GMDGeoscientific Model DevelopmentGMDGeosci. Model Dev.1991-9603Copernicus PublicationsGöttingen, Germany10.5194/gmd-11-4291-2018Dynamic hydrological discharge modelling for coupled climate model simulations of the last glacial cycle: the MPI-DynamicHD model version 3.0Dynamic hydrological discharge modelling RiddickThomasthomas.riddick@mpimet.mpg.deBrovkinVictorhttps://orcid.org/0000-0001-6420-3198HagemannStefanMikolajewiczUweMax Planck Institute for Meteorology, Bundesstraße 53, 20146 Hamburg, Germanynow at: Institute of Coastal Research, Helmholtz-Zentrum Geesthacht, Max-Planck-Straße 1, 21502 Geesthacht, GermanyThomas Riddick (thomas.riddick@mpimet.mpg.de)19October201811104291431616January201829March20183August201824September2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://gmd.copernicus.org/articles/11/4291/2018/gmd-11-4291-2018.htmlThe full text article is available as a PDF file from https://gmd.copernicus.org/articles/11/4291/2018/gmd-11-4291-2018.pdf
The continually evolving large ice sheets present in the
Northern Hemisphere during the last glacial cycle caused significant changes
to river pathways both through directly blocking rivers and through glacial
isostatic adjustment. Studies have shown these river pathway changes had a
significant impact on the ocean circulation through changing the pattern of
freshwater discharge into the oceans. A coupled Earth system model (ESM)
simulation of the last glacial cycle thus requires a hydrological discharge
model that uses a set of river pathways that evolve with Earth's changing
orography while being able to reproduce the known present-day river network
given the present-day orography. Here, we present a method for dynamically
modelling river pathways that meets such requirements by applying predefined
corrections to an evolving fine-scale orography (accounting for the changing
ice sheets and isostatic rebound) each time the river directions are
recalculated. The corrected orography thus produced is then used to create a
set of fine-scale river pathways and these are then upscaled to a coarser
scale on which an existing present-day hydrological discharge model within
the JSBACH land surface model simulates the river flow. Tests show that this
procedure reproduces the known present-day river network to a sufficient
degree of accuracy and is able to simulate plausible paleo-river networks. It
has also been shown this procedure can be run successfully multiple times as
part of a transient coupled climate model simulation.
Introduction
Results of ocean circulation models are very sensitive to
freshwater flux
.
The accurate modelling of ocean circulation requires the river runoff to be
correct for individual ocean basins and distributed with a roughly accurate
spatial pattern around each basin's edge. During the last glacial cycle, the
courses of rivers in North America, northern Europe and Siberia were
significantly altered by a combination of the physical presence of the ice
sheets directly blocking the flow of rivers and the effects of isostatic
adjustments altering the orography of ice-free areas
.
Previous studies indicate that modelling of these alterations may play an
important role in the success of a transient simulation of the last glacial
cycle . A comparison of a reconstructed
orography for the Last Glacial Maximum (LGM) to a present-day orography
indicates that the most significant changes in orography occurred close to
the ice sheet. Africa, much of South America and southern Asia were only
weakly affected by the changes in the orography. Here, we introduce a
dynamical model of river pathways and hydrological discharge for the
simulation of glacial cycles that accounts both for the physical presence of
ice sheets and for isostatic adjustments.
JSBACH is the land surface scheme of
the Max Planck Institute for Meteorology's Earth system model (MPI-ESM)
. In this paper, we use JSBACH 3.0, which has undergone
further developments since the version (JSBACH 2.0) used for the Coupled
Model Intercomparison Project 5 as
described in . These developments are a new soil carbon
model and a new five-layer soil hydrology scheme
instead of the previous bucket scheme.
In JSBACH, lateral freshwater fluxes are treated by the Hydrological
Discharge (HD) model . Although the HD
model is included in JSBACH, it can also be run independently as a standalone
model. In this model, lateral freshwater fluxes are split into three
components: base flow, overland flow and river flow. Base flow represents the
slow movement of water in the lowest layer of the soil, overland flow
represents surface flow outside of channels, and river flow represents channelled surface flow. The HD model is
run on a 0.5∘ regular latitude–longitude grid with a daily time
step. All three components of the flow from a cell are directed to one of the
cell's eight direct neighbours. Within each grid cell, river flow is modelled
through a cascade of linear reservoirs; a cascade of linear reservoirs in
each cell is necessary to accurately simulate both the translation
characteristics (which determine how fast water passes through the cell) and
retention characteristics (which determine how much water is stored in the
cell) of each cell. The number of reservoirs (nr) is set to 5
(with the exception of cells containing major lakes; however, such lakes are
switched off entirely in the version of the HD model used for dynamic
hydrological discharge modelling by this paper as their formulation is
unsuitable for modelling lakes that evolve with a changing orography). The
river outflow as a function of time Q(t) from each reservoir is modelled as
Q(t)=S(t)k,
where S(t) is the water content of the reservoir as a function of time and
k is the water retention time (also called the retention coefficient) of
each reservoir. The retention time for rivers kr is calculated
(in days) for each cell in the grid; thus,
kr=0.992daysm-1⋅Δxs0.1,
where Δx is the distance to the centre of the next downstream cell
from the centre of the cell under consideration (in metres) and defining
slope s=ΔhΔx with Δh as the change in
orography between this cell and the next downstream cell (in metres). The
sign of Δh is defined such that s is positive for a downhill slope.
s is set to a constant value of 1.315×10-5 when its original
value is either negative or zero. In this paper, the set of reservoir
retention coefficients for all three of the components of the flow for the
whole globe are known collectively as the flow parameters.
In the standard version of the HD model for the present day that is part of
JSBACH, the direction of flow is decided by a set of manually corrected
present-day river directions referred to in this paper as the manually
corrected (present-day) HD model river directions. These manually corrected
(present-day) river directions are derived by first applying a downslope
routing to a pit-filled orography; then correcting by hand to ensure the
correct paths for the world's major rivers; and finally further correcting by
hand the catchments of major rivers based on careful comparison with
reference catchments.
The surface runoff and soil drainage of a cell from the JSBACH model are
added to the overland flow and base flow, respectively, and the flow of these
through the cell is modelled in each case by a single linear reservoir. The
water retention time for overland flow reservoirs is calculated using the
average slope within a grid box itself when considered on a finer scale (the
inner slope) along with the Δx as defined above; see
for details. The method for calculating the water
retention times for base flow is similar to that given in
but takes into account some spatial variability
(Beate Müller, personal communication, 1998). Base flow retention times
tend to be roughly 3 orders of magnitude longer than those of overland and
river flow. The outflow from all three components is summed and this is used
as the input for the river flow of the next downstream cell. When evaluated
in an inter-model comparison study , the
performance of the HD model as a component of the Max Planck Institute
Hydrology Model (MPI-HM) did not differ
significantly from those of similar components of other global hydrology
models.
The challenge for a paleoclimate simulation is to develop a method for
periodically updating the river directions and flow parameters used with
sufficient accuracy . If the simulation calculates changes
in the orography from the output of an interactive ice-sheet model within a
wider ESM, then another requirement is that the river directions and flow
parameters can be recalculated quickly when it is necessary to update them.
Given the large inaccuracy in the distribution of precipitation likely to
occur in paleoclimate simulations, it will suffice to capture only the main
features of the river directions and the flow parameters especially need only
be a rough approximation. The fine details of catchment boundaries and
outflow points and the exact temporal response of the discharge model to
precipitation events will not be required. Generating river paths is however
challenging as the natural scale determining the path of rivers is often far
smaller than the scale it is feasible to provide an orography on. Examination
by eye of orography datasets shows that narrower river valleys of major
rivers are not resolved on a 0.5∘ grid, partially resolved on a
10 min grid and well resolved on a 1 min grid (although mistakes in the
paths of major rivers, e.g. the Mekong, still occur even if a 1 min
resolution orography is used). Another challenge of generating river
directions is false sinks, closed depressions that are artefacts of the
digital elevation model (DEM) and do not physically exist. Lack of detail in
the orography can mean the height of riverbeds is overestimated at some
points in narrow valleys, thus leading to apparently closed pits or sinks
being found in the orography. False sinks also appear at higher resolutions
due to various imperfections in the measurement of orography by satellite
. If river directions are generated from an
unmodified orography by the line of steepest descent, then these will be
marked as inland sink points, while they are actually unimpeded rivers.
Therefore, an algorithm is required to either fill in these false sink points
or to let rivers “carve” out of them.
Most previous ESM-based simulations of the last glacial cycle have used the
technique of extending present-day river directions to the sea
e.g.. This was a suggested method for the
Paleoclimate Modelling Intercomparison Project Phase 3 (PMIP3)
. A number of authors have tackled
the problem of modelling river routing during the last glacial cycle.
provides river maps for various time points during
the deglaciation derived directly from a 30 s orography combined with
various ice-sheet reconstructions (alongside a useful comparison of these
river maps to known data). However, this technique would be too
computationally expensive to run fully automatically every 10 years during a
transient simulation. present a dynamic river
routing and lake model for North America during the Younger Dryas that is in
many ways similar to that presented here and from which the basic principle
of upscaling of effective hydrological heights was taken. However, our new
model uses a different combination of upscaling techniques and orography
corrections from those of as well as a
different grid.
Most previous simulations of the last glacial cycle that use coupled global
circulation models (GCMs) have only treated time slices; transient
simulations have usually been run only in Earth system models of
intermediate complexity (EMICs). present a dynamic
river routing module for much of the Northern Hemisphere to produce
freshwater inflows from ice-sheet meltwater (direct precipitation was not
considered) for the CLIO ocean model , a
component of the LOVECLIM EMIC , driven by the
ice-sheet model NHISM . There method is to
transform the HYDRO1k hydrologically condition present-day orography
to a 25 km polar stereographic grid by two-dimensional
Lagrangian polynomials and use this as a base orography to which to add
ice-sheet height corrections and isostatic corrections to during a simulation of
the last deglaciation. They note the need to apply some manual corrections to
resolve blocked valleys in the present-day orography. The ESM model of
, which is a precursor to the model the method presented
here will be used in, used a simplified method to treat river routing
following similar ideas to those presented here.
The first transient synchronously coupled GCM simulation of the deglaciation
was . This used a time-varying prescribed forcing to simulate
the release of glacial meltwater from rivers. However, the PalMod project
, which the approach presented here is intended for, aims
to run simulations that limit external forcings to just solar and volcanic
forcings, thus running transient models using a fully self-consistent ESM and
clearly precluding a proscribed-forcing-based approach to meltwater runoff.
An important test of any method is the ability to accurately generate
present-day river directions. Large rivers away from the ice-covered regions
of Earth do not appear to have drastically changed their course during the
last glacial cycle, so for large areas of Earth the river directions should
be the same as the present-day river directions for the entire glacial cycle.
Early testing showed that generating river directions on a 0.5∘ grid
by simply following the line of steepest descent gives unsatisfactory results
for present-day river directions. Using the same technique on a 10 min
grid gives better results although there are still some mistakes. Our method
aims to correct those mistakes such that the present-day river directions can
be accurately reproduced on a 0.5∘ grid.
