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Spatio-Temporal Dynamics in Riverine Sediment and Water Discharge
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Between 1960-2010 based on the WBMsed v.2.0 Distributed Global Model
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Sagy Cohen1, Albert J. Kettner1, James P.M. Syvitski1
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University of Colorado, Boulder, Colorado 80309, USA.
Community Surface Dynamics Modeling System, Institute of Arctic and Alpine Research,
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Submitted to ???
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Abstract
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Quantitative description of global riverine fluxes is one of the main goals of
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contemporary hydrology and geomorphology. However gauging of large rivers is
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decreasing globally and inter-basin measurement (particularly of sediment) is sporadic at
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best outside of the U.S. Numerical models can help fill the gap in global gauging and
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provide predictive frameworks. However the multi-scale nature and heterogeneity of
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large river systems makes it a highly challenging undertaking. Quantitative understanding
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of spatio-temporal dynamics within these complex systems is a precondition for accurate
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modeling. Here we study changes in global riverine water discharge and sediment flux
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between 1960-2010 using a new version of the WBMsed model. We introduced a new
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floodplain reservoir component to better represent riverine water and sediment dynamics.
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The new model (WBMsed v.2.0) is validated here against daily data from 18 globally
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distributed stations. The results are very favorable and show considerable improvement
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over the original model. Normalized departure from mean is used to quantify spatial and
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temporal dynamics in both water discharge and sediment flux. Considerable inter-basin
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variability is observed in some regions. Continental analysis shows cycles of below and
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above average discharge and sediment. The amplitude and wavelength of these
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fluctuations vary in time and between continents. A correlation analysis between
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continental sediment and discharge shows strong correspondence in Australia and Africa
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(R2 of 0.93 and 0.87 respectively), moderate correlation in North and South America (R2
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of 0.64 and 0.73 respectively) and weak correlation in Asia and Europe (R 2 of 0.35 and
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0.24 respectively). We propose that yearly changes in inter-basin precipitation dynamics
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explain the differences in continental discharge and sediment correlation. The mechanism
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propose and demonstrated here (on the Ganges, Danube and Amazon Rivers) is that
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regions with high relief and soft lithology will amplify the effect of higher then average
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precipitation by producing an increase in sediment yield that greatly exceeds increase in
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river discharge.
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1. Introduction
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Quantifying riverine sediment flux and water discharge is an important scientific
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undertaking for many reasons. Water discharge is a key component in the global water
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cycle affecting our planet climate (Harding et al., 2011), ecology (Doll et al., 2009) and
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anthropogenic activities (e.g. agriculture, drinking water, recreation; Biemans et al.,
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2011). Sediment flux dynamics is a fundamental goal of earth-system science as it is a
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key feature of our planet geology (e.g. erosion rates; Pelletier 2012), biogeochemistry
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(e.g. landscape-evolution, carbon cycle; Syvitski and Milliman, 2007, Vörösmarty et al.,
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1997) and anthropogenic activities (e.g. water quality, infrastructure; Kettner et al.,
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2010). Our qualitative understanding and predictive capabilities of global river fluxes is
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still lacking (Harding et al., 2011). This is, in part, due to the multi-scale nature of the
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processes involved (Pelletier, 2012) and the inadequacy in global gauging of rivers
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(Fekete and Vörösmarty, 2007). Availability of measured river fluxes is decreasing
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globally (Brakenridge et al., 2012) particularly for sediment (Syvitski et al., 2005).
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Ongoing sediment fluxes to the oceans are measured for less than 10% of the Earth’s
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rivers (Syvitski et al., 2005) and intra-basin measurements are even scarcer (Kettner et
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al., 2010).
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Numerical models can fill the gap in sediment measurements (e.g. Syvitski et al.,
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2005; Wilkinson et. al., 2009) and offer predictive capabilities of future and past trends
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enabling investigations of terrestrial response to environmental and human changes (e.g.
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climate change; Kettner and Syvitski, 2009). Despite advances made in recent years (e.g.
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Pelletier, 2012; Cohen et la., 2011, Kettner and Syvitski 2008) simulating global riverine
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fluxes remains a challenge due to the complexity and heterogeneity of large river systems
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(Pelletier, 2012).
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Climate change during the 21st century is projected to alter the spatio-temporal
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dynamics of precipitation and temperature (Held and Soden, 2006; Bates et al., 2008)
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resulting in natural and anthropogenically induced changes in land-use and water
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availability (Bates et al., 2008). Estimating the effect of these spatially and temporally
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dynamic processes warrant sophisticated distributed numerical models. Using past trends
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is perhaps the best strategy for developing these models and improve our understanding
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of the dynamics and causality within these complex systems.
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In this paper we present and validate an improved version of the WBMsed global
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riverine sediment flux model (Cohen et al., 2011). In Cohen et al. (2011) we showed that
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WBMsed well predict long-term average and inter-annual sediment flux but considerably
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over estimates daily flux (by orders of magnitudes) during high discharge events and tend
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to under estimate them during low flow periods. We found that this miss-prediction is
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directly linked to miss-predictions of riverine water discharge. We determined that this is
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mostly due to the model’s water routing approach which does not limit water transfer
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capacity of rivers. This means that the model did not consider overbank flow and water
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storage at the floodplains. In a natural river system, flooding not only limit the amount of
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water that can be transported by a river but also provide a temporary reservoir which
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resupply some of the water back to the river days after the flood. The absence of such
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mechanism in the model resulted in a river system which is overly responsive to runoff
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(hence the over estimation during peek flow and under estimation during low flows). It
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should be noted that original model (WBM/WTM; Vörösmarty et al., 1998; Vörösmarty
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et al., 1989) was implemented at much courser spatial and temporal resolutions then
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WBMsed (30 arc-minute and monthly compare to 6 arc-minute and daily) so this
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simplification was reasonable. In the new model, presented here, we introduce a
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floodplain reservoir component which store overbank flow at pixel scale.
