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<p>Variability of the terrestrial water cycle, i.e. precipitation (<span class="inline-formula"><i>P</i></span>), evapotranspiration (<span class="inline-formula"><i>E</i></span>), runoff (<span class="inline-formula"><i>Q</i></span>) and water storage change (<span class="inline-formula">Δ<i>S</i></span>) is the key to understanding hydro-climate extremes. However, a comprehensive global assessment for the partitioning of variability in <span class="inline-formula"><i>P</i></span> between <span class="inline-formula"><i>E</i></span>, <span class="inline-formula"><i>Q</i></span> and <span class="inline-formula">Δ<i>S</i></span> 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 <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M9" display="inline" overflow="scroll" dspmath="mathml"><mover accent="true"><mi>P</mi><mo mathvariant="normal">‾</mo></mover></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="10pt" height="13pt" class="svg-formula" dspmath="mathimg" md5hash="f6f023cd5b241bbdf3ecfc5ed08485d1"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00001.svg" width="10pt" height="13pt" src="hess-24-381-2020-ie00001.png"/></svg:svg></span></span> between the various sinks <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M10" display="inline" overflow="scroll" dspmath="mathml"><mover accent="true"><mi>E</mi><mo mathvariant="normal">‾</mo></mover></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="11pt" height="13pt" class="svg-formula" dspmath="mathimg" md5hash="331d8fbcffe0b139132d971941c0e763"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00002.svg" width="11pt" height="13pt" src="hess-24-381-2020-ie00002.png"/></svg:svg></span></span>, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M11" display="inline" overflow="scroll" dspmath="mathml"><mover accent="true"><mi>Q</mi><mo mathvariant="normal">‾</mo></mover></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="10pt" height="13pt" class="svg-formula" dspmath="mathimg" md5hash="4918d218751c71845f1ca4aa1e7d3d55"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00003.svg" width="10pt" height="13pt" src="hess-24-381-2020-ie00003.png"/></svg:svg></span></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M12" display="inline" overflow="scroll" dspmath="mathml"><mover accent="true"><mrow><mi mathvariant="normal">Δ</mi><mi>S</mi></mrow><mo mathvariant="normal">‾</mo></mover></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="18pt" height="13pt" class="svg-formula" dspmath="mathimg" md5hash="a33393a391972ab4550bcd71dc1c990d"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00004.svg" width="18pt" height="13pt" src="hess-24-381-2020-ie00004.png"/></svg:svg></span></span> and confirm the well-known patterns with <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M13" display="inline" overflow="scroll" dspmath="mathml"><mover accent="true"><mi>P</mi><mo mathvariant="normal">‾</mo></mover></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="10pt" height="13pt" class="svg-formula" dspmath="mathimg" md5hash="c7d179fe03ddf529f7bec0b29c0df224"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00005.svg" width="10pt" height="13pt" src="hess-24-381-2020-ie00005.png"/></svg:svg></span></span> partitioned between <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M14" display="inline" overflow="scroll" dspmath="mathml"><mover accent="true"><mi>E</mi><mo mathvariant="normal">‾</mo></mover></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="11pt" height="13pt" class="svg-formula" dspmath="mathimg" md5hash="bc06230a9cffa9748349c8023b1daa2e"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00006.svg" width="11pt" height="13pt" src="hess-24-381-2020-ie00006.png"/></svg:svg></span></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M15" display="inline" overflow="scroll" dspmath="mathml"><mover accent="true"><mi>Q</mi><mo mathvariant="normal">‾</mo></mover></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="10pt" height="13pt" class="svg-formula" dspmath="mathimg" md5hash="27f0f0853d5542b99e46e5a4f8cce313"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00007.svg" width="10pt" height="13pt" src="hess-24-381-2020-ie00007.png"/></svg:svg></span></span> 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 <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M16" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">σ</mi><mi>P</mi><mn mathvariant="normal">2</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="14pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="1e5d48b31fd4bbb942e5463f1529a515"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00008.svg" width="14pt" height="16pt" src="hess-24-381-2020-ie00008.png"/></svg:svg></span></span> (the source) is partitioned between the three variability sinks <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M17" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">σ</mi><mi>E</mi><mn mathvariant="normal">2</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="14pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="1a60437b60b38be1d8e0bb6dbcace6d0"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00009.svg" width="14pt" height="16pt" src="hess-24-381-2020-ie00009.png"/></svg:svg></span></span>, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M18" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">σ</mi><mi>Q</mi><mn mathvariant="normal">2</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="15pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="978bbacbab20fe43d346ef1d3e408dcf"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00010.svg" width="15pt" height="16pt" src="hess-24-381-2020-ie00010.png"/></svg:svg></span></span> and <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M19" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">σ</mi><mrow><mi mathvariant="normal">Δ</mi><mi>S</mi></mrow><mn mathvariant="normal">2</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="17pt" class="svg-formula" dspmath="mathimg" md5hash="d00d5b0f5d50c5b70e331182e01b5a79"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00011.svg" width="20pt" height="17pt" src="hess-24-381-2020-ie00011.png"/></svg:svg></span></span> 