Using Satellite-Based Terrestrial Water Storage Data: A Review

Vol.:(0123456789) Su eys in Geophysics (2023) 44:1489–1517 h ps://doi.o g/10.1007/s10712-022-09754-9 1 3 Using Sa elli e‑Based Te es ial Wa e S o age Da a: ARe iew Vincen Humph ey1,2 · Ma hewRodell3 · Anne eEicke 4 Recei ed: 11 Augus 2022 / Accep ed: 23 No embe 2022 / Published online: 13 Janua y 2023 © The Au ho (s) 2023 Abs ac Land wa e s o age plays a key ole o he Ea h’s clima e, na u al ecosys ems, and human ac i i ies. Since he launch o he i s G a i y Reco e y and Clima e Expe imen (GRACE) mission in 2002, spacebo ne obse a ions o changes in e es ial wa e s o age (TWS) ha e p o ided a unique, global pe spec i e on na u al and human-induced changes in eshwa e esou ces. E en hough hey ha e become much used wi hin he b oade Ea h sys em science communi y, space-based TWS da ase s s ill inco po a e impo an and case-speci ic limi a ions which may no always be clea o use s no amilia wi h he unde lying p ocessing algo i hms. He e, we p o ide an accessible and illus a ed o e iew o he measu emen concep , o he main a ailable da a p oduc s, and o some equen ly encoun e ed echnical e ms and concep s. We summa ize conc e e ecommenda ions on how o use TWS da a in combina ion wi h o he hyd ological o clima ological da ase s, and guidance on how o a oid possible pi alls. Finally, we p o ide an o e iew o some o he main applica ions o GRACE TWS da a in he ields o hyd ology and clima e science. This e iew is w i en wi h he in en ion o suppo ing u u e esea ch and acili a ing he use o sa elli e-based e es ial wa e s o age da ase s in in e disciplina y con ex s. Keywo ds Te es ial wa e s o age· GRACE· Clima ology· Hyd ology· Remo e sensing· Geodesy A icle Highligh s • A summa y o he GRACE sa elli e mission, he de i ed e es ial wa e s o age da a- se s, and he main echnical e ms and concep s * Vincen Humph ey incen .humph ey@en .e hz.ch 1 Depa men o Geog aphy, Uni e si y o Zü ich, Win e hu e s asse 190, 8057Zü ich, Swi ze land 2 Ins i u e o A mosphe ic andClima e Science, ETH Zü ich, Uni e si ä s asse 16, 8092Zü ich, Swi ze land 3 Ea h Sciences Di ision, NASA Godda d Space Fligh Cen e , G eenbel , MD20771, USA 4 Ha enCi y Uni e si y Hambu g, Übe seeallee 16, 20457Hambu g, Ge many 1490 Su eys in Geophysics (2023) 44:1489–1517 1 3 • A su ey o he main challenges encoun e ed in hyd o-clima e esea ch when wo king wi h GRACE da a and how o add ess hem • An o e iew o ecen applica ions o GRACE TWS in wa e budge analyses, ex emes moni o ing, and Ea h sys em modelling 1 In oduc ion Te es ial wa e s o age (TWS) is de ined as he o al amoun o wa e s o ed on land. This includes any ype o na u al o a i icial wa e ese oi , such as g ound wa e , soil mois- u e, i e s, lakes, snowpack, glacie s, land ice, and wa e s o ed in biomass. TWS changes ep esen changes in e ms o a ailable eshwa e esou ces which can ha e impo an impac s on bo h na u al ecosys ems and human ac i i ies. In esponse o he combined in luences o na u al clima e a iabili y and human in e en ions, TWS changes un old o e a wide ange o empo al scales, anging om sho -li ed ex eme e en s caused by d ough s and loods, o seasonal a iabili y, in e -annual a iabili y, and decadal ends ela ed o, o ins ance, glacie mass loss o g oundwa e abs ac ions. As an in eg a o o changes in all wa e luxes, TWS ep esen s a key long- e m memo y a iable o he wa e cycle and he Ea h sys em in gene al, bo h esponding o and eeding back o a mosphe ic and oceanic a iabili y. TWS will change in esponse o any imbalance be ween he main wa e luxes ha a e p ecipi a ion (P), e apo anspi a ion (ET), and uno (R). Fo his eason, i ep esen s one o he key a iables o he wa e budge (Eq.1). TWS can also be exp essed as he sum o all he po en ial wa e ese oi s. He e, GW is he g oundwa e , SM is he soil mois u e, SWE is he snow wa e equi alen , SW is he su ace wa e , LI is he land ice, and BW is he biomass wa e . Space-based obse a ion o TWS changes debu ed wi h he launch o he G a i y Reco e y and Clima e Expe imen (GRACE) sa elli e