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We use the new model to simulate daily water discharge and sediment flux (at 6 arc-
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minute resolution) between 1960-2010. The results are used to calculate yearly trends
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(normalized departure from mean) at both pixel scale and continental average. In this
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paper we focus our analysis on continental-scale interplay between sediment flux and
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water discharge.
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2. Methodology
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2.1. The WBMsed v.2.0 model
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WBMsed is a fully distributed global sediment flux model (Cohen et al., 2011). It is
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an extension of the WBMplus global hydrology model (Wisser et al., 2010), part of the
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FrAMES biogeochemical modeling framework (Wollheim et al., 2008)
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Water Discharge Module
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The WBMplus model includes the water balance/transport model first introduced by
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(Vörösmarty et al., 1998; Vörösmarty et al., 1989) and subsequently modified by (Wisser
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et al., 2010; Wisser et al., 2008). At its core the surface water balance of non-irrigated
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areas is a simple soil moisture budget expressed as:
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ì
ï -g(Ws ) E p - Pa
ï
dWs / dt = í
Pa - E p
ï
DWS - E p
ïî
(
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)
Pa £ E p
E p < Pa £ DWS
(1)
Dws < Pa
driven by g(Ws) is a unitless soil function:
g Ws  
 Ws 
 

 Wc 
1 e
1  e 
(2)
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and Ws is the soil moisture, Ep is the potential evapotranspiration, Pa is the precipitation
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(rainfall Pr combined with snowmelt Ms), and Dws is the soil moisture deficit, the
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difference between available water capacity Wc, which is a soil and vegetation dependent
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variable (specified externally) and the soil moisture. The unitless empirical constant α is
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set to 5.0 following Vörösmarty et al. (1989).
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Flow routing from grid to grid cell following downstream grid cell tree topology
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(which only allows conjunctions of grid cells upstream, without splitting to form islands
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or river deltas) is implemented using the Muskingum-Cunge equation, which is a semi
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implicit finite difference scheme to the diffusive wave solution to the St. Venant
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equations (ignoring the two acceleration terms in the momentum equation). The equation
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is expressed as a linear combination of the input flow from current and previous time step
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(Qin t-1, Qin t) and the released water from the river segment (pixel) in the previous time
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step (Qout t-1) to calculate new grid-cell outflow:
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Qout t = c1 Qin t + c2 Qin t-1 + c3 Qout t-1
(3)
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The Muskingum coefficients (c1 c2 c3) are traditionally estimated experimentally from
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discharge records, but their relationships to channel properties are well established.
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Detailed descriptions are provided in (Wisser et al., 2010).
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The new floodplain reservoir module (Figure 1) adjust daily discharge, Qi, by:
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(1) when daily discharge for a given pixel, Qout t, is greater then bankfull discharge,
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Qbf, excess water (Qout t – Qbf) are removed from the river flow (i.e. Qi = Qbf) and stored
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in a virtual infinite floodplain reservoir, Qfp;
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(2) when daily river discharge is less then bankfull (Qi < Qbf) water from the
floodplain reservoir (if there are any) are returned back to the river
Qi = Qout t + b(Qbf – Qout t)Qfp
(4a)
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Qfp = Qfp – b(Qbf – Qi)
(4b)
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where b is a daily delay fraction of water flow from the floodplain to the river, b=1
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translate to no delay (open flow). The adjusted grid-cell discharge equation is thus
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and
ì
Qbf
ï
Qi = í
ïî Qout t +( b(Qbf - Qi )Q fp )
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Qout t < Qbf
(5)
In this model water on the floodplain are assumed to be stationary (i.e. it does not
flow between pixels) and not subject to evaporation or infiltration.
Bankfull discharge at a river segment is estimated based on an approach modified
from the river morphology module in the CaMa-Flood model (Yamazaki et al., 2011)
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Qout t > Qbf
Qbf = BWVbf
(6)
where B is bank height
𝐵 = 𝑀𝑎𝑥[0.5𝑄̅ 0.3 , 1.0]
(7)
where 𝑄̅ is long term average discharge, W is channel width
𝑊 = 𝑀𝑎𝑥[15𝑄̅ 0.5 , 10.0]
(8)
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and Vbf is bankfull flow velocity
𝑉𝑏𝑓 = 𝑛−1 𝑆 −1/2 𝐵2/3
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(9)
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where n is Manning's roughness coefficient (=0.03) and S, slope, is assumed to be
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constant (=0.001).
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Additional approaches for estimating bankfull discharge were extensively tested. We
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have found that the Pearson III flood frequency estimator (using a 5-year flood frequency
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parameter) resulted in favorable results. However this purely statistical methodology
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proved to be inferior to the methodology presented above for larger rivers and was
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therefore discarded.