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 <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M20" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">σ</mi><mi>P</mi><mn mathvariant="normal">2</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="14pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="99bb7f33cad33af7250d71cd254fe8de"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00012.svg" width="14pt" height="16pt" src="hess-24-381-2020-ie00012.png"/></svg:svg></span></span> is mostly partitioned between <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M21" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">σ</mi><mi>Q</mi><mn mathvariant="normal">2</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="15pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="03d9fdd8093ff790d7ef71b46b7f1685"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00013.svg" width="15pt" height="16pt" src="hess-24-381-2020-ie00013.png"/></svg:svg></span></span>, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M22" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">σ</mi><mrow><mi mathvariant="normal">Δ</mi><mi>S</mi></mrow><mn mathvariant="normal">2</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="17pt" class="svg-formula" dspmath="mathimg" md5hash="c61c41f5708c1232b01cada7d3bb420f"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00014.svg" width="20pt" height="17pt" src="hess-24-381-2020-ie00014.png"/></svg:svg></span></span> and the associated covariances with limited partitioning to <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M23" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">σ</mi><mi>E</mi><mn mathvariant="normal">2</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="14pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="7ac380857947f19b7f4dc66abc398609"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00015.svg" width="14pt" height="16pt" src="hess-24-381-2020-ie00015.png"/></svg:svg></span></span>. We also find that the magnitude of the covariance components can be large and often negative, indicating that variability in the sinks (e.g. <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M24" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">σ</mi><mi>Q</mi><mn mathvariant="normal">2</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="15pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="d819bef56ee3d3557b8881f296219e23"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00016.svg" width="15pt" height="16pt" src="hess-24-381-2020-ie00016.png"/></svg:svg></span></span>, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M25" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">σ</mi><mrow><mi mathvariant="normal">Δ</mi><mi>S</mi></mrow><mn mathvariant="normal">2</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="17pt" class="svg-formula" dspmath="mathimg" md5hash="0c6a4157788b1a38bea00d851d7fbb29"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00017.svg" width="20pt" height="17pt" src="hess-24-381-2020-ie00017.png"/></svg:svg></span></span>) can, and regularly does, exceed variability in the source (<span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M26" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">σ</mi><mi>P</mi><mn mathvariant="normal">2</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="14pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="d1820149285385cb51925828a91f3ec0"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00018.svg" width="14pt" height="16pt" src="hess-24-381-2020-ie00018.png"/></svg:svg></span></span>). 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 <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M27" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">σ</mi><mi>P</mi><mn mathvariant="normal">2</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="14pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="92dc58ed2fa2a477c16ab8a4c62782ce"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00019.svg" width="14pt" height="16pt" src="hess-24-381-2020-ie00019.png"/></svg:svg></span></span> is mostly to <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M28" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">σ</mi><mi>E</mi><mn mathvariant="normal">2</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="14pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="c7effbfe6087e331f78bb0c13add15a4"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00020.svg" width="14pt" height="16pt" src="hess-24-381-2020-ie00020.png"/></svg:svg></span></span>, but as the storage capacity increases the partitioning of <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M29" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">σ</mi><mi>P</mi><mn mathvariant="normal">2</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="14pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="0ccf32c10b9d484c453f85fe5c8242b3"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00021.svg" width="14pt" height="16pt" src="hess-24-381-2020-ie00021.png"/></svg:svg></span></span> is increasingly shared between <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M30" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">σ</mi><mi>E</mi><mn mathvariant="normal">2</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="14pt" height="16pt" class="svg-formula" dspmath="mathimg" md5hash="1449aefc2ef8562acbc5bfe36a25bcc8"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00022.svg" width="14pt" height="16pt" src="hess-24-381-2020-ie00022.png"/></svg:svg></span></span>, <span class="inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" id="M31" display="inline" overflow="scroll" dspmath="mathml"><mrow><msubsup><mi mathvariant="italic">σ</mi><mrow><mi mathvariant="normal">Δ</mi><mi>S</mi></mrow><mn mathvariant="normal">2</mn></msubsup></mrow></math><span><svg:svg xmlns:svg="http://www.w3.org/2000/svg" width="20pt" height="17pt" class="svg-formula" dspmath="mathimg" md5hash="d85a0a46bf735ef5d2b369c0f83bbd78"><svg:image xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="hess-24-381-2020-ie00023.svg" width="20pt" height="17pt" src="hess-24-381-2020-ie00023.png"/></svg:svg></span></span> 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.</p>