The HD model within JSBACH was originally designed for use in
near-present-day simulations with static river directions and flow
parameters. Several other components of the MPI-ESM that may also be expected
to change on paleo-timescales were likewise designed for use with static
input data for near-present-day simulations, e.g. the land–sea mask.
Adapting MPI-ESM to allow the static input data of such components to be
replaced with a time-varying field within the model would in some cases have a considerable negative impact on
the model's performance and/or be very technically challenging. (Both of
these difficulties would apply in the case of river directions and flow
parameters.) As these components only vary comparatively slowly with time
compared to the model's time step, it will instead be sufficient to only
update them at a set interval of 10 years. Every 10 years, during a long
transient run, MPI-ESM will halt and a number of processing scripts will be
run to update otherwise static input data before MPI-ESM is restarted for the
next 10-year section with the new input data. The input data updated will
include the river directions and flow parameters. These will then remain
constant during the next 10-year section. For transient runs where MPI-ESM is
coupled to an ice-sheet model, during each of these decennial updates,
isostatic corrections will first be calculated using a viscoelastic Earth
model, for example, the Viscoelastic Lithosphere and Mantle (VILMA) model
, and alongside the height of the
ice sheet be applied to a present-day base orography to create a general
orography for a given time. This will then act as an input to the process of
updating the river directions and flow parameters.
MethodOverview of method
The starting point for a simulation of the last glacial cycle is a simulated
10 min resolution orography for time t in the simulation including the
height of any ice sheets and isostatic corrections along with the same
10 min resolution orography for the present day; this latter orography is
hereinafter referred to as the present-day base orography. From this pair of
orographies, the height anomalies for time t with respect to the present can
be calculated and applied to a present-day reference orography to which we
also apply height corrections (as described below); this is necessary as
different present-day orographies can differ markedly due to differences in
their methods of fabrication, and thus height corrections must be applied to
the particular present-day orography they were created for. (Note it would
also be possible to work with a pair of orographies on a different
resolution, then remap the anomalies between them to a 10 min resolution.)
River directions are regenerated every 10 years by a four-step process. A
brief outline is given here; detailed descriptions of each step are given in
the subsequent sections. A flow diagram outlining the steps is given in
Fig. . Firstly, the orography for time t
is adjusted by subtracting the matching present-day base orography and adding
a given reference present-day orography (see
Sect. and also the
discussion in the preceding paragraph). Secondly, a pre-generated set of
relative height corrections for a small number of cells (or all cells in the
case of North America, where a different algorithm is used to generate the
corrections) are added to this orography (see
Sect. ). These relative height corrections are
such that when applied to the given reference present-day orography they
return a set of river directions with all of the major errors in river paths
and catchments corrected. Thirdly, a set of sinkless river directions on the
10 min grid is generated using the river carving method of
(see Sect. ).
Fourthly, these river directions are upscaled to the 0.5∘ grid
required by the HD model (see Sect. ). Flow
parameters are generated on the 0.5∘ grid using an upscaled and sink
filled version of the 10 min orography for time t (see
Sect. ).
Flow diagram illustrating the steps of the method presented here for
generating river directions and flow parameters for dynamic hydrological
discharge modelling. (Here, “upscale orography by meaning” means simply
taking the mean value of the nine 10 min DEM cells contained within the
area covered by each 30 min DEM cell as the value of that 30 min DEM
cell.)
The process described above for the generation of river directions and flow
parameters is entirely automatic. Prior to the first application of this
process, it was necessary to develop the abovementioned pre-generated set of
relative of height corrections. This development was guided and evaluated by
hand although making extensive use of automated tools to expedite the
development process and improve the accuracy of the corrections in certain
regions. Alongside these automated tools, some corrections were also made by
hand. The development of these corrections is discussed extensively in
Sect. .
A useful diagnostic derived from sets of river directions is the total
cumulative flow. For each cell, this is the total number of upstream cells
that flow, directly (i.e. without passing through any other cells first) or
indirectly (i.e. passing through other cells first), into that cell. In this
paper, we also count the cell itself within the total cumulative flow; thus,
the total cumulative flow of any cell is equal to the sum of the total
cumulative flows of all cells that directly flow into it plus 1. Total
cumulative flow is a property of the river directions as a dry system and
does not account for variations in rainfall. It also does not account for the
variation of latitude–longitude cell surface areas with latitude.
Changing the present-day base orography
The first step is to change the present-day base orography underlying any
given input orography for time t to match the present-day reference
orography used to generate the DEM corrections. In the case of all the data
generated for this paper, this present-day reference orography was ICE-5G
version 1.2 . This is done by applying the following
modification to an input orography on a cell-wise basis:
hworking orography=hstandard past orography-hpresent-day base orography+hpresent-day
reference orography,
where hworking orography and hstandard past orography
are the height values of a cell at a
given time t in a paleoclimate simulation, while hpresent-day base
orography and hpresent-day reference orography are the
present-day height values of the
given cell from two different DEMs. All these orographies will have a
10 min resolution. The present-day base orography is the base orography
that is used by a viscoelastic Earth model to produce general purpose
orographies for times in the past for a wider ESM (in a setup with a coupled
ice sheet; otherwise, it is the base orography that was used to derive the
ice-sheet reconstruction being used). The standard past orography is then the
orography derived from the present-day base orography (again, in a setup with
a coupled ice sheet; otherwise, it is just the orography reconstruction being
used) for time t via glacial height adjustments from the ice-sheet model
and isostatic adjustments from the viscoelastic Earth model. For any given
cell,
hstandard past orography=hpresent-day base orography+hglacier+Δhisostatic,
where hglacier is the vertical thickness of the ice sheet in the
cell (which is set to zero if the cell does not contain an ice sheet) for time
t and Δhisostatic is the isostatic adjustment for the
cell for time t. The present-day reference orography is the present-day
orography used in the derivation of the corrections used in the second step
of our method. The working orography is a new intermediary working orography
(for time t) specifically used by our river direction generation process;
it is this the DEM corrections are applied to in the second step of that
process.
This first step is necessary because comparisons show due to differing
methods of fabrication different 10 min present-day base orographies used
in paleoclimate simulations can differ in many cells quite widely (by as much
as several hundred metres in height in areas of very high inter-cell height
variance). These differences are systematic and are apparently due to biases
in the processing of original satellite data (often on a finer scale) to
produce the 10 min present-day orography. In the ESM setups, this method is
intended for the present-day base orography will often not be the same as the
present-day reference orography, as the present-day base orography is likely
to be set for the wider ESM setup the HD model is embedded in, while the
present-day reference orography that all the DEM corrections discussed in the
next section were generated for is ICE-5G, and it would require significant
effort to regenerate these for another reference orography. Preliminary
testing showed that the DEM corrections applied in the second step of our
method are only valid for orographies generated from the same present-day
base orography that the corrections themselves were derived for (i.e. the
present-day reference orography), and thus it is necessary to adjust the input
orography such that these corrections are still valid.
Although it is intended to use this method with all the input orographies on
a 10 min resolution, this step provides the option of alternatively using
a paleo-orography and corresponding present-day base orography that are of a
lower resolution than 10 min.
DEM corrections
The set of relative height corrections applied in the second step was
derived through comparison with a variety of sources of information on
present-day river paths and catchments. The development of these relative
height corrections was a one-time task which was guided and overseen by hand
even when some elements were automated. This set of relative height
corrections is provided as input data to each application of the main river
routing and parameter generation process which is in itself fully automatic.
Three techniques were used to generate these corrections: application by hand
to individual orography grid points, intelligent river burning applied to
selected regions and upscaling effective hydrological heights from a very
high-resolution orography. Each of these techniques is described (including
definitions of the terms “intelligent river burning” and “effective
hydrological heights”) individually below. In North America, upscaling
effective hydrological heights was used in combination with the other two
methods. Only hand application of corrections and intelligent river burning
were applied to the rest of the globe. Both combinations of techniques are
expected to produce satisfactory results; the combination of upscaling
effective hydrological heights and the other two techniques is expected to
produce slightly more accurate results in regions where river pathways
changed significantly during the last glacial cycle than just using the other
two techniques. However, upscaling effective hydrological heights was
developed after the other two techniques and it was noted that significant
additional effort was required to apply it to North America (justification of
this choice of trial region is given below); thus, it was decided not to apply
it to the rest of the globe.
The application of both of the first two methods was directed by comparison
with the manually corrected present-day HD model river directions (through
plots of total cumulative flow and catchment maps) and by comparing with
river directions generated from a finer 1 min orography (through plots of
the total cumulative flow only). Differences were resolved using the
catchment data of the HydroSHEDS database . (Online
geographical information from a wide range of sources was used to aid
interpretation.) The relative corrections applied by hand usually correct the
height of the cells of the 10 min present-day orography to the height of
the valley floor of the river under consideration observed in the 1 min
orography. Occasionally, some guesswork and judgement had to be applied to
decide what the true height of the valley floor was; in a few specific cases,
the valley was also poorly defined at a 1 min resolution (e.g. the Iron
Gates gorge on the Danube).
Intelligent burning of small manually selected regions (usually short
sections of an individual river valley) produces similar results but
automates the procedure. River directions are generated for the present day
from a “super-fine” 1 min orography using the same carving algorithm as
described below and the total cumulative flow is generated from these
super-fine river directions. The 1 min orography is masked outside a selected
region and then further masked within that region where the super-fine total
cumulative flow is below a given threshold. Then, the height of each cell in
the 10 min orography is replaced with the highest unmasked height (if any)
within the area of the 1 min orography that corresponds to that 10 min
cell (as long as that height is lower than the present height of the cell in
the 10 min orography; otherwise, it is left unmodified). This quickly burns
a river from the super-fine 1 min orography into the 10 min orography
but, unlike regular stream burning techniques
, only to the
depth observed in a finer orography. Thus, the height of the riverine cells in
the burnt area remains realistic to within the accuracy of a finer orography;
thus, the possibility of the river changing direction during the glacial cycle
due to changes in the orography remains unimpeded. Note stream burning should
not be confused with the largely unrelated technique of river carving. The
total cumulative flow threshold mentioned can differ for each region where
intelligent burning is applied and is set by hand for each case such that
only the cells of the super-fine orography through which the main river flows
in the region of application in question remain unmasked. The results of each
application of intelligent burning were examined carefully by eye before
proceeding. Once the burning process is complete, the changes in the 10 min
orography for the present day are converted to relative changes in height
(suitable for application at any time during the glacial cycle) by
subtracting the original unmodified version of the orography.
Corrections generated using either one or the other of the first two methods
(or a combination of the two) were applied all across the globe to eliminate
all significant errors seen in the river directions derived from a 10 min
orography, with the exception of some problems related to true sinks which
were ignored, as true sinks will not be used when generating dynamic river
directions. Hand application of corrections was usually used where only a few
cells needed to be changed; intelligent burning was used where an error in
the river directions for a particular section of a river needed a larger
number of corrections to resolve. Similar results could have been achieved
using application of corrections by hand alone but this would have been
significantly more time consuming.
