Auxiliary Material for Paper 2006gl025845
Relationship between river size and nutrient removal
W. M. Wollheim and C. J. Vorosmarty
Institute for the Study of Earth, Oceans, and Space, University of New Hampshire,
Durham, New Hampshire, USA
B. J. Peterson
Ecosystems Center, Marine Biological Laboratory, Woods Hole, Massachusetts, USA
S. P. Seitzinger
Institute of Marine and Coastal Sciences, Rutgers/NOAA Cooperative Marine
Education and Research Program, Rutgers-State University of New Jersey,
New Brunswick, New Jersey, USA
C. S. Hopkinson
Ecosystems Center, Marine Biological Laboratory, Woods Hole, Massachusetts, USA
Wollheim, W. M., C. J. Vorosmarty, B. J. Peterson, S. P. Seitzinger, and C. S. Hopkinson (2006),
Relationship between river size and nutrient removal,
Geophys. Res. Lett., 33, L06410, doi:10.1029/2006GL025845.
Introduction
This electronic supplement contains two auxiliary figures in eps
format and two auxiliary tables in ascii text format. The
captions accompanying these figures and tables are listed below.
1.2006gl025845-fs01.eps (Auxiliary Figure S1).
Proportion of total inputs to the river network removed by the
entire 7th order river network for various levels of vf, using
the hydrologic and geomorphic characteristics of the base
scenario. The proportion removed for each vf level corresponds
with the cumulative removal across all orders shown in Figure 2C.
2.2006gl025845-fs02.eps (Auxiliary Figure S2).
Sensitivity of nutrient removal by the entire 7th order network
to changes in runoff and selected hydraulic and geomorphic
parameters using the model in Equation 3. Each model scenario
represents a single factor change from the base scenario
(scenario 1, Auxiliary Table S1). The cumulative proportion of
removal in small (orders 1 4) and larger rivers (order 5-7) is
distinguished. Scenarios altered runoff (r.o., scenario 2 and 3);
the downstream width constant, a, and exponent, b (in w=aQ^b,
scenarios 4-7); the mean length of stream in the first order
basin (L1, scenarios 8-9), which influences the length of all
downstream orders using geomorphic principles; the factor change
in mean length from one order to the next (RL, scenarios 10-11);
and vf (scenarios 12-13). The parameter values used in each
scenario correspond with values observed in real networks.
3. 2006gl025845-ts01.txt (Auxiliary Table S1).
Characteristics of typical streams defined by order within the
7th order basin. Assumes the mean drainage area ratio Ra = 4.2;
the stream number ratio Rb = 3.5; the mean length ratio Rl = 2.3;
the drainage area of first order basins A1 = 1 km2; and the mean
length of first order basin stream L1 = 1.5 km, runoff = 500 mm/yr,
and vf = 35 m/yr. The ratios refer to the factor change in the
characteristic from one order to the next. The 7th order basin
geomorphology depicted here is comparable to similar sized basins in
Seitzinger et al. [2002]. Direct drainage is the proportion of watershed
area draining directly to each stream order, with drainage to all
first order streams known, and direct drainage to the remaining
stream orders determined by the proportion of total length in
each order relative to the total length of all order 2 through 7
streams [Seitzinger et al. 2002]. Direct inputs of N to each
stream order j (I) are calculated as Direct Drainage * Drainage
Area Specific N Load (= 100 kgN/km2/yr) * Total Basin Area (=
5489 km2). Mean discharge is for the downstream end of each
stream order (Qj) based on basin area and assuming uniform
runoff. Mean depth (h); width (w), velocity (v), are based on
empirical power laws (w = aQ^b, h = cQ^d, v = eQ^f) using the
parameters of HYD1 (Table 1) and are defined for Q at the
midpoint of stream order j (Qmid_j). Qmid_j is determined
assuming a linear Q increase along each reach defined by stream
order: Qmid_j = 2 * Qj-1 + (Qj - 2 * Qj-1) / 2. To define Qmid_1,
we assume first order channels originate where two zero order
flow paths join (A0 = A1 / RA). HL assumes upstream inputs that
experience the entire mean length of order j, Qmid_j, and mean
width. Removal is the proportion of upstream inputs removed in
each reach = 1 - exp(-vf/HL).
3.1 Column "Order" is the stream order.
3.2 Column "Direct" is the proportion of the entire order 7 basin
area draining directly to each stream order class (unitless)
3.3 Column "Length" is the mean length of stream in each order
class (in kilometers)
3.4 Column "Mean Basin Area" is the mean drainage area at the
downstream end of each order class (in square kilometers)
3.5 Column "Numbers" is the number of streams in each order class
(unitless)
3.7 Column "Q" is the mean discharge at the downstream end of
each order class (in cubic meters per second)
3.8 Column "Qmid" is the mean discharge at the midpoint of each
order class (in cubic meters per second)
3.9 Column "Depth" is the mean depth at the midpoint of each
order class (in meters)
3.10 Column "Width" is the mean width at the midpoint of each
order class (in meters)
3.11 Column "Velocity" is the mean velocity at the midpoint of
each order class (in meters per second)
3.12 Column "HL" is the mean hydraulic load, assuming Q and width
at the midpoint and the entire mean length of the order class (in
meters per year)
3.13 Column `Removal" is the proportion of upstream inputs
removed within each stream order (unitless)
4. 2006gl025845-ts02.txt (Auxiliary Table S2). Transition
probabilities from one stream order to the next based on GUH
methods [Rodriguez-Iturbe and Rinaldo 1997]. In our model,
transitions from source order j to receiving order j+1
distinguish between those that enter the upstream end of order
j+1 (the two streams of order j that form order j+1) and those
that enter at intermediate points in order j+1. The probability
of order j entering the upstream end of order j+1 is equal 2 /
Rb, which for Rb of 3.5 is equal to 0.571.