248 lines
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ReStructuredText
248 lines
15 KiB
ReStructuredText
.. _rst_River Transport Model (RTM):
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Model for Scale Adaptive River Transport (MOSART)
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=================================================
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.. _Overview MOSART:
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Overview
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---------
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MOSART is a river transport model designed for applications across local,
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regional and global scales :ref:`(Li et al., 2013b) <Lietal2013b>`. A
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major purpose of MOSART is to provide freshwater input for the ocean
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model in coupled Earth System Models. MOSART also provides an effective
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way of evaluating and diagnosing the soil hydrology simulated by land
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surface models through direct comparison of the simulated river flow
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with observations of natural streamflow at gauging stations
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:ref:`(Li et al., 2015a)<Lietal2015a>`. Moreover, MOSART provides a
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modeling framework for representing riverine transport and transformation
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of energy and biogeochemical fluxes under both natural and human-influenced
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conditions ( :ref:`(Li et al., 2015b) <Lietal2015b>`.
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.. _Routing Processes:
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Routing Processes
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------------------
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MOSART divides each spatial unit such as a lat/lon grid or watershed into
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three categories of hydrologic units (as shown in
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:numref:`Figure MOSART conceptual diagram`): hillslopes
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that convert both surface and subsurface runoff into tributaries,
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tributaries that discharge into a single main channel, and the main channel
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that connects the local spatial unit with upstream/downstream units through the
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river network. MOSART assumes that all the tributaries within a spatial unit
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can be treated as a single hypothetical sub-network channel with a transport
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capacity equivalent to all the tributaries combined. Correspondingly, three
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routing processes are represented in MOSART: 1) hillslope routing: in each
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spatial unit, surface runoff is routed as overland flow into the sub-network
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channel, while subsurface runoff generated in the spatial unit directly enters
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the sub-network channel; 2) sub-network channel routing: the sub-network channel
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receives water from the hillslopes, routes water through the channel and discharges
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it into the main channel; 3) main channel routing: the main channel receives water
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from the sub-network channel and/or inflow, if any, from the upstream spatial units,
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and discharges the water to its downstream spatial unit or the ocean.
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.. Figure 14.1. MOSART conceptual diagram
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.. _Figure MOSART conceptual diagram:
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.. figure:: mosart_diagram.png
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:width: 800px
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:height: 400px
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MOSART only routes positive runoff, although negative runoff can be generated
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occasionally by the land model (e.g., :math:`q_{gwl}`). Negative runoff in any
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runoff component including :math:`q_{sur}`, :math:`q_{sub}`, :math:`q_{gwl}`
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is not routed through MOSART, but instead is mapped directly from the spatial unit
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where it is generated at any time step to the coupler.
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In MOSART, the travel velocities of water across hillslopes, sub-network and main
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channel are all estimated using Manning’s equation with different levels of
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simplifications. Generally the Manning’s equation is in the form of
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.. math::
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:label: 14.1
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V = \frac{R^{\frac{2}{3}} S_{f}}{n}
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where :math:`V` is the travel velocity (m s :sup:`-1` ), :math:`R` is the hydraulic
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radius (m). :math:`S_{f}` is the friction slope that accounts for the effects
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of gravity, friction, inertia and other forces on the water. If the channel slope
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is steep enough, the gravity force dominates over the others so one can approximate
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:math:`S_{f}` by the channel bed slope :math:`S` , which is the key assumption
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underpinning the kinematic wave method. :math:`n` is the Manning’s roughness
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coefficient, which is mainly controlled by surface roughness and sinuosity of the
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flow path.
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If the water surface is sufficiently large or the water depth :math:`h` is
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sufficiently shallow, the hydraulic radius can be approximated by the water depth.
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This is the case for both hillslope and sub-network channel routing.
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.. math::
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:label: 14.2
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R_{h} = h_{h}
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R_{t} = h_{t}
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Here :math:`R_{h}` (m) and :math:`R_{t}` (m) are hydraulic radius for hillslope and
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sub-network channel routing respectively, and :math:`h_{h}` (m) and :math:`h_{t}`
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(m) are water depth during hillslope and sub-network channel routing respectively.
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For the main channel, the hydraulic radius is given by
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.. math::
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:label: 14.3
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R_{r} = \frac{A_{r}}{P_{r}}
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where :math:`A_{r}` (m :sup:`2` ) is the wetted area defined as the part of the
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channel cross-section area below the water surface, :math:`P_{r}` (m) is the
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wetted perimeter, the perimeter confined in the wetted area.