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Sediment Flux Module
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Similar to the first version of the model (WBMsed; Cohen et al., 2011) the sediment
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flux module is a spatially explicit implementation of the BQART and Psi basin outlet
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models (Syvitski and Milliman, 2007 and Morehead et al., 2003 respectively). In order to
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simulate these models continuously in space (i.e. pixel-scale) we assume that each pixel
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is an outlet of its upstream contributing area. The BQART model simulate long-term (30+
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years) average suspended sediment loads ( Qs) for a basin outlet
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Qs = wBQ
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Qs = 2wBQ
0.31
A0.5 RT for T ≥ 2°C,
0.31
A0.5 R for T < 2°C,
(10a)
(10b)
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where  is a coefficient of proportionality that equals 0.02 for units of kg s-1, Q is the
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long-term average discharge for each cell, A is the basin upstream contributed area of
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each cell, R is the relative relief difference between the highest relief of the contributed
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basin to that cell and the elevation of that particular cell, and T is the average temperature
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of the upstream contributed area. The B term accounts for important geological and
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human factors through a series of secondary equations and lookup tables, and includes
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the effect of glacial erosion processes (I), lithology (L) that expresses the hardness of the
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rock, sediment trapping due in reservoirs (TE) and a human-influenced soil erosion factor
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(Eh) (Syvitski and Milliman, 2007):
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B=IL(1-TE)Eh
(11)
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The Psi equation is applied to resolve sediment flux on a daily time step from the
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long-term sediment flux estimated by BQART (Eq. 10). A classic way to calculate the
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daily suspended sediment fluxes would be by Qs = aQ1+b, however Morehead et al.
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(2003) developed the Psi equation such that the model is capable of capturing the intra-
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and inter-annual variability that natural river systems have:
æ Qs[i] ö
æ Q[i] öC (a )
ç
÷ = y[i]ç ÷
è Qs ø
è Qø
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(12)
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where Qs[i] is the sediment flux for each grid cell, Q[i] is the water discharge leaving the
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grid cell, [i] describes a lognormal random distribution, [i] is revering to a daily time
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step, and C(a) is a normally distributed annual rating exponent (Syvitski et al., 2005) with:
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E() = 1
s (y) = 0.763(0.99995)
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(13a)
Q
(13b)
and
E(C)=1.4 – 0.025T+0.00013R+0.145ln( Qs)
(13c)
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(C)=0.17+0.0000183 Q
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where E and  are respectively the mean and the standard deviation. Equations (13a–d)
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are reflecting the different variability behavior of various sizes of river systems, where
(13d)
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large rivers with high discharges tend to have less intra-annual variability in the sediment
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flux than smaller systems (Morehead et al., 2003).
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In WBMsed.v2.0 sediment reaching the floodplain reservoir will be deposited at a
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user defined rate. In this paper, for the sake of simplicity, we assume that all the sediment
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in the overbank flow is deposited on the floodplain. This means that flood water returning
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to the river are sediment free. The effect of this process is a reduction in sediment flux as
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a function of flood frequency.
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2.2. Departure and Continental Trend Analysis
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Temporal changes in sediment flux and water discharge are quantified with
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normalized departure. Departure is the difference between long-term average and a value
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at a point in time. For example, departure (D) in water discharge is
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Dt = Qt -Q
(14)
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where t is for a specific point in time at a given time-scale. Here we calculate yearly
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departure so Qt is the mean discharge for year t (e.g. 1960). In order to allow a unitless
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comparison between pixels and between parameters we use normalized departure
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Dt =
(Qt - Q)
Q
(15)
This is equivalent to the percent difference between long-term average and yearly mean.
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Continental departure was calculated by averaging yearly and long-term sediment and
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discharge in all the pixels within each continent and using these values in equation 15.
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Continental departure can also be calculated by averaging the pixel scale departure. The
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latter approach, not used here, will bias the results toward highly fluctuating pixels and
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can differ considerably from the first approach.
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2.2. Simulation settings
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In this paper, water discharge and sediment flux predictions are from a daily, global
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scale simulation at 6 arc-minute spatial resolution. The precipitation dataset used is the
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GPCCfull monthly time steps (with supplementary daily fraction dataset) at 30 arc-
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minute spatial resolution. The flow routing (network) dataset used is the
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STN+HydroSHEDS at 6 arc-minute spatial resolution. A comprehensive list of the model
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input datasets is provided in (Cohen et al., 2011). All datasets are available on the
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CSDMS
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(http://csdms.colorado.edu/wiki/HPCC_portal).
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limitations, described below, a filter was applied to mask pixels with contributing area
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smaller then 40,000 km2 and average discharge smaller then 30 m3/s.
High
Performance
Computer
In
light
of
the
Cluster
model
accuracy
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3. Results
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3.1. Model validation
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The WBMsedv.2 model is evaluated in 12 globally distributed sites from the Global
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Runoff Database (ref. ALBERT?) and 6 U.S. sites (Fig. 2; Table 1). The U.S. sites are a
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subset of the sites used in Cohen et al. (2011) to evaluate the first version of WBMsed.
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These sites are from the USGS ‘Water Data for the Nation’ website (U.S. Geological
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Survey, 2012) providing daily sediment flux and water discharge data between 1997-
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2007. Daily sediment flux data is scarce outside the U.S. The 12 global sites used only
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provide water discharge data at different time frames. The sites were chosen to represent
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a wide geographical settings and river size.
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For the global sites (Fig. 3) WBMsedv.2 predictions are overall quite good.
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Predictions for the Niger, Mekong and Amazon Rivers are exceptionally good. The
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Yellow, Danube, Amu Darya Rivers show less favorable results but overall are also quite
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well predicted. The Yukon site is under predicted due to underestimation of the bankfull
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discharge value at this point. This is evident by the cutoff in peek discharge predictions.