mission in 2002. Be o e 2002, he e we e mainly wo ways ha TWS changes could be es ima ed. Fi s , hey can be es ima ed as he esidual o he o he obse ed wa e luxes wi hin he wa e budge equa ion (Eq.1). O cou se, his app oach equi es su icien ly accu a e es ima es o p ecipi a ion, e apo- anspi a ion and uno luxes (Oki e al. 1995; Hi schi and Sene i a ne 2017). The second app oach is o es ima e TWS as he sum o indi idually obse ed o modelled ese oi s (Eq.2). In his case, one can ei he ely on es ima es om a hyd ological model o use ex ensi e g ound obse a ions, p o ided hese a e a ailable (Rodell and Famiglie i 2001). Depending on he clima e ype, ce ain o hese TWS componen s may domina e TWS a iabili y (e.g., snow and ice in pola and alpine egions) while o he s, like biomass wa e , can be sa ely igno ed (Rodell e al. 2005; Ge i ana e al. 2017). Bo h o hese app oaches ha e se ious limi a ions. In pa icula , hese indi ec es ima es accumula e he measu emen o es ima ion e o s p esen in all he o he e ms, leading o po en ially la ge unce ain ies. The GRACE mission p o ided he i s di ec obse a ions o TWS changes a he con i- nen al scale (Wah e al. 1998, 2004; Tapley e al. 2004). The mission’s goal was o measu e e y small a ia ions o he Ea h’s g a i y ield which a e caused by he edis ibu ion o (1) dTWS d =P−ET − R (2) TWS =GW +SM +SWE +SW +LI +BW 1491 Su eys in Geophysics (2023) 44:1489–1517 1 3 masses o e land, a mosphe e, and oceans. In he nex sec ion, we will discuss he mission concep and da a p oduc s in mo e de ail. Du ing he i s yea s o he GRACE mission, ob aining p ecise es ima es o TWS changes om he aw GRACE obse a ions equi ed de eloping and es ing new e ie al algo i hms and pos p ocessing s a egies. Those ech- niques ha e since hen made eno mous p og ess, and GRACE-based TWS obse a ions ha e eached a le el o ma u i y enabling hem o be used in a wide a ie y o applica ions, such as moni o ing o eshwa e esou ces and assimila ion in o nume ical hyd ological models (Tapley e al. 2019; Rodell e al. 2018). Following he success o he pionee ing GRACE mission, g a ime ic TWS emo e sensing has en e ed a new phase whe e se e al successo missions a e being p oposed and implemen ed (Wiese e al. 2011; Elsaka e al. 2013; Pail e al. 2015; Haagmans e al. 2020; Flech ne e al. 2021). The objec i e is o bo h ex end he exis ing da a eco d and imp o e he spa io empo al esolu ion o he inal da a p oduc s. In 2018, jus one yea a e he ini ial GRACE mission ended, he succes- so GRACE Follow-On mission was success ully launched (Lande e e al. 2020). Some e o s ha e also been in es ed in p oducing publicly a ailable long- e m TWS eco ds ha co e he p e-GRACE e a as well, mainly by means o da a assimila ion, machine lea ning, and s a is ical econs uc ions (Kuma e al. 2016; Humph ey and Gudmundsson 2019; Li e al. 2021). Using only geode ic obse a ions om sa elli e lase anging (SLR), Löche and Kusche (2020) ha e ecen ly been able o ex end he GRACE eco d back o 1992. We p o ide in his a icle an o e iew o g a ime ic TWS obse a ions, o hei usage, and o some o hei applica ions. Sec ion2 p o ides a summa y o he GRACE mission, o he main a ailable hyd ological da a p oduc s, and o some equen ly encoun e ed con- cep s and issues ha a e pa o he p ocessing algo i hms. Sec ion3 e iews some o he equen challenges associa ed o using GRACE da a p oduc s and o e s guidance as o how o add ess hem. Sec ion4 e iews a selec ion o applica ions ha illus a e he use o space-based TWS obse a ions in hyd ology and Ea h sys em sciences. 