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For hillslopes, sub-network and main channels, a common continuity equation can
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be written as
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.. math::
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:label: 14.4
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\frac{dS}{dt} = Q_{in} - Q_{out} + R
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where :math:`Q_{in}` (m :sup:`3` s :sup:`-1` ) is the main channel flow from
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the upstream grid(s) into the main channel of the current grid, which is zero for
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hillslope and sub-network routing. :math:`Q_{out}` (m :sup:`3` s :sup:`-1` ) is
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the outflow rate from hillslope into the sub-network, from the sub-network into
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the main channel, or from the current main channel to the main channel of its
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downstream grid (if not the outlet grid) or ocean (if the current grid is the
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basin outlet). :math:`R` (m :sup:`3` s :sup:`-1` ) is a source term, which
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could be the surface
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runoff generation rate for hillslopes, or lateral inflow (from hillslopes) into
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sub-network channel or water-atmosphere exchange fluxes such as precipitation
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and evaporation. It is assumed that surface runoff is generated uniformly
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across all the hillslopes. Currently, MOSART does not exchange water with
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the atmosphere or return water to the land model so its function is strictly
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to transport water from runoff generation through the hillslope, tributaries,
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and main channels to the basin outlets.
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.. _Numerical Solution MOSART:
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Numerical Solution
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----------------------------
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The numerical implementation of MOSART is mainly based on a subcycling
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scheme and a local time-stepping algorithm. There are two levels of
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subcycling. For convenience, we denote :math:`T_{inputs}` (s),
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:math:`T_{mosart}` (s), :math:`T_{hillslope}` (s) and
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:math:`T_{channel}` (s) as the time steps of runoff inputs (from CLM
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to MOSART via the flux coupler), MOSART routing, hillslope routing, and
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channel routing, respectively. The first level of subcycling is between
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the runoff inputs and MOSART routing. If :math:`T_{inputs}` is 10800s
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and :math:`T_{mosart}` is 3600s, three MOSART time steps will be
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invoked each time the runoff inputs are updated. The second level of
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subcycling is between the hillslope routing and channel routing. This
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is to account for the fact that the travel velocity of water across
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hillslopes is usually much slower than that in the channels.
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:math:`T_{hillslope}` is usually set as the same as :math:`T_{mosart}`,
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but within each time step of hillslope routing there are a few time
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steps for channel routing, i.e.,
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:math:`T_{hillslope} = D_{levelH2R} \cdot T_{channel}`. The local
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time-stepping algorithm is to account for the fact that the travel
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velocity of water is much faster in some river channels (e.g., with
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steeper bed slope, narrower channel width) than others. That is, for
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each channel (either a sub-network or main channel), the final time
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step of local channel routing is given as
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:math:`T_{local}=T_{channel}/D_{local}`. :math:`D_{local}` is
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currently estimated empirically as a function of local channel slope,
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width, length and upstream drainage area. If MOSART crashes due to a
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numerical issue, we recommend increasing :math:`D_{levelH2R}` and, if
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the issue remains, reducing :math:`T_{mosart}`.
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.. _Parameters and Input Data:
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Parameters and Input Data
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---------------------------------
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MOSART is supported by a comprehensive, global hydrography dataset at 0.5
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:sup:`o` resolution. As such, the fundamental spatial unit of MOSART is a 0.5
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:sup:`o` lat/lon grid. The topographic parameters (such as flow direction,
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channel length, topographic and channel slopes, etc.) were derived using the
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Dominant River Tracing (DRT) algorithm (:ref:`Wu et al., 2011<Wuetal2011>` ;
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:ref:`Wu et al. 2012 <Wuetal2012>`). The DRT algorithm produces the topographic
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parameters in a scale-consistent way to preserve/upscale the key features of
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a baseline high-resolution hydrography dataset at multiple coarser spatial
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resolutions. Here the baseline high-resolution hydrography dataset is the
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1km resolution Hydrological data and maps based on SHuttle Elevation
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Derivatives at multiple Scales (HydroSHEDS)
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(:ref:`Lehner and Döll, 2004 <LehnerDoll2004>` ;
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:ref:`Lehner et al., 2008 <Lehneretal2008>`). The channel geometry
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parameters, e.g., bankfull width and depth, were estimated from empirical
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hydraulic geometry relationships as functions of the mean annual discharge.