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The other two arctic rivers (Lena and Ob) are also under predicted. This indicates that the
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model has a tendency to under predict arctic rivers. This may be due to lower accuracy in
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precipitation dataset for the higher latitudes but may also be due inaccuracies in the
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model snow melt module.
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Discharge at the Congo site is over predicted at about a factor of 2 despite the fact
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that the other three tropical rivers (Amazon, Niger and Mekong) are very well predicted.
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It may be due to the location of this gauging station on a particularly wide section of the
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Congo River (near the city of Kinshasa). This demonstrate the inherent uncertainty in
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river gauging which was estimated, for small watersheds, to have an error of 6-19% for
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water discharge and over 9-53% for sediment flux (Harmel et al., 2006).
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The Orange site is poorly predicted. It is likely due to the fact that it is located at the
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Vioolsdrif Dam which is used to store irrigation water. Although WBMsed include a
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dams and reservoirs component, predicting exact dam operation magnitude and schedule
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at a global scale is extremely challenging. This is particularly true for dryer environment
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and where reservoir water are extensively used for irrigation as is the case here.
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In the U.S. sites (Fig. 4) discharge predictions by WBMsedv.2 are very favorable.
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They are considerably better than the original model (Cohen et al., 2011) which typically
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over predicted peek discharge by over an order of magnitude. Sediment flux is over
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predicted in all but two sites (Illinois and Skunk). Even so these prediction are
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considerably better then the original WBMsed model where peek sediment flux was
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orders of magnitude higher then the observed flux (Cohen et al., 2011). The lower
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Mississippi site is considerably over predicted while sediment predictions are improved
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upstream (the Illinois site is even under predicted). The model predicted a large increase
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in sediment flux downstream while the observed data show that sediment flux at the
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lower Mississippi is lower then in the upper Mississippi. This can be explained by the
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fact that the Mississippi River is heavily engineered which significantly reduce sediment
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flux downstream. The results show that the model cannot yet fully represent such heavily
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engineered river in terms of sediment flux predictions.
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At the Skunk site the model well predicts discharge but considerably under predict
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sediment flux. We think that this is because this small basin has a high density of
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agricultural activity. WBMsed human-influenced soil erosion factor (Eh; Eq. 11) is a
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function of population density and a country’s GDP (Syvitski et al., 2007b). This limits
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the effective spatial resolution of Eh in WBMsed. As a result it may under estimate
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agriculturally rice basins in developed countries as these regions, with high GDP and low
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population density, will yield a very low Eh. These results demonstrate the spatial
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limitations of the WBMsed sediment module and prompt the need to introduce a more
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sophisticated and spatially explicit human/land-use erosion factor.
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3.2. Distributed departure analysis
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Figure 5 demonstrate the advantage of using departure analysis for comparing yearly
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river dynamics even when model predictions are less favorable (this figure is for the
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upper Mississippi site which was over predicted by a factor of 2 (Fig. 3)). It shows that
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despite differences in some years (most notably 2010) the overall trend calculated was
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very similar. Moreover using normalized departure eliminated under and over predictions
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and allows a robust analysis as long as the modeled fluctuations scale accurately (which
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validation results indicate that they are in most instances).
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Figure 6 shows that departure intra-basin variability can be significant. For example
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in the 1980s map the Amazon basin has a very high departure in its southern tributaries
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and low departure in its middle and northern parts. The Mississippi Basin in the 1990s
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map has a particularly high departure in its middle reaches. This kind of variability can
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only be measured using a dense net of gauging stations, which is a rarity. This
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demonstrates the usability of distributed continental model.
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Tropical rivers show relatively low fluctuations (i.e. low departure). One clear
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exception is the southwestern reaches of the Amazon during the 1980s that yielded very
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high above average sediment (positive departure). The processes leading to this will be
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discussed later. Eastern Australia show low sediment yield during the 1960s and 2000s,
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likely due to prolonged droughts during these decades. The maps do however shows that
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inter-continental variability in Australia can be considerable (e.g. 1990s). Below we
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discuss the interplay between precipitation, discharge and sediment that may lead to these
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spatio-temporal dynamics.
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3.3. Continental departure analysis
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Figures 7-9 shows yearly normalized departure in each continents for sediment flux
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and discharge. Figures 10 show the correlation between these datasets. Below we
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describe the results for each continent.
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Asia: Two to three years cycles of above and below average discharge (Figure 8) with
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decreasing amplitude with time i.e. fluctuations are smaller in recent years. Sediment flux
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also fluctuate but at cycles of a year or two (Figure 7). The last decade exhibits a
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decreasing trend in sediment flux which does not strongly corresponds to discharge. This
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disconnects between discharge and sediment departures is evident in the correlation plot
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(Figure 9) with a R2 of only 0.35. The fluctuations amplitude is the lowest of all the
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continents possibly due to the size of the landmass which average the signal.
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North America: Below average discharge and sediment for most of the 1960s and
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early 70s followed by cycles of positive and negative departure with a wavelength of
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several years. Sediment trends corresponds well to discharge (R2=0.64; Figure 9)
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however the amplitude of the sediment flux is much greater (maximum of over 200%
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compared to about 50%). Overall, periods of high sediment flux are short and intense
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though their intensity is lower in recent years.
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Europe: Below average discharge in the early 1960s followed by cycles of positive
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and negative departure at a wavelength of a few years particularly after the mid 1980s.
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Sediment departure poorly corresponds to discharge (R2=0.24) most notably in the 1980s
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and most of the 1990s in which sediment is continuously below average while discharge
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is fluctuating. Possible explanation is discussed later.