2 GRACE Mission, Common Te ms, andDa a P oduc s 2.1 Mission Concep The o e all p inciple o he GRACE mission is o measu e ime- a ying anomalies in he Ea h’s g a i y ield, om which e es ial wa e s o age changes can be in e ed (Tap- ley e al. 2004; Wah e al. 2004). Because he wa e cycle and he global a mosphe ic ci cula ion con inuously edis ibu e eno mous amoun s o wa e mass a ound he globe, his causes local and ex emely small changes in he Ea h’s g a i a ional a ac ion. Such changes a e on he o de o 10–8m s−2, which is a billion imes smalle han he a e - age alue o g = 9.81m s−2 (Wou e s e al. 2014). S ill, his is subs an ial enough o in lu- ence he o bi s o sa elli es, especially when hey ha e a ela i ely low al i ude (i.e. ini ially 500km o he GRACE sa elli es). A empo a y excess in wa e mass, o ins ance we soils caused by hea y ains, p o- duces a empo a ily s onge g a i a ional accele a ion a ha loca ion. This in u n leads o mino a ia ions in he beha iou o a spacec a along i s usual o bi ( ela i e o wha happens when he TWS is close i s long- e m mean). The spacec a expe iences a s onge g a i a ional pull when app oaching a posi i e mass anomaly, leading o an along- ack accele a ion, ollowed by a decele a ion immedia ely a e passing he anomaly (Fig.1). Insi ua ions whe e wa e mass is lacking (i.e. du ing a d ough ), he opposi e beha iou 1492 Su eys in Geophysics (2023) 44:1489–1517 1 3 is seen and along- ack decele a ion is ollowed by accele a ion. He e, i becomes ob i- ous ha one key cha ac e is ic o GRACE is ha i es ima es mass anomalies ela i e o he long- e m a e age g a i y ield. In o he wo ds, GRACE p o ides es ima es o e es- ial wa e s o age anomalies ( TWSA =TWS −TWS ). Nei he he o al amoun o TWS no i s long- e m a e age ( TWS ) can be measu ed wi h GRACE. To measu e g a i y ield a ia ions (and in e wa e mass changes om hem), he i s GRACE mission used a pai o win sa elli es, wi h he i s spacec a lying abou 220km ahead o he o he . The sa elli es we e equipped wi h h ee-dimensional accele ome e s o measu e a mosphe ic d ag and o he non-g a i a ional accele a ions, and he change in dis ance be ween he wo spacec a (on a e age 220km apa ) was con inuously measu ed wi h a K-band mic owa e in e e ome e o a p ecision o abou 1μm pe second. GRACE Follow-On can achie e nanome e p ecision wi h i s lase anging ins umen . These measu emen s a e needed o p ecisely moni o changes in he o bi al ajec o y o each sa elli e. The o bi s a e u he cons ained wi h obse a ions om he on-boa d GPS ecei e s and s a came as. O cou se, only subs an ial mass changes ( ypically occu ing o e a la ge spa ial ex en ) can be eco e ed wi h his me hod. A he global scale (summing all land a eas), he al e n- ance be ween we and d y seasons causes seasonal changes in global TWS (clea ly isible in GRACE da a) o abou 6000 giga ons (equi alen o 6000 km3 o wa e ) (Reage e al. 2016). This seasonal change in land wa e s o age causes global sea le el o all and ise by abou 17mm e e y yea as wa e is exchanged be ween land and oceans. GRACE sa elli es can also moni o TWS anomalies a smalle spa ial scales, o e a eas as small as 150,000 Fig. 1 Measu emen p inciple o he GRACE mission. The wo GRACE sa elli es ollow each o he a an al i ude o abou 500km, sepa a ed by a dis ance o abou 220km. When a egion expe iences an excess in mass, he g a i a ional a ac ion is locally s onge , causing he leading sa elli e o accele a e owa ds he posi i e mass anomaly. As a esul he dis ance be ween he wo spacec a inc eases un il he ailing sa el- li e ca ches up. These a ia ions in o bi al beha iou a e hen used o in e ime-dependen mass changes a he Ea h’s su ace. Backg ound c edi : eepik.com 1493 Su eys in Geophysics (2023) 44:1489–1517 1 3 km2 a mid-la i udes, and down o 50,000 km2 nea he poles, whe e he sa elli e g ound acks a e close oge he (Fig.2; Rowlands e al. 2005; Swenson e al. 2006; Vishwaka ma e al. 2018). As will be seen in he nex sec ions, he e a e many ac o s which con ol he accu acy and esolu ion o GRACE da a o a speci ic use case. Ve y o en, choices in e ie al echniques and pos p ocessing algo i hms may ha e di e en impac s on he in e - p e abili y o he da a. He e, we p o ide an o e iew o he main concep s and e ms ha a e commonly encoun e ed when wo king wi h use -le el GRACE da a. 2.2 Sphe ical ha monics Since he ini ial yea s o he GRACE mission, he s anda d app oach o p ocessing GRACE g a i y da a o in e mass change has been o ep esen he Ea h’s g a i y ield using sphe ical ha monics. Sphe ical ha monics a e unc ions ha a e pa icula ly con