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The Manning roughness coefficients for overland and channel flow were
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calculated as functions of landcover and water depth. For more details
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on the methodology to derive channel geometry and the Manning’s roughness
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coefficients, please refer to
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:ref:`Getirana et al. (2012) <Getiranaetal2012>` . The full list of
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parameters included in this global hydrography dataset is provided in
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:numref:`Table MOSART Parameters`. Evaluation of global simulations
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by MOSART using the aforementioned parameters is described in
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:ref:`Li et al. (2015b) <Lietal2015b>` .
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.. _Table MOSART Parameters:
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.. table:: List of parameters in the global hydrography dataset
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+-------------------------+---------------+------------------------------------------------------------------------------------------------------------------------------------+
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| Name | Unit | Description |
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+=========================+===============+====================================================================================================================================+
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| :math:`F_{dir}` | \- | The D8 single flow direction for each coarse grid cell coded using 1 (E), 2 (SE), 4 (S), 8 (SW), 16 (W), 32 (NW), 64 (N), 128 (NE) |
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+-------------------------+---------------+------------------------------------------------------------------------------------------------------------------------------------+
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| :math:`A_{total}` | km :sup:`2` | The upstream drainage area of each coarse grid cell |
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+-------------------------+---------------+------------------------------------------------------------------------------------------------------------------------------------+
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| :math:`F_{dis}` | m | The dominant river length for each coarse grid cell |
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+-------------------------+---------------+------------------------------------------------------------------------------------------------------------------------------------+
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| :math:`S_{channel}` | \- | The average channel slope for each coarse grid cell |
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+-------------------------+---------------+------------------------------------------------------------------------------------------------------------------------------------+
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| :math:`S_{topographic}` | \- | The average topographic slope (for overland flow routing) for each coarse grid cell |
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+-------------------------+---------------+------------------------------------------------------------------------------------------------------------------------------------+
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| :math:`A_{local}` | km :sup:`2` | The surface area for each coarse grid cell |
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+-------------------------+---------------+------------------------------------------------------------------------------------------------------------------------------------+
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| :math:`D_{p}` | m :sup:`-1` | Drainage density, calculated as the total channel length within each coarse grid cell divided by the local cell area |
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+-------------------------+---------------+------------------------------------------------------------------------------------------------------------------------------------+
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| :math:`D_{r}` | m | The bankfull depth of main channel |
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+-------------------------+---------------+------------------------------------------------------------------------------------------------------------------------------------+
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| :math:`W_{r}` | m | The bankfull width of main channel |
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+-------------------------+---------------+------------------------------------------------------------------------------------------------------------------------------------+
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| :math:`D_{t}` | m | The average bankfull depth of tributary channels |
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+-------------------------+---------------+------------------------------------------------------------------------------------------------------------------------------------+
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| :math:`W_{t}` | m | The average bankfull width of tributary channels |
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+-------------------------+---------------+------------------------------------------------------------------------------------------------------------------------------------+
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| :math:`n_{r}` | \- | Manning’s roughness coefficient for channel flow routing |
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+-------------------------+---------------+------------------------------------------------------------------------------------------------------------------------------------+
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| :math:`n_{h}` | \- | Manning’s roughness coefficient for overland flow routing |
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+-------------------------+---------------+------------------------------------------------------------------------------------------------------------------------------------+
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Difference between CLM5.0 and CLM4.5
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-------------------------------------
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1. Routing methods: RTM, a linear reservoir method, is used in CLM4.5 for
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river routing, whilst in CLM5.0, MOSART is an added option for river routing
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based on the more physically-based kinematic wave method.
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2. Runoff treatment: In RTM runoff is routed regardless of its sign so
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negative streamflow can be simulated at times. MOSART routes only non-negative
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runoff and always produces positive streamflow, which is important for
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future extensions to model riverine heat and biogeochemical fluxes.
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3. Input parameters: RTM in CLM4.5 only requires one layer of a spatially varying
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variable of channel velocity, whilst MOSART in CLM5.0 requires 13 parameters that
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are all available globally at 0.5 :sup:`o` resolution.
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4. Outputs: RTM only produces streamflow simulation, whilst MOSART
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additionally simulates the time-varying channel velocities, channel water depth, and
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channel surface water variations.
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