Proceed<strong>in</strong>gs of <strong>the</strong> Exeter Symposium,<br />
July 1996). IAHS Publ. no.236., pp. 65–71.<br />
Ruddiman, W.F., Prell, W.L., Raymo, M.E., 1989. Late Cenozoic<br />
uplift <strong>in</strong> sou<strong>the</strong>rn Asia and <strong>the</strong> American West: rationale for general<br />
circulation model<strong>in</strong>g experiments. Journal of Geophysical<br />
Research 94, 18379–18391.<br />
Stichl<strong>in</strong>g, W., 1973. <strong>Sediment</strong> loads <strong>in</strong> Canadian <strong>river</strong>s. In: Fluvial<br />
Processes and Morphology, Proceed<strong>in</strong>gs, 9th Canadian Hydrology<br />
Symposium. National Research Council of Canada, Associate<br />
Committee on Geodesy and Geophysics, Subcommittee of<br />
Hydrology, pp. 39–72.<br />
Strakhov, N.M., 1967. Pr<strong>in</strong>ciples of Lithogenesis, Vol. 1, pp. 245. Oliver<br />
and Boyd, Ed<strong>in</strong>burgh.<br />
Stone, M., Saunderson, H.C., 1996. Regional patterns of sediment<br />
<strong>yield</strong> <strong>in</strong> <strong>the</strong> Laurentian Great Lakes bas<strong>in</strong>. In: Wall<strong>in</strong>g, D.E., Webb,<br />
B.W. (Eds.), Erosion and <strong>Sediment</strong> Yield: Global and Regional<br />
Perspectives (Proceed<strong>in</strong>gs of <strong>the</strong> Exeter Symposium, July 1996).<br />
IAHS Publ. no. 236., pp. 125–131.<br />
Trimble, S.W., 1981. Changes <strong>in</strong> sediment storage <strong>in</strong> <strong>the</strong> Coon Creek<br />
bas<strong>in</strong>, Driftless Area, Wiscons<strong>in</strong>, 1853–1975. Science 214, 181–<br />
183.<br />
Wall<strong>in</strong>g, D.E., Webb, B.W., 1983. Patterns of sediment <strong>yield</strong>. In: Gregory,<br />
K.J. (Ed.), Background to Palaeohydrology. John Wiley &<br />
Sons Ltd, pp. 69–100.
X.X. Lu et al. / Environmental Modell<strong>in</strong>g & Software 18 (2003) 339–353<br />
353<br />
Wall<strong>in</strong>g, D.E., 1983. The sediment delivery problem. Journal of<br />
Hydrology 65, 209–237.<br />
Waythomas, C.F., Williams, G.P., 1988. <strong>Sediment</strong> <strong>yield</strong> and spurious<br />
correlation—toward a better portrayal of <strong>the</strong> annual suspended<br />
sediment load of <strong>river</strong>s. Geomorphology 1, 309–316.<br />
Yu, J.R., Shi, L.R., Feng, M.H., Li, R.H., 1991. The surface erosion<br />
and fluvial silt <strong>in</strong> <strong>the</strong> upper reaches of Changjiang River. (<strong>in</strong><br />
Ch<strong>in</strong>ese) Bullet<strong>in</strong> of Soil and Water Conservation 11 (1), 9–17.