Figure shows how applying an
appropriate correction corrects a problem in the catchment of the Danube.
Comparison of the Danube catchment showing the catchment (grey area)
and rivers with a total cumulative inflow greater than or equal to 75 cells
(blue cells) derived from (a) manually corrected 0.5∘ HD
model river directions as a reference, (b) automatically generated
river directions for a 10 min grid and (c) automatically
generated river directions for a 10 min grid once height corrections have
been applied to a few selected cells in the orography.
We define the effective hydrological height of a cell within a DEM as the
elevation of the river sill within the cell. This is namely the height of the
highest point in the “most likely” river pathway through the cell when
examining the internal structure of the cell's height within a much finer
DEM. The most likely river pathway is defined as the path whose maximum
elevation while transversing the cell is lowest, disregarding any paths that
do not cross a significant fraction of the cell. The basic principle of
upscaling effective hydrological heights was adopted from
. The actual algorithm used here is different
from that of and was developed specifically for
this paper; however, the results achieved should be very similar for most
grid cells (differences may occur along catchment boundaries and for narrow
channels crossing the border between two cells at a very acute angle). The
technique of upscaling effective hydrological heights was only used for North
America (the land boundary of its application being the narrowest point of
Central America to minimise any possible edge effects) as this was seen as a
critical region for palaeohydrology, and Tarasov and Peltier have previously
shown this technique to be effective in this region. Upscaling effective
hydrological heights could also potentially be applied beneficially to
Eurasia; however, we decided against doing so because of the significant
additional effort required.
We give here a brief outline of the algorithm; more detailed descriptions of
the algorithm are given in
Appendices and
. The algorithm used
here works by exploring possible paths through each of a set of sections of a
fine orography that correspond to the individual cells of a coarse orography.
This is performed by flooding each coarse cell on a fine-cell-by-fine-cell
basis according to height while filling in any false sinks if necessary. (By
the term “flooding”, we mean here processing the cells of the fine DEM in
the order they would fill with water if the entire coarse cell was to be
gradually filled with water starting from the lowest point on the cell's
boundary and assuming the cell was surrounded by a continuous rising body of
water such that disconnected basins within the cell could start filling from
separate edges.) A path is a pair of cells connected by a particular sequence
of intermediary cells, each one of which directly neighbours (including
diagonally) the next cell and the previous cell in the sequence. Paths start
from the edges of the section (or next to points marked as sea in a land–sea
mask) and continue until they meet another edge (or point neighbouring the
sea). When a path is finished, it is tested to see if its length exceeds a
threshold; this rejects short paths that only cross a single corner of the
cell and therefore are not representative of a flow “across” the cell. If
it returns back to the edge from which it started, then the greatest
perpendicular separation of the path at any point from its starting edge must
also exceed a threshold; this rejects paths that flow back to the same edge
unless they represent a meander of a significant size. If the path passes
these tests, then it is accepted as the lowest valid path through the cell.
As any false sinks will have been filled by the algorithm while searching for
the path, the last point on the path will be the highest (or joint highest)
point on the path. The height of this point is then taken to be the new
effective hydrological height of the corresponding coarse cell. Various
aspects of the algorithm are illustrated in
Fig. ; these are best understood in
conjunction with the two aforementioned appendices.
Diagrams illustrating various aspects of the orography upscaling
algorithm. In panel (a), the division of a DEM grid into sections is shown;
the upscaling algorithm processes each section separately to produce an
effective hydrological height for each section. Panel (b) shows the
initial cells (see main text of
Appendix ) added to the queue at
the start of the algorithm including the neighbours of a sea point.
Panel (c) shows three paths: two complete but rejected because they do not
meet the selection criteria (see main text) for a valid lowest path, and one
incomplete. The short path in the bottom left corner is complete but its
length is too short for it to qualify as the lowest valid path through the
cell; the longer path on the right is also complete but it returns to the
same edge it started at without having met the required maximum separation
from the initial edge threshold. The path in the middle, which branches from
the short path in the bottom left, is incomplete and a cell at its end is
undergoing processing. Half this cell's neighbours have been added to the
queue; the other half have been skipped because they have already been
processed. In panel (d), we show a valid lowest path through the cell that
returns to its initial edge but meets both of the selection criteria, while in
panel (e), we show a valid lowest path through the cell that spans two
different edges and has several incomplete paths branching off it.
The parameters MinimumPathThreshold and
MinimumSeparationFromInitialEdgeThreshold (whose use is described in
Appendix ) are both set to
0.5×ScaleFactor, where
ScaleFactor=number of latitude points in the
coarse grid/number of latitude points in the fine
grid.
Originally MinimumPathThreshold was set to
1.0×ScaleFactor to mirror the equivalent parameter in Tarasov
and Peltier's method; however, it was noted that this resulted in narrow
channels running near parallel across the border between two cells being
“blocked” (both cells having much higher effective hydrological heights
than the rest of the channel and thus causing errors in the river directions
generated from the upscaled orography created). The current value prevents
these blockages and ensures at least one of the two cells the channel runs
through has the same hydrological height as the rest of the channel. The
algorithm given here can be used on both hydrologically conditioned
orographies such as HYDRO1k (as used by
) and normal (unconditioned) orographies (with
false sinks).
For this paper, we upscale the unconditioned 30 s orography SRTM30 PLUS
to a 10 min grid using the effective
hydrological height orography upscaling algorithm described above. The
orography upscaling process (which need only be run once) takes approximately
25 min to run for the entire globe (from which the section for North
America is then extracted) on a single core of a 2015 MacBook Pro laptop.
This extracted section then forms another component of the set of height
corrections once it has been combined with any existing corrections in this
region.
Where existing corrections from the first two techniques were present in
North America, the lower value out of the existing correction and the upscaled
effective hydrological height was used. Once complete, the corrections were
converted to relative corrections by subtracting the original unmodified
10 min orography. While in many places the application of upscaled
effective hydrological heights improves North American river paths, in some
places, the application of this technique introduced new errors. These errors
were corrected by a second round of corrections applied by hand. (It was the
necessity to verify changes in the river paths after applying effective
hydrological heights and make a second round of additional corrections by
hand that required significant additional effort which, as noted above, in
turn drove our decision to limit the application of the upscaling of
effective hydrological heights to North America.)
When these corrections are applied to an orography for a time other than the
present day, any relative corrections that are beneath ice sheets are
temporarily suppressed until the region becomes ice-free once more; thus, the
original unmodified height is always used for ice sheets. The corrected
orography for a time in the past, t, to which the river carving algorithm
is applied in the next section will at a given cell be
hcorrected orography=hworking orography+ΔhDEM correction,if hglacier=0hworking orography,otherwise,
where ΔhDEM correction is the fixed relative DEM correction
for the given cell from the set of relative DEM corrections whose development
has been discussed extensively in this section; hcorrected
orography is the height of the corrected orography at the given cell for
time t; hworking orography is the height of the intermediary
working orography as defined in the previous section; and
hglacier is again the
vertical thickness of the ice sheet in the cell (which is set to zero if the
cell does not contain an ice sheet) for time t.
False sink removal
In the third step, the problem of false sinks is solved by using an algorithm
that carves rivers out of sinks from the sink's deepest point
. ( gives a good general
overview of priority queue based sink filling algorithms including the
particularly clear presentation of the river carving algorithm from
that was followed in the writing of the code for
this paper.) The algorithm of imitates water
draining from an area through a narrow valley that is not resolved in the DEM
because the resolution is insufficient. This gives very similar results to
sink filling except that it gives better directions for rivers within the
sink itself; although this is most likely unimportant for the final result,
it can aid the visual comparison of river paths. This algorithm produces
river directions directly and neither modifies the input orography itself nor
needs to produce a modified copy of it (although in the code written for this
paper, it can if required create such a copy for purely diagnostic purposes).
Both this algorithm and the orography upscaling algorithm are based around
the abstract data type called the priority queue. In the context of these
algorithms, a priority queue is a queue where the cells are kept ordered by
ascending height. (More generally a priority queue is any queue kept ordered
using a given comparison operator.) In this algorithm, the queue is initially
filled with land cells that neighbour the ocean. At each step, the cell
at the head of the queue (with the
lowest height) is removed and processed. Its direct neighbours are assigned
river directions pointing to the cell and then added to the queue themselves
unless they have already had directions assigned to them previously (in which
case they are ignored as they were processed previously; the river direction
assigned to them is unchanged and they are not added to the queue again). By
following this procedure when the lowest point on the lip of a sink is
reached, the algorithm will follow the river down to the bottom of the sink
marking a river path that carves out of the sink (i.e. flows uphill) from the
bottom to the lip of the sink. Within the sink, cells not directly
neighbouring the exit path will
drain towards the bottom of the sink where they will join the exit path. The
possibility exists to mark some points as potential true sinks (i.e. real
endorheic basins); if these are in a sink, then they are treated as the
outflow point for that sink; otherwise, processing continues normally.
However, this option is not used as it has been decided to remove all true
sinks completely when generating dynamic river directions. This closes the
water balance using the assumption that precipitation in an endorheic basin
would eventually end up in a neighbouring non-endorheic basin either through
atmospheric recirculation or via a slow seepage of ground water. This
assumption is made in the absence of a full model of dynamic lakes; it may be
removed if these are treated by further work. In this absence of dynamic
lakes, it is necessary to make this assumption (or a similar assumption that
the water flowing to true sinks can be redistributed directly into the ocean)
as water conservation is critical for multi-millennial transient paleoclimate
simulations. The effects of omitting true sinks are effectively the effects
of not modelling dynamic lakes; these effects are discussed in
Sect. . It is still useful to include true sinks
when generating data for validation against known modern-day river direction
information (which also includes true sinks).
Upscaling procedure
The fourth step upscales the 10 min river directions that have been
generated to a 0.5∘ grid using a variant of the Cell Outlet Tracing
with an Area Threshold (COTAT)+ upscaling algorithm .
This algorithm itself contains three major steps. The grid cells of the finer
grid, referred to as pixels, are grouped into sections corresponding to the
cells of the coarse grid (these sections are then themselves referred to as
cells). The first step is to identify the outlet pixel of each coarse grid
cell. This is the pixel with the highest cumulative outflow which meets at
least one of two criteria. The first criterion is that the path leading to
the pixel through the cell (along the line of greatest overall cumulative
flow) satisfies a minimum path length threshold. The second criterion is that
the pixel drains the largest number of pixels within the cell in question.