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Africa: Above average discharge and sediment throughout the 1960s followed by a
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relatively low amplitude cycles of negative and positive departure at a wavelength of
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several years. Strong correspondence between sediment and discharge (R2=0.87). The
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very high sediment and discharge throughout the 1960s is largely in contrast to the other
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continents. This may be explains by the timing of dam constructions in different
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continents. Compared to North America, Europe and Asia, increase in large dam
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construction has started later in Africa (1970s; World Commission on Dams, 2000).
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South America: Early 1960s has a weak positive departure for discharge but a weak
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negative departure for sediment. Correspondence between sediment and discharge
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improves with time and is overall quite strong (R2=0.73). Most of the 1970s show above
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average discharge and sediment but with relatively low amplitude. From the late 1970s
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onward cycles of negative and positive departure with low amplitude.
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Australia: Very strong correlation between sediment and discharge (R2=0.93). Below
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average departure during the 1960s and early 1970s. Very high positive departure during
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the 1970s followed by cycles of negative and positive departure at an amplitude of
340
several years. Below average discharge and sediment between 2002-2008. These very
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distinct cycles of below and above average discharge and sediment are likely due to the
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periodic long droughts in Australia.
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Global: Cycles of below and above average discharge and sediment with a general
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trend of decreasing wavelength with time. Sediment relatively well corresponds to
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discharge departure (R2=0.66). General trend of decreasing sediment and, to a lesser
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extent, discharge with time.
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4. Discussion
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Agreement between water discharge and sediment flux departure (Figure 9) vary
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considerably between continents. The goodness of fit cannot be readily explained by the
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size or heterogeneity of a continent (e.g. both Asia and Europe has weak correlation) or
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any other clear geographical attribute. Weak correlation between discharge and sediment
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means that yearly changes in water discharge explain only some of the yearly fluctuations
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in sediment. This means that other parameters are driving the temporal changes in
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simulate sediment dynamics. These parameters are likely to have some degree of spatial
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as well as temporal variability to lead to a weak correlation. For example dam
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construction may lead to considerable reduction in sediment flux due to trapping
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(Vörösmarty et al., 2003; Syvitski and Kettner, 2011.) but will not necessarily
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significantly reduce water discharge at a yearly time scale (Biemans et al., 2011). Even
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though a new dam will change the ratio between sediment and water discharge (i.e.
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sediment concentration) the change will be mostly constant in time (from the beginning
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of the dam operation onward) and will therefore not significantly weaken the correlation
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but will change its trend. It is therefore safe to assume that fluctuating rather then
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trending parameters will lead to a weaker correlation between discharge and sediment
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yearly departure as calculated here.
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At a basin scale the spatial and temporal variability in precipitation may have a major
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effect on discharge and sediment dynamics. For example Syvitski and Kettner [2007]
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showed that the correlation between sediment flux and water discharge in the Po River
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basin (in northern Italy) change considerably depending on the source of the sediment in
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the basin. Relief and lithology can act as an amplifier of precipitation patterns as greater
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rainfall and snowfall in high relief areas and soft (erodible) lithology may increase
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sediment delivery to the river. Land-use and vegetation spatio-temporal dynamics and the
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location of reservoirs (Syvitski and Kettner, 2007) can also be important parameters in
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this context.
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In WBMsed human erosivity and lithology are input parameters to the long-term
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sediment flux, BQART, equation (Eh and L in Eq. 5) which simulate trends but smooth
377
year to year fluctuations. Relief is a parameter in both the long-term sediment equation (R
378
in Eq. 5) and the daily sediment flux, Psi, equation (Eq. 6-7). We propose that inter-basin
379
patterns of relief and, to a lesser extent, lithology coupled with spatio-temporal variability
380
in precipitation will amplify or dampen sediment flux dynamics. This amplification or
381
dampening of sediment yield will lead to localized (space and time) changes in the
382
relationship between discharge and sediment resulting in weaker correlation between
383
their respective departures. To investigate this theory we study three outliers in Figure 9
384
by mapping discharge and sediment departure in their respective continents and years.
385
In 1971 predicted sediment flux in Asia was nearly 60% above average while
386
discharge was only 5% above average (Figure 9). The Ganges River is a good example of
387
this pattern (Figure 10). The Ganges Basin received above average precipitation that year
388
(explaining the above average discharge) including over the western reaches of the
389
Himalaya range. Some parts of the Himalaya received below average precipitation
390
resulting in lower then average discharge in the two north-eastern tributaries of the
391
Ganges. The two north-western tributaries shows the greatest difference between
392
sediment and discharge departure. The greatly above average sediment flux in these
393
branches of the Ganges (leading to above average sediment flux at the main river stem)
19
394
are the result of above average precipitation on both the Himalaya and the erosive
395
lithology at the floodplains. The southern tributaries also received above average
396
precipitation that year resulting in above average discharge and sediment. However since
397
they drain much lower relief and less erosive lithology they show good correspondence
398
between discharge and sediment.
399
Europe was predicted to have a very high sediment flux (more then 80% above
400
average) during 1965 while water discharge was predicted at just slightly above average
401
(about 5%; Figure 9). The Danube River basin in central Europe received above average
402
precipitation at its upper (western) reaches and below average in its lower reaches during
403
that year (Figure 11). Disconnect between discharge and sediment seems to originate at
404
the upper reaches of the river. The lithology in this region is not particularly erosive
405
though some patches of highly erosive (loess) lithology are also included in its drainage
406
basin. The cause of the enhance sediment prediction seems to be due to the increased
407
precipitations over the Alphas and perhaps over the Loess patches on the floodplain.
