4. Terrestrial Water Storage

4.1. Models

4.1.1. GLDAS

Uses GLDAS model outputs from the NASA Goddard Space Flight Center (GSFC) Hydrological Sciences Laboratory (HSL) Global Land Data Assimilation System Version 2 (GLDAS-2) [20]. GLDAS outputs are downloaded using the gesdisc_gldas_sync.py program. GLDAS version 2.1 is forced with a combination of model and observation data. Additionally, the GLDAS project produces two months of “early production stream” products that are run without the forcing data. Here, monthly terrestrial water storage (TWS) estimates are calculated by combining the soil moisture (SoilMoist), snow water equivalent (SWE) and total canopy storage (CanopInt) outputs.

4.1.2. ERA5-Land

Uses ERA5-Land model outputs computed by ECMWF. ERA5-Land outputs are downloaded using the cds_land_retrieve.py program following the cdsapi documentation. Here, monthly terrestrial water storage (TWS) estimates are calculated by combining the soil moisture (swvl1, swvl2, swvl3, swvl4), snow water equivalent (sd and snowc) and skin reservoir (src) outputs.

4.2. Background

Monthly anomalies in terrestrial water storage are calculated by removing a multi-annual mean (typically 2003 – 2007). Before converting to spherical harmonics, the terrestrial water storage estimates are masked to remove urbanized, glaciated and permafrost regions. Terrestrial water storage anomalies are converted to spherical harmonics following Wahr et al. [30] [Equation 4.1].

(4.1)\[\begin{split} \left\{\begin{matrix}\tilde{C}_{lm}(t) \\[-4pt] \tilde{S}_{lm}(t) \end{matrix} \right\} = \frac{3}{4\pi a\rho_{e}}\frac{1+k_l}{2l+1}\int\sigma(\theta,\phi,t)~P_{lm}(\cos\theta) \left\{\begin{matrix}\cos{m\phi} \\[-4pt] \sin{m\phi} \end{matrix} \right\}~d\Omega\end{split}\]

4.3. Framework

Figure 4.1: GLDAS Spherical Harmonics Framework