These are introduced so that the river direction of the cell is determined by
the main river flowing through the cell excluding any rivers that just skirt
through a corner of the cell unless they have a tributary which drains a
large fraction of the cell itself. The second step is to decide a flow
direction for each cell. For each cell, the flow path is traced downstream
from the chosen outlet pixel until its total cumulative flow has increased by
a set amount or it exits from the direct neighbours of the central cell. The
river direction points towards the cell where the downstream tracing
finishes. This increases the use of diagonal river directions compared to
simply choosing the cell that the outlet pixel directly flows into. The third
step is to remove the rare situation of crossing river directions by
redirecting the flow direction of the cell whose outlet pixel has the lower
total cumulative flow into the same cell as the cell whose outlet pixel has
the higher total cumulative flow flows into. However, this third step is not
used in the variant of the algorithm used here. Although rivers crossing is
clearly unphysical if it did occur, it would not negatively affect the
quality of the upscaling in terms of the mapping of catchments to river
mouths. Instead, two scans are run to identify rarely occurring loops in the
upscaled flow directions and reprocess the cells where they are occurring to
remove them; in each case, favouring preserving the river with the highest
total cumulative flow.
Flow parameters
The flow parameters are determined using a 0.5∘ orography created by
upscaling the 10 min orography for time t by simply averaging the
orography values of the fine grid cells within each coarse grid cell. False
sinks are removed from this upscaled orography using a conventional
pit-filling priority flood algorithm
(without applying a slope
across sinks being filled, so filled sinks are perfectly flat) before it is
used to derive the flow parameters. The flow parameters are generated using
the same procedure as used for the regular HD model with a few modifications.
It was observed in preliminary tests that sink filling occurs across a range
of landscapes from rugged to flat, and thus generating reservoir retention
coefficients for cells within filled sinks as if they were always in an
extremely flat region could produce overall an unrealistically slow rate of
discharge along rivers. Thus, when generating retention coefficients, if 0≥s (meaning either that the cell and its downstream neighbour are both filled
sink cells or that the river is flowing uphill when considered on the
0.5∘ scale or the region is actually completely flat to within the
accuracy of the DEM), then the value of s is replaced with
s=1.31×10-5, a slope value that was observed to produce a typical
flow rate. This mostly applies to the generation of river flow retention
coefficients; however, it may also be relevant for the generation of overland
retention coefficients in a few cells. River reservoir retention coefficients
use the Δx and s values from the orography for time t upscaled to
the 0.5∘ grid. Overland flow retention coefficients use present-day
inner-slope values from the current JSBACH model where those are non-zero
along with the Δx values for time t (Δx is different for
cells with river directions parallel/perpendicular to the grid and those with
river directions at an oblique angle to the grid and thus varies with time);
otherwise, they are generated by a similar technique to the river flow
retention coefficients using data from time t only. Base flow retention
coefficients use a similar approach, using existing data for the present day
where available to account for spatial variability otherwise reverting to the
original formulation of . This approach to overland
flow and base flow retention coefficients is chosen for simplicity; accurate
representation of temporal changes in these parameters is not considered to
be important provided plausible values are used throughout the transient
simulation.
The initial reservoirs for starting a transient paleoclimate simulation are
set by adapting the present-day initial reservoirs from the existing HD
model. Using a set of present-day river directions and flow parameters
generated by the method presented in this paper, points that are ocean due to
land–sea mask differences (possible as present-day land–sea masks can vary),
lakes, negative flows (possible due to P-E on glaciers) and wetlands are
all removed and replaced with the value(s) of the highest (non-removed)
direct neighbour or if that is not possible then the global average(s) (for
that/each reservoir type). This setup was run for a year for the present day.
It is observed that the model reaches equilibrium or very close to
equilibrium after running half a year when no lakes or wetlands are
included. The restart file from this run provides starting values for
transient paleoclimate simulations using dynamical hydrological discharge
after performing the same set of operations as above on it again (though
obviously there are no lakes or wetlands to remove) using the river
directions and flow parameters generated from the starting orography and
land–sea mask of the transient climate simulation. The initial reservoirs for
periodic restarts of a transient paleoclimate simulation (that occur after
stopping to recalculate river directions and flow parameters and any other
slow processes necessary) are taken from the restart file produced at the end
of the previous run segment. If changes in the land–sea mask have created new
land, then all of the reservoirs in the new land cells are initialised to
zero, while if changes in the land–sea mask have flooded land, then the contents of
all of the reservoirs in the flooded land cells are released into the ocean.
Code and performance
Both the sink filling and river carving algorithms and the orography
upscaling algorithm are written in (object-oriented) C++ and share a single
code base. The river catchments on the 10 min scale used in figures are
also generated simultaneously to river carving by the same code. This is
effectively an application of the algorithm of
and . The COTAT+ variant used is written in
object-oriented Fortran 2003. Other ancillary tasks are performed in Fortran
90 or Python. Both the sink filling/river carving/orography upscaling
algorithms and the COTAT+ river direction upscaling algorithm are designed to
be easily extendable to other grids (such as the triangular grid of the
ICON-ESM; ). The total runtime of the code required to
generate river directions and flow parameters for a given time slice on a
modern desktop PC with a (multi-core) 3.5 GHz Intel processor is about
1 min. It is clear from these results that the performance of this code
presents no significant issues and it will clearly not impede the performance
of the coupled climate model simulations in which it is intended to be
embedded. Given the short runtime of the code, parallelisation was deemed
unnecessary.
Evaluation for the present day
River directions were evaluated using the total cumulative flow and river
catchments. An evaluation of the areas of catchments of major rivers derived
from the river directions generated from a 10 min orography using the
method presented here shows that in most cases they match those of the
manually corrected river directions currently used in JSBACH to within
5 %. Evaluation by eye confirms that the catchment shapes are also very
similar. All significant disagreements were identified as being due to minor
deficiencies in the manually corrected JSBACH river directions by cross
checking against the HydroBASINS catchments. HydroBASINS are a part of the
HydroSHEDS dataset . Adjustments were made to discount
discrepancies due to uncorrected true sinks in the river directions derived
from the 10 min orography (as noted above, some true sink related errors
were ignored in the creation of the corrected orography as all true sinks
will be removed for actual paleoclimate simulations).
Figure
shows zoomed sections comparing the catchments of three major rivers chosen
as examples for the manually corrected 0.5∘ present-day HD model
river directions and for those derived from the 10 min river directions
generated from a corrected 10 min present-day orography. While good
agreement is generally observed in these three examples, a number of
differences are clear around the edges of the catchments. Each difference
comprising more than one or two cells has been checked against various
sources of hydrological information; in every case, the difference is either
due to a minor error in the manually corrected JSBACH river directions or lies in an area of desert with no discernible rivers.
Comparison of the manually corrected 0.5∘ catchments for
the present day (“default HD”) to those of the 10 min directions
generated from a corrected 10 min present-day orography (“dynamic HD”)
for the Nile, Mekong and Mississippi.
The upscaling algorithm upscales catchment areas to within an accuracy of
1–2 % or less in almost all cases for the present-day river
directions. Evaluation by eye shows that catchment shapes are also extremely
similar before and after upscaling. An example of the successful upscaling of
the catchment of the Mississippi is given in
Fig. . As can be observed, only a few
isolated single cell differences occur. Two cases occur where some additional
water enters one catchment and is lost from another catchment. However, if
this comparison is repeated for river directions generated without true
sinks, then these problems disappear. The only significant problem is the
upper reaches of the Mekong catchment being incorrectly directed into the
Yangtze, while some water from the Salween River is diverted into the Mekong
(thus, overall, the total area of the Mekong catchment is roughly correct but
the Salween catchment's total area is
too small and the Yangtze's too great,
and the actual location of all three rivers' catchments is partially
incorrect). This is illustrated in Fig. .
This problem is due to the COTAT+ algorithm being unable to cope with the
three rivers flowing very close to each other in Yunnan province, China. This
could be fixed by allowing non-local flows and using an algorithm like the
FLOW algorithm but this would require considerable
modification of the existing JSBACH HD model. Another possibility would be to
run both COTAT+ and an algorithm that generates non-local flows and use the
latter to identify and remove disconnects in the former by slightly
displacing river paths where necessary.
Comparison of the upscaled catchments of the Mississippi and Mekong
on a 0.5∘ grid to the original 10 min version.
Figure shows a
validation of the automatically generated and upscaled river directions
against the manually corrected river directions. Although many differences
are observed, most of these do not affect which outlet drains which area.
Differences that result in a significant change in outlet position for a
significant area (more than a couple of cells) have been checked against
various sources of hydrological information (primarily HydroBASINS); in all
cases, they are either due to minor errors in the manually corrected JSBACH
river directions or lie in areas of desert with no
discernible rivers (with the exception of differences connected to the Mekong
for which the automatically generated and upscaled river directions are
erroneous due to a deficiency of the upscaling procedure as previously
discussed).
Comparison of the most significant present-day river catchments
derived using the method presented here (“dynamic HD”) to the manually
corrected HD model river directions. Discrepancies are shown in red; areas of
catchments that are common between both models are marked in grey. The three
different shades of grey are used to pick out individual river catchments; no
significance is attached to the shade chosen for each river. Dynamic HD river
paths (defined as cells with a cumulative flow of 100 cells or more) are
marked to aid orientation.
The flow parameters derived for the present day using the method presented
here (including the removal of inland sink points) were compared to the those
currently in JSBACH by running the model for 1 year in a standalone setup
with rainfall data as a forcing and comparing the total daily discharge into
the ocean (including inland sinks in the case of the current model). The
results (not shown) show a very close match; the small discrepancies observed
are expected as the current JSBACH model includes inland sinks, lakes and
wetlands, all excluded in the dynamic HD model presented here.
The present-day river directions and flow parameters generated using the
method presented in this paper have been applied in a pre-industrial-control
simulation using the current coarse-resolution (CR) version of MPI-ESM. The
simulation was started from a steady-state simulation obtained after a long
(more than 6000-year) spin-up with the manually corrected present-day HD
model river directions and flow parameters. The results (not shown) indicate
only small local changes, especially in surface salinity close to river
mouths. The only exception to this was that the total water flux into the
Indo-Pacific was increased and the total water flux into the Atlantic was
reduced when using dynamic river directions. The reason for this is that the
flow into inland sinks in Asia that was spread evenly around the world's
river mouths when using manually corrected HD river directions was now added
to rivers flowing into the Indo-Pacific (as inland sinks had been removed).
The large-scale circulation remained largely unchanged.
Application to an LGM simulation
Figure shows a comparison of the
0.5∘ river directions derived by the dynamic HD method presented here
using the present-day ICE-6G_C orography and the reconstructed LGM ICE-6G_C
orography . The main differences
from the present day that are observed in North America at the LGM are an
expansion of the catchment of the Mississippi to drain a significant area of
the ice sheet surface into the Gulf of Mexico and an expansion of the Yukon
to drain part of the northwestern ice sheet surface into the Pacific Basin.
In Eurasia, the flow of a large number of rivers in western Siberia and
Scandinavia is blocked by the Fennoscandian ice sheet at the LGM. This forces
these rivers to flow either west or east along the ice-sheet edge (and thus
merge to form two very large rivers). To the west, this continues until the
flow pathway reaches the North Atlantic Ocean at the western end of the ice
sheet; to the east, the flow pathway eventually makes a short detour south
before reaching the Arctic Ocean just beyond the eastern end of the ice sheet.
Elsewhere on the globe, at the LGM, rivers simply extend from their present-day
mouths to the new extended LGM shoreline.