408
The last example is South America where sediment flux was predicted to be about
409
60% above average during 1982 while water discharge predictions were less then 20%
410
above average (Figure 9). The Madeira River (the biggest tributary of the Amazon River)
411
received above average precipitation at its upper reaches (Figure 12) resulting in above
412
average discharge. The Madre de Dios tributary yielded a considerably higher sediment
413
departure compared to its neighboring Beni tributary. This seems to be due to the high
414
precipitation in its mountainous upper reaches and the lithologically erosive floodplain.
415
The same has been predicted in the Mamore tributary where its east upstream branch
416
(low relief and a mixture of high and low erosivity) received very high precipitation
20
417
resulting in above average discharge and sediment while its west upstream branch (high
418
relief and higher erosivity) yielded only moderately positive discharge departure but high
419
sediment departure.
420
These three examples demonstrate that the intra-basin distribution of precipitation has
421
a substantial effect of its sediment yield. In the above analysis we only considered three
422
degrees of freedom (precipitation, relief and lithology) however most large river systems
423
will demonstrate more complex interplays (e.g. land-use, vegetation, human
424
infrastructure). This demonstrates the attractiveness of distributed numerical models as
425
they allow us to isolate portions of these highly complex systems. This is important as
426
future climate change is expected to have a significant effect on global precipitation
427
dynamics (Held and Soden, 2006; Bates et al., 2008). It is therefore necessary to develop
428
distributed predictive capabilities i.e. spatially explicit models, to enable more intelligent
429
adaptation strategies. An interesting advancement toward this goal is to study the effect
430
of precipitation dynamics driven by the El Niño/Southern Oscillation (ENSO) cycles on
431
discharge and sediment fluxes. This will be the focus of future work.
432
433
5. Conclusions
434
A new version of the WBMsed model was presented and tested. The WBMsed v.2.0
435
include a virtual floodplain reservoir component designed to simulate spatially and
436
temporally variable storage of overbank floodwater. The new model much better predict
437
riverine water discharge and sediment flux. However the validation results shows that the
438
model can reliably simulate only large rivers (above 40,000 km2) due to input data
439
resolution and difficulty in determining bankfull discharge at a pixel scale. This prompts
21
440
the need for more sophisticated and spatially explicit parameterization of human,
441
vegetation and land-use dynamics. This will be the focus of future model developments.
442
We used normalized departure from mean to compare yearly changes in sediment and
443
discharge between 1960-2010. The results show considerable inter-basin dynamics,
444
particularly in temperate regions. Tropical rivers showed relatively low year-to-year
445
fluctuations. Continental average departure showed a complex fluctuation pattern in
446
sediment and discharge with a wavelength varying from over a decade to a single year.
447
These cycles varied in time and between continents.
448
We found considerable discrepancy between discharge and sediment fluctuations in
449
some continents (most notably Asia and Europe). We proposed that the intra-basin
450
patterns of precipitation might enhance or dampen sediment yield as a function of relief
451
and lithology explaining some of the differences shown between continents as, for
452
example, Australia (with its low relief and hard lithology) showed very strong correlation
453
between discharge and sediment fluctuations. In years with high precipitation in high
454
relief and soft lithology regions sediment yield increase will be greater then water
455
discharge. This was demonstrated on the Ganges, Danube and Amazon Basins during
456
years with high discrepancy between discharge and sediment (1971, 1965 and 1982
457
respectively).
458
Other spatially and/or temporally variable parameters will likely have a considerable
459
effect on sediment-discharge relationship. For example land-use and vegetation patterns
460
were shown to have a strong correlation to sediment yield. These parameters were not
461
investigated her. However as future climate change is expected to significantly change
462
precipitation, land-use and vegetation patterns these, and other, parameters needs to be
22
463
considered. A systematic parametric study is therefore warranted and will be the focus of
464
future investigations.
465
466
Acknowledgments
467
This research is made possible by NASA under grant number PZ07124. We gratefully
468
acknowledge CSDMS for computing time on the CU-CSDMS High-Performance
469
Computing Cluster.
470
471
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472
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473
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545
26
546
Table 1. Characteristics of 12 global and 6 USGS hydrological stations (Figure 2) used to validate WBMsed daily sediment and
547
discharge fluxes. The sites drainage area is from the gauging stations metadata and the WBMsed drainage area is the model calculated
548
contributing area for each location.
River Name
Country
Yukon
Yellow
Amur
Niger
Danube
Lena
Ob
Congo
Orange
Mekong
Amu Darya
Amazon
Mississippi at Tarbert Landing, MS
Mississippi at Thebes, IL
Missouri at Nebraska City, NE
Illinois at Valley City, IL
Skunk at Augusta, IA
San Joaquin near Vernalis, CA
USA
China
Russia
Nigeria
Romania
Russia
Russia
Congo
South Africa
Cambodia
Uzbekistan
Brazil
USA
USA
USA
USA
USA
USA
Coordinates
Lat/Long (dd)
64.78/-141.2
37.53/118.3
50.63/137.12
7.8/6.76
45.22/28.73
70.74/127.35
66.63/66.6
-4.3/15.3
-28.76/17.73
11.58/104.94
42.34/59.72
-1.94/-55.59
31.00/91.62
37.21/89.46
40.68/95.84
39.70/90.64
40.75/91.27
37.67/121.35
Site drainage WBMsed drainage
area (km2)
area (km2)
286 186
293 963
811 229
737 619
1 866 473
1 730 000
2 469 310
NaN
784 896
807 000
2 429 967
2 430 000
2 478 666
2 430 000
3 640 766
3 475 000
823 111
850 530
755 444
663 000
670 002
450 000
4 683 872
4 640 300
3 206 630
2 913 477
1 841 230
1 847 179
1 056 940
1 061 895
69 450
69 264
11 202
11 168
22 772
35 058
549
550
551
27
552
Figure 1. Schematics of the WBMsed v.2.0 floodplain reservoir component.
