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.