Comparison of the most significant rivers at the LGM and present day
generated by the method described in this paper using the ICE-6G_C
reconstructed orography for the LGM. Rivers are shown where the cumulative
flow to a given grid cell (on the HD grid) is greater than or equal to 100
cells. The various colours show various rivers that existed only at the LGM
(green), only at the present day (pink) or at both (blue). The catchments of
major rivers are marked. Differences
between the catchments are shown in red; areas of catchments that are common
between both time slices are marked in grey. The three different shades of
grey are used to pick out individual river catchments; no significance is
attached to the shade chosen for each river. Continental shelves which were
exposed as dry land at the LGM by the significantly lower sea level are also
marked. Rivers shown on the surface of ice sheets are topographically defined
rivers, and thus their presence does not necessarily imply that there were
rivers running off the northern slopes of the Laurentide and Fennoscandian
ice sheets.
To validate our approach, we compared river directions generated with our
method for the LGM to river directions generated directly from a fabricated
LGM orography on a 30 s grid created by adding the difference between the
reconstructed LGM ICE-6G_C orography and the present-day ICE-6G_C orography
to the present-day SRTM30 PLUS orography. Here, we used the ICE-6G_C
orographies on a 10 min grid; we converted the difference between them to
a 30 s grid to match that of the SRTM30 PLUS orography by assigning each
30 s cell the value of the 10 min cell it would lie within were the
10 min grid overlaid on the 30 s grid. (This resulted in a blocky
structure to the resultant fabricated orography.) We then applied the river
carving algorithm as described in Sect.
directly to the fabricated 30 s orography and compared the catchments of
the rivers produced to those produced by applying our method to the
reconstructed LGM ICE-6G_C orography.
Examination of the results indicates no significant differences in the
catchments produced in regions near the ice sheets with the exception of two
changes in the region of Alaska. The first of these is simply the combination
of two adjacent river mouths to a single river mouth in the catchments
generated from the fabricated 30 s orography. The second is the loss of
some of its catchment by the Yukon near 65∘ N, 130∘ W, in
the catchments generated from the 30 s fabricated orography. Investigation
shows this is because fine detail of narrow valleys not present in the
present-day ICE-6G_C orography or the reconstructed LGM ICE-6G_C orography
is “printed” from the SRTM30 PLUS orography onto the surface of the ice
sheet by the fabrication process used; this fine detail allows a river to
flow into a catchment to the north following a river pathway in the
underlying orography rather than west into the Yukon as it does in the river
directions generated using our dynamic HD method. Given the considerable
thickness of the ice sheet at this point, it is likely this would not occur physically but the detail of the
underlying orography would be smoothed over by the ice sheet.
To test the effect of dynamically modelling river directions at the LGM
against the approach typically used in climate model simulations of this
time slice of simply extending the present-day rivers to the new shoreline,
two simulations were performed using the boundary conditions from the MPI-ESM
LGM simulation of . Both simulations integrated the
same model as for the present-day experiments discussed above using the
restart files from , but the river direction file
differed between the two simulations. One used dynamic river directions
generated as described in this paper using the ICE-6G_C orography
reconstruction; the other simply extended the present-day river directions
(including inland sink points) used in JSBACH as standard to the new
coastlines. This is consistent with the PMIP3 approach
for coupled LGM simulations.
Analysis of the two runs is based on climatologies of the last 500 years.
Figure shows the difference in freshwater flux
into the ocean between the two simulations (including both river outflow and
P-E over the ocean surface) on the ocean grid.
Figure shows the total
freshwater flux into the Indo-Pacific and Atlantic basins as an integrated
total from the North Pole to each specific latitude (the implied southward
ocean freshwater transport). In both basins, a number of localised dipoles are
observed; these represent minor differences in the position of the mouth of
major rivers and will have very little effect on global circulation patterns.
The overall freshwater influx into the Atlantic is reduced and the overall
freshwater flux into the Indo-Pacific increased when using dynamic river
directions; this change is likely at least partially due to the removal of
inland sink points. A significant increase in the catchment of the
Mississippi (and thus its outflow) occurs with dynamic river directions, while
to the north the St. Lawrence ceases to exist (although a significant amount
of water continues to drain off the ice sheet in this area); thus, there is an
overall movement of freshwater southwards. As expected, the Fennoscandian
ice sheet causes a significant lateral movement of water to its ends when
using dynamic river directions. In the Pacific, the main change observed is
the merging of the Yangtze and Yellow rivers at their mouths when using
dynamic river directions; this produces a large peak in the river outflow but
this peak is offset by two troughs on either side. With dynamic river
directions, the outflow from the Yukon is significantly increased and water is
diverted from the North American Arctic coast to the northern Pacific coast of
North America. In the Indian and southern Pacific basins, little overall
change is observed, though there are several large local dipoles.
Changes in the freshwater flux into the ocean between simulations
run in the MPI-ESM model of the LGM using extended present-day river
directions and using dynamic river directions. The changes are defined such
that an increase in the version using dynamic river directions is positive. A
symmetrical logarithmic colour scale is used: above 1, the colour scale is
logarithmic; between 1 and -1, the colour scale is linear; below -1, the
colour scales according to the negation of the logarithm of the change's
magnitude.
Comparison of the implied southward ocean freshwater transport
between simulations run in the MPI-ESM model of the LGM using extended
present-day river directions and using dynamic river directions for
(a) the Atlantic Ocean and (b) the Indo-Pacific. Plot
(c) gives the difference between the two simulations for both
basins. The freshwater transport is defined such that a net addition of
freshwater to the ocean (via precipitation and river discharge) is positive
and a net removal of freshwater (via evaporation) is negative.
The changes in the freshwater input from rivers have a marked effect on the
North Atlantic/Arctic climate system. The changes in continental runoff due
to using dynamic river directions lead to a substantial increase in the
surface salinity not only in the Newfoundland area but also in the Labrador
Sea. This is shown in Fig. . Consequences are
enhanced convection in the Labrador Sea, enhanced heat release to the
atmosphere, reduced winter sea ice cover and a warming of the atmospheric
temperature. An increase in the sea surface temperature (SST) of almost
1 ∘C is observed in the subpolar northwest Atlantic. In the
Norwegian Sea and the Irminger Sea, salinity is reduced when using dynamic
river directions. The enhanced stability then reduces convection and the
upward mixing of heat in the ocean to the surface. The consequences are a
reduction in the SST by about 1∘C and enhanced sea ice cover.
Changes in the surface ocean salinity between simulations run in the
MPI-ESM model of the LGM using extended present-day river directions and
using dynamic river directions. The changes are defined such that an increase
in the version using dynamic river directions is positive.
These changes in freshwater flux forcing have also consequences for the ocean
circulation. In the northwest Atlantic, the subtropical gyre expands
northward in the western half of the basin and the subpolar gyre becomes
weaker and contracts when using dynamic river directions. However, these
changes have only a negligible effect on the Atlantic meridional overturning
circulation.
Application to a selected sequences of times during deglaciation
As a demonstration of the modelling of the dynamic evolution of river
pathways in North America by the technique presented here, we show in
Fig. the major
rivers and the most important catchments as generated by the technique for a
sequence of four times selected from the last deglaciation . The ice-sheet
height and isostatic adjustments are taken from ICE-6G_C, while the
land–sea mask is generated using the technique given in
.
Discussion and conclusionsLimitations
Limitations of the dynamic river routing technique presented in this paper
include the lack of dynamic lakes and wetlands (thus requiring the removal of
all true sinks), the lack of sill erosion and the poor performance of the
upscaling algorithm where several major rivers flow in parallel in close
proximity.
It was decided to omit dynamic lakes from our method for two reasons.
Firstly, the inclusion of dynamic lakes would need direct alteration of the
existing HD model code (as opposed to simply altering the input file which
contains the river directions and flow parameters); as a component of a ESM,
this would likely require a considerable quantity of technical work.
Secondly, our method cannot distinguish between false sinks and true sinks;
the corrections we apply should considerably reduce the number of false sinks
in the orographies we use but will not eliminate them. Further processing
could solve this second issue but would require the development of further
tools. The direct effect of the omission of lakes on the freshwater flux into
the ocean will be an inability to model outburst floods that may have played
an important role in sudden climate change events such as the Younger Dryas
. The reduced outflow that occurs when
lakes sometimes become closed basins e.g., either
because a previous outlet has been blocked and the enclosed basin formed is
yet to completely fill with water or because they have a negative water
balance because of evaporation, will also be missed. Indirectly, the omission
of lakes may affect the climate through missing lake–atmosphere interactions
and precludes both the inclusion of
the mass of the water in the lakes as a feedback to the viscoelastic Earth
model and the modelling of lacustrine calving of ice sheets where they are in
direct contact with an adjacent lake.
Linked to the lack of lakes (and their associated outburst floods), our model
lacks sill erosion; such changes in sill height could affect the preferred
outlet of enclosed basins. For example, considerable erosion of the southern
outlet of Lake Agassiz occurred e.g.; the
difference between the current sill height and previous higher sill heights
may have had a deciding effect on which outlet overflowed in earlier phases
of the lake's development. argues that in the case
of Lake Agassiz as spillways were usually incised after an outlet overflowed, it is likely isostatic
adjustments and physical blocking by the ice sheets were the primary drivers
of watershed rearrangement during the deglaciation. However, given the
complex history of Lake Agassiz, it is possible some outlets may have
overflowed at several separate times during the deglaciation, thus partly
invalidating this argument.
Comparison of rivers generated using the method presented here for
four times during the last deglaciation using the ICE-6G_C orography
reconstruction. Rivers are shown where the cumulative flow to a given grid
cell (on the 0.5∘ grid) is greater than or equal to 75 cells. The
catchments for the Mississippi, St. Lawrence and Mackenzie rivers are marked.
Note the diversion of the St. Lawrence to a different mouth point for the two
older times. Rivers shown on the surface of ice sheets are topographically
defined rivers, and thus their presence does not necessarily imply that there
were rivers running off the northern slopes of the Laurentide and
Fennoscandian ice sheets.
Another important limitation is the lack of verification for time slices
other than the present day; the orography corrections made are largely aimed
at producing the correct present-day river directions from a present-day
orography but it is possible that some features of the orography may be
unimportant for present-day hydrology but critical for hydrology at other
points in the last glacial cycle. This is partly addressed by the use of an
orography upscaling technique for North America.
Inaccuracies in the orographies of times in the past may also occur due to
the model used for calculating isostatic corrections. There are a variety of
approaches to viscoelastic Earth modelling with differing assumptions
; errors from
simplified schemes in particular could affect river routing. When using this
method as part of a ESM coupled to an ice-sheet model, errors in the
simulated size and thickness of the ice sheet will be passed onto the
viscoelastic Earth model and thus may drive changes in the river routing that
deviate considerably from those observed historically. The degree to which
inaccuracies in the underlying orographies of times in the past affect river
routings (either because of “latent” inaccuracies in the present-day
orography or inaccuracies in the isostatic corrections used to transform the
present-day orography to orographies of times in the past) is not clear and
presents itself as a possible topic for further study.
