Inter-annual variability of the global terrestrial water cycle

Variability of the terrestrial water cycle, i.e. precipitation (inline-formulaP), evapotranspiration (inline-formulaE), runoff (inline-formulaQ) and water storage change (inline-formulaΔS) is the key to understanding hydro-climate extremes. However, a comprehensive global assessment for the partitioning of variability in inline-formulaP between inline-formulaE, inline-formulaQ and inline-formulaΔS is still not available. In this study, we use the recently released global monthly hydrologic reanalysis product known as the Climate Data Record (CDR) to conduct an initial investigation of the inter-annual variability of the global terrestrial water cycle. We first examine global patterns in partitioning the long-term mean inline-formula $M9inlinescrollmathml\stackrel{normal\; ‾}{P}$ 10pt13ptsvg-formulamathimgf6f023cd5b241bbdf3ecfc5ed08485d1 hess-24-381-2020-ie00001.svg10pt13pthess-24-381-2020-ie00001.png between the various sinks inline-formula $M10inlinescrollmathml\stackrel{normal\; ‾}{E}$ 11pt13ptsvg-formulamathimg331d8fbcffe0b139132d971941c0e763 hess-24-381-2020-ie00002.svg11pt13pthess-24-381-2020-ie00002.png , inline-formula $M11inlinescrollmathml\stackrel{normal\; ‾}{Q}$ 10pt13ptsvg-formulamathimg4918d218751c71845f1ca4aa1e7d3d55 hess-24-381-2020-ie00003.svg10pt13pthess-24-381-2020-ie00003.png and inline-formula $M12inlinescrollmathml\stackrel{normal\; ‾}{\mathrm{normal\; \Delta }S}$ 18pt13ptsvg-formulamathimga33393a391972ab4550bcd71dc1c990d hess-24-381-2020-ie00004.svg18pt13pthess-24-381-2020-ie00004.png and confirm the well-known patterns with inline-formula $M13inlinescrollmathml\stackrel{normal\; ‾}{P}$ 10pt13ptsvg-formulamathimgc7d179fe03ddf529f7bec0b29c0df224 hess-24-381-2020-ie00005.svg10pt13pthess-24-381-2020-ie00005.png partitioned between inline-formula $M14inlinescrollmathml\stackrel{normal\; ‾}{E}$ 11pt13ptsvg-formulamathimgbc06230a9cffa9748349c8023b1daa2e hess-24-381-2020-ie00006.svg11pt13pthess-24-381-2020-ie00006.png and inline-formula $M15inlinescrollmathml\stackrel{normal\; ‾}{Q}$ 10pt13ptsvg-formulamathimg27f0f0853d5542b99e46e5a4f8cce313 hess-24-381-2020-ie00007.svg10pt13pthess-24-381-2020-ie00007.png according to the aridity index. In a new analysis based on the concept of variability source and sinks we then examine how variability in the precipitation inline-formula $M16inlinescrollmathml{\mathrm{italic\; \sigma }}_P^{\mathrm{normal\; 2}}$ 14pt16ptsvg-formulamathimg1e5d48b31fd4bbb942e5463f1529a515 hess-24-381-2020-ie00008.svg14pt16pthess-24-381-2020-ie00008.png (the source) is partitioned between the three variability sinks inline-formula $M17inlinescrollmathml{\mathrm{italic\; \sigma }}_E^{\mathrm{normal\; 2}}$ 14pt16ptsvg-formulamathimg1a60437b60b38be1d8e0bb6dbcace6d0 hess-24-381-2020-ie00009.svg14pt16pthess-24-381-2020-ie00009.png , inline-formula $M18inlinescrollmathml{\mathrm{italic\; \sigma }}_Q^{\mathrm{normal\; 2}}$ 15pt16ptsvg-formulamathimg978bbacbab20fe43d346ef1d3e408dcf hess-24-381-2020-ie00010.svg15pt16pthess-24-381-2020-ie00010.png and inline-formula $M19inlinescrollmathml{\mathrm{italic\; \sigma }}_{\mathrm{normal\; \Delta }S}^{\mathrm{normal\; 2}}$ 20pt17ptsvg-formulamathimgd00d5b0f5d50c5b70e331182e01b5a79 hess-24-381-2020-ie00011.svg20pt17pthess-24-381-2020-ie00011.png along with the three relevant covariance terms, and how that partitioning varies with the aridity index. We find that the partitioning of inter-annual variability does not simply follow the mean state partitioning. Instead we find that inline-formula $M20inlinescrollmathml{\mathrm{italic\; \sigma }}_P^{\mathrm{normal\; 2}}$ 14pt16ptsvg-formulamathimg99bb7f33cad33af7250d71cd254fe8de hess-24-381-2020-ie00012.svg14pt16pthess-24-381-2020-ie00012.png is mostly partitioned between inline-formula $M21inlinescrollmathml{\mathrm{italic\; \sigma }}_Q^{\mathrm{normal\; 2}}$ 15pt16ptsvg-formulamathimg03d9fdd8093ff790d7ef71b46b7f1685 hess-24-381-2020-ie00013.svg15pt16pthess-24-381-2020-ie00013.png , inline-formula $M22inlinescrollmathml{\mathrm{italic\; \sigma }}_{\mathrm{normal\; \Delta }S}^{\mathrm{normal\; 2}}$ 20pt17ptsvg-formulamathimgc61c41f5708c1232b01cada7d3bb420f hess-24-381-2020-ie00014.svg20pt17pthess-24-381-2020-ie00014.png and the associated covariances with limited partitioning to inline-formula $M23inlinescrollmathml{\mathrm{italic\; \sigma }}_E^{\mathrm{normal\; 2}}$ 14pt16ptsvg-formulamathimg7ac380857947f19b7f4dc66abc398609 hess-24-381-2020-ie00015.svg14pt16pthess-24-381-2020-ie00015.png . We also find that the magnitude of the covariance components can be large and often negative, indicating that variability in the sinks (e.g. inline-formula $M24inlinescrollmathml{\mathrm{italic\; \sigma }}_Q^{\mathrm{normal\; 2}}$ 15pt16ptsvg-formulamathimgd819bef56ee3d3557b8881f296219e23 hess-24-381-2020-ie00016.svg15pt16pthess-24-381-2020-ie00016.png , inline-formula $M25inlinescrollmathml{\mathrm{italic\; \sigma }}_{\mathrm{normal\; \Delta }S}^{\mathrm{normal\; 2}}$ 20pt17ptsvg-formulamathimg0c6a4157788b1a38bea00d851d7fbb29 hess-24-381-2020-ie00017.svg20pt17pthess-24-381-2020-ie00017.png ) can, and regularly does, exceed variability in the source (inline-formula $M26inlinescrollmathml{\mathrm{italic\; \sigma }}_P^{\mathrm{normal\; 2}}$ 14pt16ptsvg-formulamathimgd1820149285385cb51925828a91f3ec0 hess-24-381-2020-ie00018.svg14pt16pthess-24-381-2020-ie00018.png ). Further investigations under extreme conditions revealed that in extremely dry environments the variance partitioning is closely related to the water storage capacity. With limited storage capacity the partitioning of inline-formula $M27inlinescrollmathml{\mathrm{italic\; \sigma }}_P^{\mathrm{normal\; 2}}$ 14pt16ptsvg-formulamathimg92dc58ed2fa2a477c16ab8a4c62782ce hess-24-381-2020-ie00019.svg14pt16pthess-24-381-2020-ie00019.png is mostly to inline-formula $M28inlinescrollmathml{\mathrm{italic\; \sigma }}_E^{\mathrm{normal\; 2}}$ 14pt16ptsvg-formulamathimgc7effbfe6087e331f78bb0c13add15a4 hess-24-381-2020-ie00020.svg14pt16pthess-24-381-2020-ie00020.png , but as the storage capacity increases the partitioning of inline-formula $M29inlinescrollmathml{\mathrm{italic\; \sigma }}_P^{\mathrm{normal\; 2}}$ 14pt16ptsvg-formulamathimg0ccf32c10b9d484c453f85fe5c8242b3 hess-24-381-2020-ie00021.svg14pt16pthess-24-381-2020-ie00021.png is increasingly shared between inline-formula $M30inlinescrollmathml{\mathrm{italic\; \sigma }}_E^{\mathrm{normal\; 2}}$ 14pt16ptsvg-formulamathimg1449aefc2ef8562acbc5bfe36a25bcc8 hess-24-381-2020-ie00022.svg14pt16pthess-24-381-2020-ie00022.png , inline-formula $M31inlinescrollmathml{\mathrm{italic\; \sigma }}_{\mathrm{normal\; \Delta }S}^{\mathrm{normal\; 2}}$ 20pt17ptsvg-formulamathimgd85a0a46bf735ef5d2b369c0f83bbd78 hess-24-381-2020-ie00023.svg20pt17pthess-24-381-2020-ie00023.png and the covariance between those variables. In other environments (i.e. extremely wet and semi-arid–semi-humid) the variance partitioning proved to be extremely complex and a synthesis has not been developed. We anticipate that a major scientific effort will be needed to develop a synthesis of hydrologic variability.