Water flux from river to floodplain
Water flux from floodplain to river
553
554
28
555
Figure 2. Gauging stations used for validation. U.S. station (inner map) include both water discharge and sediment flux while global
556
stations include only water discharge.
557
29
558
Figure 3. Daily time series of water discharge used for validation for the globally
559
distributed sites (Figure 2).
16,000
12,000
Yukon River - 286,186 km2
WBMsedv2
12,000
10,000
8,000
6,000
4,000
Observed
10,000
Water Discharge (m3 /s)
Water Discharge (m 3/s)
Yellow - 811,229 km2
Observed
14,000
WBMsedv2
8,000
6,000
4,000
2,000
2,000
0
Jan-60 Jan-63 Jan-66 Jan-69 Jan-72 Jan-75 Jan-78 Jan-81 Jan-84 Jan-87 Jan-90 Jan-93 Jan-96 Jan-99 Jan-02 Jan-05
40,000
Amur River - 1,866,473 km2
Observed
WBMsedv2
35,000
0
Jan-60
30,000
Jan-64
Jan-66
Jan-68
Jan-70
Jan-72
Jan-74
Jan-76
Jan-78
Jan-80
Jan-82
Jan-84
Jan-86
Jan-88
Niger - 2,469,310 km2
Observed
WBMsedv2
25,000
Water Discharge (m 3/s)
Water Discharge (m3 /s)
30,000
20,000
25,000
15,000
20,000
15,000
10,000
10,000
5,000
5,000
0
Jan-60 Jan-63 Jan-66 Jan-69 Jan-72 Jan-75 Jan-78 Jan-81 Jan-84 Jan-87 Jan-90 Jan-93 Jan-96 Jan-99 Jan-02 Jan-05
20,000
2
Danube - 784,896 km
Observed
WBMsedv2
18,000
0
Jan-70 Jan-72 Jan-74 Jan-76 Jan-78 Jan-80 Jan-82 Jan-84 Jan-86 Jan-88 Jan-90 Jan-92 Jan-94 Jan-96 Jan-98 Jan-00 Jan-02 Jan-04
220,000
2
Lena - 2,429,967 km
Observed
WBMsedv2
200,000
180,000
Water Discharge (m 3/s)
16,000
Water Discharge (m3 /s)
Jan-62
160,000
14,000
140,000
12,000
120,000
10,000
100,000
8,000
6,000
4,000
60,000
40,000
2,000
0
Jan-60
50,000
80,000
20,000
Jan-63
Jan-66
Jan-69
Jan-72
Jan-75
Jan-78
Jan-81
Jan-84
Jan-87
Jan-90
Jan-93
Ob - 2,478,666 km2
Jan-96
Jan-99
Jan-02
Observed
WBMsedv2
45,000
0
Jan-78
130,000
Jan-80
Jan-82
Jan-84
Jan-86
Jan-88
Jan-90
Jan-92
Jan-94
Jan-96
Observed
WBMsedv2
110,000
Water Discharge (m 3/s)
Water Discharge (m3 /s)
40,000
35,000
30,000
25,000
20,000
15,000
10,000
Jan-98
Congo - 3,640,766 km2
90,000
70,000
50,000
30,000
5,000
0
Jan-78
Jan-80
Jan-82
6,000
Jan-84
Jan-86
Jan-88
Jan-90
Jan-92
10,000
Jan-60
Jan-94
Jan-62
Jan-64
Jan-66
Jan-68
80,000
Orange - 823,111 km2
Observed
5,000
Jan-70
Jan-72
Jan-74
Jan-76
Jan-78
Jan-80
Jan-82
Meknong - 755,444 km2
Observed
70,000
WBMsedv2
WBMsedv2
Water Discharge (m 3/s)
Water Discharge (m 3/s)
60,000
4,000
50,000
3,000
40,000
30,000
2,000
20,000
1,000
0
Jan-60
7,000
10,000
Jan-63
Jan-66
Jan-69
Jan-72
Jan-75
Jan-78
Jan-81
Jan-84
Jan-87
Jan-90
Jan-93
Jan-96
Jan-99
Amu Darya - 670,002 km2
0
Jan-60
350,000
Jan-61
Jan-62
Jan-63
Jan-64
Jan-65
6,000
5,000
Jan-68
Jan-69
Jan-70
Jan-71
Jan-72
Jan-73
Observed
WBMsedv2
300,000
250,000
4,000
200,000
3,000
150,000
2,000
100,000
1,000
560
Jan-67
Water Discharge (m 3/s)
Water Discharge (m3/s)
WBMsedv2
Jan-66
Amazon - 4,683,872 km2
Observed
0
Jan-60
Jan-61
Jan-62
Jan-63
Jan-64
Jan-65
Jan-66
Jan-67
Jan-68
Jan-69
Jan-70
Jan-71
Jan-72
Jan-73
50,000
Jan-70
Jan-72
Jan-74
Jan-76
Jan-78
Jan-80
Jan-82
Jan-84
Jan-86
Jan-88
Jan-90
Jan-92
Jan-94
561
562
30
Jan-96
80,000
25,000
Mississippi - 2,913,477 km2
Mississippi - 1,847,179 km2
Observed
70,000
Observed
WBMsedv2
WBMsedv2
20,000
Discharge (m 3/s)
Discharge (m3/s)
60,000
50,000
40,000
30,000
15,000
10,000
20,000
5,000
10,000
0
Jan-97
160,000
Jan-98
Jan-99
Jan-00 Mississippi