A further limitation is the sudden step change in the application of
orography corrections from ice-free ground (where orography corrections are
applied) to the surface of the ice sheet (where orography corrections are
suppressed until the area becomes ice-free again). This may be unrealistic in
the case of a thin ice sheet which will likely continue to follow the
contours of the land below it including any narrow valleys which are not
resolved in the 10 min DEM and thus require orography corrections. It is
unclear if this would ever have a deciding influence on the routing of any
important river pathways. In
Sect. , the addition of fine
detail of the underlying orography affected the Yukon catchment at the LGM;
however, it is not clear how physically plausible this fine detail being
observed on the surface of the ice sheet was in this case given the thickness
of the ice sheet where it occurred.
This method is only aimed at producing river directions for the last glacial
cycle. Its accuracy would very likely decrease for glacial cycles further
back in time because it is based upon a set of corrections derived using the
present-day orography and it does not account for geomorphic processes other
than isostatic depression and rebound. For the same reason, it would be
unsuitable for application to periods before the Quaternary where the
configuration of the landmasses was substantially different.
Conclusions
The method presented here provides an effective procedure for the generation
of dynamic river directions and flow parameters for paleoclimate simulations.
Individually, both of the key elements of the method, the application of
relative height corrections to a fine orography and the upscaling of a fine
set of river directions to a coarse one, have been shown to function to
within the required level of accuracy. A special set of relative orography
corrections has been used for North America derived using an orography
upscaling technique based on the one used successfully by
. Overall, when the method presented here is
applied to the present day, it reproduces the results of a fixed present-day
hydrological discharge model to a high level of accuracy and all significant
discrepancies have been shown either to be in very dry regions or due to
minor errors in the fixed river directions (in further comparison to a more
detailed set of present-day river catchments) or to have negligible effect on
the point freshwater is discharged into the ocean. The only exception to this
is a problem occurring with the upscaling of the Yangtze, Mekong and Salween
rivers in Yunnan province, China. The method is computationally fast enough
to be run frequently as part of a wider model reconfiguration process during
coupled paleoclimate simulations.
When used in a non-transitory simulation of the present-day climate, it has
been shown that the differences in the ocean system that occur using dynamic
river directions and flow parameters compared to the existing fixed river
directions and flow parameters are not substantial and limited to localised
salinity changes. It has been shown that using dynamic river directions and
flow parameters has a significant effect on the water flux to the ocean when
applied to the LGM, increasing outflow from the Mississippi and redirecting
water from the Mackenzie into the Yukon on the ice sheet itself along with a
major lateral movement of freshwater to the ends of the Fennoscandian
ice sheet. Coupled simulations for the LGM indicate that these changes in the
freshwater flux entering the ocean have a significant effect on the global
ocean circulation through changes to the North Atlantic/Arctic climate system
and these effects are also transferred to the atmosphere.
In summary, we have shown that modelling changes in hydrological discharge is
important for modelling ocean circulation at the LGM and have presented a
method by which changes in hydrological discharge can be modelled for
transient coupled climate model simulations of the last glacial cycle.
A version of the code is available under the three-clause
BSD license on Zenodo at https://doi.org/10.5281/zenodo.1326547. This omits elements of the flow parameter generation code
discussed in Sect. that are part of the
existing HD model's parameter generation code and must be excluded for
licensing reasons. A complete version of the code is stored within the JSBACH
3 model repository in the Apache version control system (SVN) of the Max
Planck Institute for Meteorology
(https://svn.zmaw.de/svn/cosmos/branches/mpiesm-landveg/contrib/dynamic_hd_code/,
last access: 16 October 2018) at revision 9313 under the Max Planck
Institute for Meteorology Software License Version 2. For access to this
complete version of the code (including the omitted elements), contact the
lead author.
The final set of relative height corrections (as discussed
in Sect. ) is available as a NetCDF file under
the Creative Commons Attribution 4.0 License on Zenodo at
https://doi.org/10.5281/zenodo.1326394.
Outline of the orography upscaling algorithm
The algorithm's structure is based on that of the priority flood algorithm
; however, it requires
substantial modification from this original basis to carry the extra
information required for orography upscaling and to accommodate the necessity
of sometimes going back along sections of previously rejected paths from the
opposite direction in order to explore all possible paths. Central to this
algorithm is the priority queue abstract data type, as described in
Sect. . An outline of the algorithm is given
here; a more formal description using pseudo-code is given in
Appendix . (In
addition, a flow diagram illustrating the steps of the algorithm is given in
the Supplement.) The algorithm comprises the following steps:
Split the fine gridded orography into sections, each of which corresponds to
one cell of the coarse orography. This is illustrated in
Fig. a. (This step corresponds to lines
4 and 11 of Algorithm 1 in the pseudo-code description.)
Loop over the sections. For each section of the fine orography, calculate an
effective height and then replace the height of the coarse orography cell
that section corresponds to with this effective height. This step corresponds
to lines 10–19 of Algorithm 1 in the pseudo-code description. The effective
hydrological height of each section is calculated as follows:
(This step prepares the initial content of the priority queue we will
later iterate over.) Push each cell from along the section's edges onto a
priority queue ordered by cell height. Also, push all cells neighbouring
cells marked as sea in a fine-scale land–sea mask onto the queue. This is
illustrated in Fig. b. This first set
of cells added to the queue is henceforth referred to as initial cells. (Sea
cells themselves are not added to the queue here or elsewhere in this
algorithm. Note when using a fine-scale land–sea mask the land–sea
boundaries are not limited to running along section boundaries – hence the
necessity of adding their neighbours explicitly.) In the following
description, we refer to the path leading to a particular cell as that cell's
path; paths can be of any length greater than zero – sometimes, these paths
comprise only the cell itself. For each cell, store values of the following: the cell's height, its
position, a unique identifier of the starting edge of the cell's path (which
will be the edge the cell is on for initial cells), a path length value set
to 1 for initial cells (or 2 if the cell is a diagonal neighbour
of a sea cell), the farthest separation of the cell's path from its initial
edge (which is set to zero for initial cells), a unique identifier of the
cell's pseudo-catchment (a unique identifier of the starting point of the
cell's path – which for initial cells will simply be a unique identifier of
the cell itself) and the initial height of the cell's path (the height of the
starting point of the cell's path – which naturally for initial cells will
be the height of the cell itself except if it is the neighbour of a sea point
in which case it will be sea level).
This step corresponds to Algorithm 2 in the pseudo-code description.
(This step sets up storage arrays for variables that need to be stored
as a spatial field. This completes the initialisation.) Set up a boolean array
flagging cells already processed with the same dimensions as the section.
Mark as processed in this array cells neighbouring cells marked as sea; mark
all other cells as unprocessed. Set up two arrays with the same dimensions as
the section to contain the unique identifiers of the cells' pseudo-catchments
and the initial heights of the cells' paths. This step corresponds to lines
6–8 and 14–15 of Algorithm 1 in the pseudo-code description.
(This step starts a loop over the contents of the priority queue;
unless we break from the loop, each iteration spans from this step to the end
of step (e). In this step itself, we fetch the next cell to be processed from
the queue and update one of its properties.) Pop the lowest height cell off
the queue. Calculate the separation of this cell from its path's initial edge
and update the farthest separation of the cell's path from its initial edge
with this new value if it is greater than the current value. Mark the cell as
processed in the boolean array flagging cells already processed. This step
corresponds to lines 2–4 of Algorithm 3 in the pseudo-code description.
(This step checks if the current cell is the end of a valid path
(which will by design be the lowest valid path) through the fine orography
section. If it is, we use its height as the effective hydrological height of
the corresponding coarse cell and move on to processing the next section of
the fine orography.) If the cell is an edge cell or neighbours a cell marked
as sea in the land–sea mask, then check if the cell satisfies the parameter
MinimumPathThreshold. If it has returned to the same edge that its
path started from, then check if the parameter
MinimumSeparationFromInitialEdgeThreshold is satisfied. If the check
passes (or both the checks pass if the second check was also made), then take
the height of this cell as the effective height for the section and finish
processing this section and move to the next iteration of the loop opened in
step 2. Examples of paths failing the check(s) are given in
Fig. c, while examples of paths passing
the check(s) are given in Fig. d and e.
This step corresponds to lines 5–12 of Algorithm 3 in the pseudo-code
description.
(This step iterates over the neighbours of the current cell, skipping
those that have already been processed unless they require reprocessing. Each
neighbour that has not been skipped has its properties updated as appropriate
and is added to the priority queue, along with being marked as processed.
Also, values that would be necessary for potential future reprocessing are
written to the appropriate spatial storage arrays at the neighbour's
position. Reprocessing is required when the algorithm has been working
progressively on two separate pseudo-catchments that have now met at a
certain point. In order to explore all the possible paths, it is necessary for
one of these catchments to be reprocessed and added to the other catchment
starting from the meeting point. The reprocessed catchment should be the one
that started from a higher initial point to ensure that all paths run from a
lower point to a higher one (even if they pass even higher points still en
route). Here, two criteria are used to correctly enact such a reprocessing
when it is required.) Loop over all the neighbours of the cell (as
illustrated in Fig. c). Hereinafter, we
referred to the cell whose neighbours are being considered as the centre
cell. For each neighbouring cell:
If the neighbouring cell is not marked as already processed in the boolean
array flagging processed cells, then continue to step (ii) without making any
checks. If the neighbouring cell is marked as already processed, then check
the following:
The neighbour's initial path height (as read from the array of the initial
path heights of processed cells) is greater than that of the centre cell. In
the case that the path heights are equal, use a tie-breaking criterion
based on the unique identifiers of the centre cell's and neighbouring cell's
pseudo-catchments to decide if to skip the neighbour or not; this prevents
infinite loops. The unique identity of the neighbouring cell's
pseudo-catchment is read from the array of the unique identifiers of cells'
pseudo-catchments.
The neighbour's path started from a different point to the centre cell's
(also based on the unique identifiers of the centre cell's and neighbouring
cell's pseudo-catchments).
If both these criteria are met, then continue to step (ii); otherwise, skip
processing this neighbour and move on to the next iteration of the loop.
Mark the neighbour as processed in the array of processed cells.
Write (overwriting previous values where necessary) the unique identifier of the centre cell's pseudo-catchment
and the initial height of the centre cell's path to the respective arrays of those variables at the neighbour's position.
Push the neighbouring cell onto the queue using the values of the centre cell apart from path
length and cell height which are both replaced with new values. For path length, a new value is calculated
by adding the distance from the centre cell to the neighbouring cell (either 1 or 2 if
it is a diagonal neighbour) to the centre cell's existing path length and for cell height
whichever is higher out of the centre cell's height and the neighbour's height is used (thus, for cell height, the new value may be the same as the old value).
Once all the neighbours have been processed, return to step (c). This step corresponds to
lines 13–26 of Algorithm 3 in the pseudo-code description.
