Figure 2. Histogram of total volume of water impoundment. Main
figure: Total integrated volume of water impounded as a function time
based on the GRanD database without (blue) and with (red) seepage
considered. Right axis shows the equivalent GMSL fall associated with
the impoundment. Inset: Extension of both curves in the main figure to
include projected water impoundments for reservoirs under construction
(‘Const.’) and Planned. Seepage for the column labeled ‘Const.’ is
estimated only from the GRanD database to the year 2025. Seepage for the
column labeled ‘Planned’ is estimated from the GRanD database to the
year 2035, plus ten years of seepage from those reservoirs in the
“under construction” category.
3.2 Spatial Variation in Sea Level
For each of the 9,724 records in our combined database, we generate a
gravitationally consistent prediction of the GRD fingerprint by solving
a version of the so-called sea level equation (Farrell and Clark, 1976)
that includes the feedback into sea level of impoundment-induced
perturbations in the Earth’s rotation vector and shoreline migration
(Mitrovica and Milne, 2003), although the latter is negligible in the
calculations performed here. The results are generated using the
pseudo-spectral algorithm of Kendall et al . (2005) applied to a
1-D elastic Earth model in which an initial guess to the fingerprint is
iteratively improved until convergence is reached. Three such iterations
are generally sufficient to establish convergence. Mitrovica et
al. (2011) have shown that our neglect of lateral variations in mantle
density and elastic constants, which is motivated by the high
computational requirements of 3-D simulations, introduces a small, 1%
error in the fingerprints. We adopt the depth-varying elastic and
density structure reported by the seismically inferred Preliminary
Reference Earth Model (Dziewonski and Anderson, 1981) and the
calculations are based on a spherical harmonic truncation at degree and
order 512. Test calculations at tide gauge sites using a spherical
harmonic truncation level of 1024 show negligible differences with those
reported below.
An example GRD fingerprint is shown for Manicouagan Reservoir (the sixth
largest in our dataset, with a capacity of 162 km3) in
Fig. S1. The amplitude of the sea level rise close to the reservoir
exceeds the GMSL changes associated with this impoundment by over an
order of magnitude, and the zone of predicted sea level rise extends
~2000 km from the location of the reservoir. In the
far-field of the reservoir the predicted sea level fall reaches an
amplitude ~35% greater than the GMSL change. Moreover,
the signal due to rotational effects is evident in the global
fingerprint (note in Fig. S1 the decreased magnitude south of Australia
and the increased magnitudes over eastern Asia and southern South
America).
In the absence of significant shoreline migration, the computed GRD
fingerprints add linearly. Taking advantage of this linearity, we have
constructed a net sea level fingerprint for every calendar year,
accounting for the various time series of reservoir impoundment and
seepage rates. Fingerprints for a selected set of years are shown in
Fig. 3. The full suite of annual fingerprints for the period 1900 –
2011 is available at doi.org/10.5281/zenodo.3751986. A comparison with
the fingerprint of Fiedler and Conrad (2010) is shown in Fig. S2.