Jan-01
Jan-02
Jan-03
- 2,913,477
km2
Jan-04
Jan-05
Jan-06
0
60,000Jan-97
Jan-07
Jan-98
Jan-99
Jan-00
Jan-01
Jan-02Mississippi
2
Jan-03
Jan-04
1,847,179
km
Jan-05
Jan-06
Observed
140,000
WBMsedv2
Sediment Flux (kg/s)
Sediment Flux (kg/s)
120,000
100,000
80,000
60,000
Jan-07
Observed
WBMsedv2
50,000
40,000
30,000
20,000
40,000
10,000
20,000
0
Jan-97
Jan-98
Jan-99
Jan-00
4,000
Jan-01
Jan-02
Jan-03
Jan-04
Jan-05
Jan-06
0
Jan-97
Jan-07
Missouri - 1,061,895 km2
Jan-00
Discharge (m 3 /s)
2,500
2,000
1,500
Jan-01
Jan-02
Jan-03
Jan-04
Jan-05
Illinois - 69,264 km2
WBMsedv2
2,500
2,000
1,500
500
500
0
Jan-97
18,000
Jan-98
Jan-99
Jan-00
Jan-01
Jan-03
MissouriJan-02
- 1,061,895
km2 Jan-04
Jan-05
Jan-06
0
2,000Jan-97
Jan-07
Observed
16,000
WBMsedv2
Sediment Flux (kg/s)
14,000
12,000
10,000
8,000
6,000
Jan-98
Jan-99
Jan-00
Jan-01
Illinois Jan-02
- 69,264 Jan-03
km2
Jan-04
Jan-05
Jan-06
Jan-07
1,800
Observed
1,600
WBMsedv2
1,400
1,200
1,000
800
600
4,000
400
2,000
200
0
Jan-97
Jan-98
Jan-99
Jan-00
900
Jan-01
Jan-02
Jan-03
Skunk - 11,168
Jan-04
Jan-05
Jan-06
0
Jan-97
Jan-07
Jan-98
Jan-99
Jan-00
1,800
km2
Observed
800
Jan-01
Jan-02
Jan-03
Jan-04
Jan-05
San Joaquin - 35,058 km2
Jan-06
Jan-07
Observed
1,600
WBMsedv2
WBMsedv2
700
1,400
Discharge (m 3 /s)
Discharge (m 3 /s)
Jan-07
1,000
1,000
600
500
400
300
200
1,200
1,000
800
600
400
100
200
0
3,000
Jan-97
Jan-98
Jan-99
Jan-00
Jan-01
SkunkJan-02
- 11,168Jan-03
km2
Jan-04
Jan-05
Jan-06
0
500 Jan-97
Jan-07
Observed
WBMsedv2
Sediment Flux (kg/s)
2,500
Sediment Flux (kg/s)
Jan-06
Observed
3,000
WBMsedv2
3,000
Discharge (m 3 /s)
Jan-99
Observed
3,500
Sediment Flux (kg/s)
Jan-98
3,500
2,000
1,500
1,000
Jan-98
Jan-99
Jan-00
Jan-01
Jan-02
Jan-03
San
Joaquin
- 35,058
km2
Jan-04
Jan-05
Jan-06
Jan-07
450
Observed
400
WBMsedv2
350
300
250
200
150
100
500
563
564
565
0
Jan-97
50
Jan-98
Jan-99
Jan-00
Jan-01
Jan-02
Jan-03
Jan-04
Jan-05
Jan-06
Jan-07
0
Jan-97
Jan-98
Jan-99
Jan-00
Jan-01
Jan-02
Jan-03
Jan-04
Jan-05
Jan-06
Jan-07
Figure 4. Daily time series of water discharge (top plots) and sediment flux (bottom
plots) used for validation of the U.S. sites (Figure 2).
566
567
31
568
Figure 5. Comparison between modeled and gauged departure (1991-2010) for the upper
569
Mississippi station (Table 1 and Figure 2).
570
571
572
573
574
575
576
577
32
578
Figure 6. Decadal sediment departure maps.
579
33
580
Figure 7. Average continental sediment flux departure plots (1960-2010).
581
582
583
584
585
34
586
Figure 8. Average continental water discharge departure plots (1960-2010).
587
588
589
590
591
35
592
Figure 9. Continental scatter plots between sediment flux (x axis; Figure 7) and water
593
discharge (y axis; Figure 8) departure.
594
36
595
Figure 10. Southeast Asia departure for 1971 for: (top) sediment flux overlaying a
596
lithology factor map and (bottom) water discharge overlaying precipitation departure
597
map.
598
599
600
601
37
602
Figure 11. Europe departure for 1965 for: (top) sediment flux overlaying a lithology
603
factor map and (bottom) water discharge overlaying precipitation departure map.
604
605
606
607
608
38
609
Figure 12. South America departure for 1982 for: (top) sediment flux overlaying a
610
lithology factor map and (bottom) water discharge overlaying precipitation departure
611
map.
612
39