Orography upscaling algorithm pseudo-code
The main body of the algorithm is given as pseudo-code in Algorithm 1 while
two important sub-algorithms used by the main algorithm are given in
Algorithms 2 and 3. In these algorithms, we use ← to denote the
assignment operator and = to denote a test for equality. Variables written
in italicised camel case are containers: specifically, either arrays,
annotated cell objects or a priority queue. Italicised lower case variables
(with or without a subscript) are simply numbers (or coordinates in the case
of pos), while words in full-sized capitals are function names and words in
small capitals are either externally supplied parameters or
constants/identifiers. Words in lower case bold represent flow control
structures (“if” statements, while loops, for all loops, return statements and
sub-algorithm calls) or logical operators. Brackets represent the
initialisation of an object/structure using a group of variables with given
values unless they are positioned directly after an array variable, in which
case they represent indexing of that array using the position indicator
enclosed within the brackets, they are used in an “if” statement, in which case they
indicate the order of operations, or they are positioned after a function, in
which case they enclose arguments to the function. The variables
CC, CF, pos and N store coordinates within a DEM
grid that locate a cell within that DEM; note these are different from
annotated cell objects which allow the storage of further information about a
cell in addition to its position. For CF, pos and N, these are
positions within a fine-scale orography; for CC, these are
positions within the coarse DEM to be produced by this algorithm. These
positions can be used to index arrays.
At input, FineDEM is an array of orography on a fine scale and
FineLandSeaMask an array of the land–sea mask on the same scale
using possible states Land and Sea (in practice usually
represented by a boolean array), while CoarseDEMDimensions is the
required dimensions of the coarse DEM to be produced. Also required are
values for the parameters MinimumPathThreshold and
MinimumSeparationFromInitialEdgeThreshold and a value for the
constant SeaLevel representing the sea-level datum to be used
(normally zero). RiverMouth, TopEdgeID,
BottomEdgeID, LeftEdgeID and RightEdgeID must be
unique identifiers. NoData is a simple null value used to fill array
elements for which a value is yet to be calculated. At output,
CoarseDEM is an orography of effective hydrological heights on the
given coarse scale.
The Supplement related to this article is available online at: https://doi.org/10.5194/gmd-11-4291-2018-supplement
The manuscript was prepared by TR with substantial contributions from UM in Sects. and
. TR designed the orography
upscaling algorithm and wrote the code specific to this project.
Part of the code used for the generation of retention coefficients was adapted from that used in the HD model developed
by SH. Coupled modern-day deglaciation and LGM climate simulations were performed by
UM. All authors contributed to the development of ideas and scientific direction.
The authors declare that they have no conflict of interest.
Acknowledgements
This work was funded by the German Federal Ministry of Education and Research
(BMBF) through the PalMod project, grant no. 01LP1513C. We thank Florian
Ziemen for providing the code used for plotting ocean variables and for
reviewing the manuscript prior to submission. We thank Dai Yamazaki and Lev
Tarasov for their constructive and insightful reviews.
The article processing charges for this
open-access publication were covered by the Max Planck
Society. Edited by: Olivier Marti
Reviewed by: Lev Tarasov and Dai Yamazaki
ReferencesAlkama, R., Kageyama, M., Ramstein, G., Marti, O., Ribstein, P., and
Swingedouw, D.: Impact of a realistic river routing in coupled
ocean–atmosphere simulations of the Last Glacial Maximum climate, Clim.
Dynam., 30, 855–869, 10.1007/s00382-007-0330-1, 2008.Argus, D. F., Peltier, W. R., Drummond, R., and Moore, A. W.: The Antarctica
component of postglacial rebound model ICE-6G_C (VM5a) based on GPS
positioning, exposure age dating of ice thicknesses, and relative sea level
histories, Geophys. J. Int., 198, 537–563, 10.1093/gji/ggu140,
2014.Bahadory, T. and Tarasov, L.: LCice 1.0 – a generalized Ice Sheet System
Model coupler for LOVECLIM version 1.3: description, sensitivities, and
validation with the Glacial Systems Model (GSM version D2017.aug17), Geosci.
Model Dev., 11, 3883–3902, 10.5194/gmd-11-3883-2018, 2018.
Barnes, R., Lehman, C., and Mulla, D.: Priority-flood: An optimal
depression-filling and watershed-labeling algorithm for digital elevation
models, Comput. Geosci., 62, 117–127, 2014.Becker, J. J., Sandwell, D. T., Smith, W. H. F., Braud, J., Binder, B.,
Depner,
J., Fabre, D., Factor, J., Ingalls, S., Kim, S.-H., Ladner, R., Marks, K.,
Nelson, S., Pharaoh, A., Trimmer, R., Rosenberg, J. V., Wallace, G., and
Weatherall, P.: Global Bathymetry and Elevation Data at 30 Arc Seconds
Resolution: SRTM30_PLUS, Mar. Geod., 32, 355–371,
10.1080/01490410903297766, 2009.Beucher, N. and Beucher, S.: Hierarchical queues: general description and
implementation in mamba image library, available at:
http://cmm.ensmp.fr/~beucher/publi/HQ_algo_desc.pdf (last access: 16 October 2018),
2011.
Beucher, S. and Meyer, F.: The morphological approach to segmentation: the
watershed transformation, Opt. Eng., 34, 433–481, 1992.
Braconnot, P., Harrison, S. P., Otto-Bliesner, B., Abe-Ouchi, A., Jungclaus,
J., and Peterschmitt, J.-Y.: The Paleoclimate Modeling Intercomparison
Project contribution to CMIP5, CLIVAR Exchanges, 16, 15–19, 2011.
Braconnot, P., Harrison, S. P., Kageyama, M., Bartlein, P. J.,
Masson-Delmotte,
V., Abe-Ouchi, A., Otto-Bliesner, B., and Zhao, Y.: Evaluation of climate
models using palaeoclimatic data, Nat. Clim. Change, 2, 417–424, 2012.Broecker, W. S., Kennett, J. P., Flower, B. P., Teller, J. T., Trumbore, S.,
Bonani, G., and Wolfli, W.: Routing of meltwater from the Laurentide Ice
Sheet during the Younger Dryas cold episode, Nature, 341, 318–321,
10.1038/341318a0, 1989.Fisher, T. G.: Strandline analysis in the southern basin of glacial Lake
Agassiz, Minnesota and North and South Dakota, USA, Geol. Soc. Am. Bull.,
117, 1481–1496, 10.1130/B25752.1, 2005.Giorgetta, M. A., Jungclaus, J., Reick, C. H., Legutke, S., Bader, J.,
Böttinger, M., Brovkin, V., Crueger, T., Esch, M., Fieg, K., Glushak, K.,
Gayler, V., Haak, H., Hollweg, H.-D., Ilyina, T., Kinne, S., Kornblueh, L.,
Matei, D., Mauritsen, T., Mikolajewicz, U., Mueller, W., Notz, D., Pithan,
F., Raddatz, T., Rast, S., Redler, R., Roeckner, E., Schmidt, H., Schnur, R.,
Segschneider, J., Six, K. D., Stockhause, M., Timmreck, C., Wegner, J.,
Widmann, H., Wieners, K.-H., Claussen, M., Marotzke, J., and Stevens, B.:
Climate and carbon cycle changes from 1850 to 2100 in MPI-ESM simulations for
the Coupled Model Intercomparison Project phase 5, J. Adv. Model. Earth Sy.,
5, 572–597, 10.1002/jame.20038, 2013.Goelzer, H., Janssens, I., Nemec, J., and Huybrechts, P.: A dynamic
continental runoff routing model applied to the last Northern Hemisphere
deglaciation, Geosci. Model Dev., 5, 599–609,
10.5194/gmd-5-599-2012, 2012.Goll, D. S., Brovkin, V., Liski, J., Raddatz, T., Thum, T., and Todd-Brown,
K.
E. O.: Strong dependence of CO2 emissions from anthropogenic land cover
change on initial land cover and soil carbon parametrization, Global
Biogeochem. Cy., 29, 1511–1523, 10.1002/2014GB004988, 2015.Goosse, H. and Fichefet, T.: Importance of ice-ocean interactions for the
global ocean circulation: A model study, J. Geophys. Res.-Oceans, 104,
23337–23355, 10.1029/1999JC900215, 1999.Goosse, H., Brovkin, V., Fichefet, T., Haarsma, R., Huybrechts, P., Jongma,
J., Mouchet, A., Selten, F., Barriat, P.-Y., Campin, J.-M., Deleersnijder,
E., Driesschaert, E., Goelzer, H., Janssens, I., Loutre, M.-F., Morales
Maqueda, M. A., Opsteegh, T., Mathieu, P.-P., Munhoven, G., Pettersson, E.
J., Renssen, H., Roche, D. M., Schaeffer, M., Tartinville, B., Timmermann,
A., and Weber, S. L.: Description of the Earth system model of intermediate
complexity LOVECLIM version 1.2, Geosci. Model Dev., 3, 603–633,
10.5194/gmd-3-603-2010, 2010.Haddeland, I., Clark, D. B., Franssen, W., Ludwig, F., Voß, F., Arnell,
N. W., Bertrand, N., Best, M., Folwell, S., Gerten, D., Gomes, S., Gosling,
S. N., Hagemann, S., Hanasaki, N., Harding, R., Heinke, J., Kabat, P.,
Koirala, S., Oki, T., Polcher, J., Stacke, T., Viterbo, P., Weedon, G. P.,
and Yeh, P.: Multimodel Estimate of the Global Terrestrial Water Balance:
Setup and First Results, J. Hydrometeorol., 12, 869–884,
10.1175/2011JHM1324.1, 2011.
Hagemann, S. and Dümenil, L.: Documentation for the Hydrological
Discharge
Model, Tech. Rep. 17, Max Planck Institute for Meteorology, Bundesstraße
55, 20146, Hamburg, Germany, 1998a.Hagemann, S. and Dümenil, L.: A parametrization of the lateral waterflow
for the global scale, Clim. Dynam., 14, 17–31, 10.1007/s003820050205,
1998b.Hagemann, S. and Dümenil Gates, L.: Validation of the hydrological cycle
of
ECMWF and NCEP reanalyses using the MPI hydrological discharge model, J.
Geophys. Res.-Atmos., 106, 1503–1510, 10.1029/2000JD900568, 2001.Hagemann, S. and Stacke, T.: Impact of the soil hydrology scheme on simulated
soil moisture memory, Clim. Dynam., 44, 1731–1750,
10.1007/s00382-014-2221-6, 2015.Hostetler, S. W., Bartlein, P. J., Clark, P. U., Small, E. E., and Solomon,
A. M.: Simulated influences of Lake Agassiz on the climate of central North
America 11,000 years ago, Nature, 405, 334–337, 10.1038/35012581,
2000.
IPCC: Climate Change 2013: The Physical Science Basis. Contribution of
Working
Group I to the Fifth Assessment Report of the Intergovernmental Panel on
Climate Change, Cambridge University Press, Cambridge, United Kingdom and New
York, NY, USA, 2013.Klockmann, M., Mikolajewicz, U., and Marotzke, J.: The effect of greenhouse
gas concentrations and ice sheets on the glacial AMOC in a coupled climate
model, Clim. Past, 12, 1829–1846, 10.5194/cp-12-1829-2016,
2016.
Krinner, G., Mangerud, J., Jakobsson, M., Crucifix, M., Ritz, C., and
Svendsen,
J. I.: Enhanced ice sheet growth in Eurasia owing to adjacent ice-dammed
lakes, Nature, 427, 429–432,, 2004.Latif, M., Claussen, M., Schulz, M., and Brücher, T.: Comprehensive Earth
system models of the last glacial cycle, EOS, 97, 10.1029/2016EO059587,
2016.Lehner, B. and Grill, G.: Global river hydrography and network routing:
baseline data and new approaches to study the world's large river systems,
Hydrol. Process., 27, 2171–2186, 10.1002/hyp.9740, 2013.Lewis, C., Forbes, D., Todd, B., Nielsen, E., Thorleifson, L., Henderson, P.,
McMartin, I., Anderson, T., Betcher, R., Buhay, W., Burbidge, S.,
Schröder-Adams, C., King, J., Moran, K., Gibson, C., Jarrett, C., Kling,
H., Lockhart, W., Last, W., Matile, G., Risberg, J., Rodrigues, C., Telka,
A., and Vance, R.: Uplift-driven expansion delayed by middle Holocene
desiccation in Lake Winnipeg, Manitoba, Canada, Geology, 29, 743–746,
10.1130/0091-7613(2001)029<0743:UDEDBM>2.0.CO;2, 2001.
Licciardi, J. M., Teller, J. T., and Clark, P. U.: Freshwater Routing by the
Laurentide Ice Sheet During the Last Deglaciation, in: Mechanisms of Global
Climate Change at Millennial Time Scales, edited by: Clark, P. U., Webb,
R. S., and Keigwin, L. D., pp. 177–201, American Geophysical Union,
Washington, DC, USA, 1999.Liu, Z., Otto-Bliesner, B. L., He, F., Brady, E. C., Tomas, R., Clark, P. U.,
Carlson, A. E., Lynch-Stieglitz, J., Curry, W., Brook, E., Erickson, D.,
Jacob, R., Kutzbach, J., and Cheng, J.: Transient Simulation of Last
Deglaciation with a New Mechanism for Bølling-Allerød Warming, Science,
325, 310–314, 10.1126/science.1171041, 2009.
Maidment, D.: GIS and hydrological modelling: an assessment of progress,
in:
Third International Conference on GIS and Environmental Modelling,
Third International Conference on GIS and Environmental Modelling,
Santa Fe, NM, USA, 596–610, 20–25 January 1996.
Maier-Reimer, E. and Mikolajewicz, U.: Experiments with an OGCM on the cause
of the Younger Dryas, in: Oceanography 1988, edited by: Ayala-Castanares, A.,
Wooster, W., and Yanez-Arancibia, A., UNAM Press, Mexico, 87–99, 1989.Mangerud, J., Jakobsson, M., Alexanderson, H., Astakhov, V., Clarke, G.,
Henriksen, M., Hjort, C., Krinner, G., Lunkka, J., Möller, P., Murray,
A., Nikolskaya, O., Saarnisto, M., and Svendsen, J. I.: Ice-dammed lakes and
rerouting of the drainage of northern Eurasia during the Last Glaciation,
Quaternary Sci. Rev., 23, 1313–1332, 10.1016/j.quascirev.2003.12.009,
2004.Martinec, Z.: Spectral–finite element approach to three-dimensional
viscoelastic relaxation in a spherical earth, Geophys J. Int., 142, 117–141,
10.1046/j.1365-246x.2000.00138.x, 2000.Meccia, V. L. and Mikolajewicz, U.: Interactive ocean bathymetry and
coastlines for simulating the last deglaciation with the Max Planck Institute
Earth System Model (MPI-ESM-v1.2), Geosci. Model Dev. Discuss.,
10.5194/gmd-2018-129, in review, 2018.Metz, M., Mitasova, H., and Harmon, R. S.: Efficient extraction of drainage
networks from massive, radar-based elevation models with least cost path
search, Hydrol. Earth Syst. Sci., 15, 667–678,
10.5194/hess-15-667-2011, 2011.
Mizgallewicz, P. and Maidment, D.: Modelling agricultural transport in
Midwest
Rivers using Geographic Information Systems, Tech. Rep. 96–6, Centre for
Research Water Resources, University of Texas, Austin, TX, USA, 1996.Paz, A. R., Collischonn, W., and Lopes da Silveira, A. L.: Improvements in
large-scale drainage networks derived from digital elevation models, Water
Resour. Res., 42, W08502, 10.1029/2005WR004544, 2006.
Peltier, W.: Global glacial isostasy and the surface of the ice-age Earth:
the
ICE-5G (VM2) model and GRACE, Annu. Rev. Earth Pl. Sc., 32, 111–149, 2004.Peltier, W. R., Argus, D. F., and Drummond, R.: Space geodesy constrains ice
age terminal deglaciation: The global ICE-6G_C (VM5a) model, J. Geophys.
Res.-Sol. Ea., 120, 450–487, 10.1002/2014JB011176, 2015.Reick, C. H., Raddatz, T., Brovkin, V., and Gayler, V.: Representation of
natural and anthropogenic land cover change in MPI-ESM, J. Adv. Model. Earth
Sy., 5, 459–482, 10.1002/jame.20022, 2013.Riddick, T. C.: ThomasRiddick/DynamicHD release_version_3.0
(Version release_version_3.0), Zenodo,
10.5281/zenodo.1326547, 2018a.Riddick, T. C.: Dynamic HD Model Relative Orography Corrections (Version 1.0)
[Data set], Zenodo, 10.5281/zenodo.1326394, 2018b.Rooth, C.: Hydrology and ocean circulation, Prog. Oceanogr., 11, 131–149,
10.1016/0079-6611(82)90006-4, 1982.
Saunders, W.: Preparation of DEMs for Use in Environmental Modeling Analysis,
1999 ERSI User Conference, San Diego, CA, USA, 24–30 July 1999.Schiller, A., Mikolajewicz, U., and Voss, R.: The stability of the North
Atlantic thermohaline circulation in a coupled ocean-atmosphere general
circulation model, Clim. Dynam., 13, 325–347, 10.1007/s003820050169,
1997.Schneck, R., Reick, C. H., and Raddatz, T.: Land contribution to natural CO2
variability on time scales of centuries, J. Adv. Model. Earth Sy., 5,
354–365, 10.1002/jame.20029, 2013.Soille, P. and Gratin, C.: An Efficient Algorithm for Drainage Network
Extraction on DEMs, J. Vis. Commun. Image R., 5, 181–189,
10.1006/jvci.1994.1017, 1994.Spada, G., Barletta, V. R., Klemann, V., Riva, R. E. M., Martinec, Z.,
Gasperini, P., Lund, B., Wolf, D., Vermeersen, L. L. A., and King, M. A.: A
benchmark study for glacial isostatic adjustment codes, Geophys. J. Int.,
185, 106–132, 10.1111/j.1365-246X.2011.04952.x, 2011.Stacke, T. and Hagemann, S.: Development and evaluation of a global dynamical
wetlands extent scheme, Hydrol. Earth Syst. Sci., 16, 2915–2933,
10.5194/hess-16-2915-2012, 2012.Stouffer, R. J., Yin, J., Gregory, J. M., Dixon, K. W., Spelman, M. J.,
Hurlin,
W., Weaver, A. J., Eby, M., Flato, G. M., Hasumi, H., Hu, A., Jungclaus,
J. H., Kamenkovich, I. V., Levermann, A., Montoya, M., Murakami, S., Nawrath,
S., Oka, A., Peltier, W. R., Robitaille, D. Y., Sokolov, A., Vettoretti, G.,
and Weber, S. L.: Investigating the Causes of the Response of the
Thermohaline Circulation to Past and Future Climate Changes, J. Climate, 19,
1365–1387, 10.1175/JCLI3689.1, 2006.
Tarasov, L. and Peltier, W.: A calibrated deglacial drainage chronology for
the
North American continent: evidence of an Arctic trigger for the Younger
Dryas, Quaternary Sci. Rev., 25, 659–688, 2006.Taylor, K. E., Stouffer, R. J., and Meehl, G. A.: An Overview of CMIP5 and
the
Experiment Design, B. Am. Meteorol. Soc., 93, 485–498,
10.1175/BAMS-D-11-00094.1, 2012.
Teller, J. T.: Meltwater and precipitation runoff to the North Atlantic,
Arctic, and Gulf of Mexico from the Laurentide Ice Sheet and adjacent regions
during the Younger Dryas, Paleoceanography, 5, 897–905,
10.1029/PA005i006p00897, 1990.USGS: HYDRO1k, available at: https://lta.cr.usgs.gov/HYDRO1K (last
access: 16 October 2018), 2017.Wang, L. and Liu, H.: An efficient method for identifying and filling surface
depressions in digital elevation models for hydrologic analysis and
modelling, Int. J. Geogr. Inf. Sci., 20, 193–213,
10.1080/13658810500433453, 2006.
Whitehouse, P.: Glacial isostatic adjustment and sea-level change: State of
the art report, Tech. rep., Swedish Nuclear Fuel and Waste Management Co,
Stockholm, Sweden, 2009.Wickert, A. D.: Reconstruction of North American drainage basins and river
discharge since the Last Glacial Maximum, Earth Surf. Dynam., 4, 831–869,
10.5194/esurf-4-831-2016, 2016.Yamazaki, D., Oki, T., and Kanae, S.: Deriving a global river network map and
its sub-grid topographic characteristics from a fine-resolution flow
direction map, Hydrol. Earth Syst. Sci., 13, 2241–2251,
10.5194/hess-13-2241-2009, 2009.Yamazaki, D., Ikeshima, D., Tawatari, R., Yamaguchi, T., O'Loughlin, F.,
Neal,
J. C., Sampson, C. C., Kanae, S., and Bates, P. D.: A high-accuracy map of
global terrain elevations, Geophys. Res. Lett., 44, 5844–5853,
10.1002/2017GL072874, 2017.Zängl, G., Reinert, D., Rípodas, P., and Baldauf, M.: The ICON
(ICOsahedral Non-hydrostatic) modelling framework of DWD and MPI-M:
Description of the non-hydrostatic dynamical core, Q. J. Roy. Meteor. Soc.,
141, 563–579, 10.1002/qj.2378, 2015.Ziemen, F. A., Rodehacke, C. B., and Mikolajewicz, U.: Coupled ice
sheet–climate modeling under glacial and pre-industrial boundary conditions,
Clim. Past, 10, 1817–1836, 10.5194/cp-10-1817-2014, 2014.Ziemen, F. A., Kapsch, M.-L., Klockmann, M., and Mikolajewicz, U.: Heinrich
events show two-stage climate response in transient glacial simulations,
Clim. Past Discuss., 10.5194/cp-2018-16, in review, 2018.Zweck, C. and Huybrechts, P.: Modeling of the northern hemisphere ice sheets
during the last glacial cycle and glaciological sensitivity, J. Geophys.
Res.-Atmos., 110, D07103, 10.1029/2004JD005489, 2005.