enien o app oxima ing he non-sphe ical shape o he Ea h o i s g a i y ield (Wah e al. 1998). The so-called low-deg ee and low-o de (S okes) coe icien s o hese sphe ical ha monics ep esen la ge-scale ea u es (like he Ea h’s obla eness), while highe -deg ee and highe - o de coe icien s ep esen ea u es a inc easingly ine spa ial scales. The e is an uppe limi o he numbe o coe icien s which can be obus ly es ima ed wi h a gi en se o GRACE measu emen s. I insu icien obse a ions a e a ailable, high-deg ee coe icien s will be e y unce ain. Wi h a mon h’s wo h o GRACE measu emen s, i is gene ally accep ed ha one can eliably es ima e sphe ical ha monic coe icien s up o a deg ee and o de o a leas 60. This numbe pu s a ha d limi on he esul ing spa ial esolu ion o he mass change es ima es, a abou 330 × 330km. Including a highe numbe o (less obus ) coe icien s wi h he aim o including mo e de ailed spa ial ea u es is o cou se possible (e..g., a deg ee/o de 120, esolu ion would be abou 160km); howe e , his will inc ease Fig. 2 Sa elli e g ound acks o he GRACE mission ( igu e by To s en Maye -Gü , Technische Uni e - si ä G az) 1494 Su eys in Geophysics (2023) 44:1489–1517 1 3 he unce ain y o he solu ion and lead o a much highe le el o noise. As a esul , mo e in ense spa ial il e ing (smoo hing) will be needed o educe his noise, which o en has he e ec o damping he eco e ed TWS dynamics. In some o he GRACE li e a u e, a esolu ion o abou 3° × 3° (330 × 330km) has been p oposed as a possible comp omise be ween ha ing he highes possible esolu ion while s ill limi ing he le el o noise glob- ally (Wa kins e  al. 2015). Thus, many o he a ailable mon hly GRACE hyd ological p oduc s based on sphe ical ha monics a e using solu ions ha a e e e ed o as up o (o unca ed o) deg ee and o de 60 (Fig.3a). No e ha he ade-o be ween he numbe o obse a ions used o cons ain he solu ion and he achie able spa ial esolu ion also makes i possible o gene a e weekly o e en daily GRACE p oduc s albei a lowe spa ial esolu- ion o wi h educed accu acy (Ku enbach e al. 2012). Finally, we no e ha some o he low-deg ee coe icien s (like C20, a coe icien ela ed o he Ea h’s obla eness) a e no pa icula ly well measu ed by GRACE and a e o en eplaced wi h da a om o he sou ces like sa elli e lase anging (SLR) (Loomis e al. 2020). 2.3 Mass Concen a ion Blocks (Mascons) The p ima y al e na i e o sphe ical ha monics o p ocessing GRACE da a and de i ing mass anomalies is o use he so-called mass concen a ion blocks (abb e ia ed as mascons) (Rowlands e al. 2005, 2010). A mascon co esponds o a small, p ede ined egion on he Ea h’s su ace, o ins ance a 3° ec angula g id cell (Fig.3b). The app oach applies ime- dependen mascon pa ame e s o adjus a s a ic ( o wa d modelled) g a i y ield so ha i ma ches he ime-dependen mass su pluses o de ici s. This p ocedu e is di e en om sphe ical ha monics in he sense ha a mascon is no a ep esen a ion o he global g a i y ield, bu ins ead se es o quan i y a local mass anomaly. The s a ic g a i y ield is ypi- cally a sphe ical ha monic solu ion based on se e al yea s o GRACE da a ha ac s as a high- esolu ion and low-noise e e ence. An ad an age o ha ing loca ion-dependen mas- con pa ame e s is ha hey can be mo e easily cons ained based on a p io i in o ma ion, hus p o iding some imp o emen in e ms o he achie able spa ial esolu ion, especially Fig. 3 TWS anomalies o he mon h o Decembe 2015, as eco e ed in wo di e en GRACE p oduc s. a Sphe ical ha monic solu ion om he GeoFo schungsZen um (GFZ) and b mass concen a ion (mascon) solu ion om he Je P opulsion Labo a o y (JPL). No e ha he mass anomalies a e mo e concen a ed bu also blockie in he mascon solu ion. Bo h da ase s we e ob ained om NASA’s GRACE Tellus websi e which p o ides a collec ion o da a p oduc s sui ed o hyd ological applica ions. In Decembe 2015, he e was a la ge d ough o e mos o he Amazon basin which caused a signi ican nega i e TWS anomaly as illus a ed he e. Sou ce da a: a GRC Tellus Land RL06 (GFZ), b JPL RL06M Ve sion 2.0 (as lis ed in Table1) 1495 Su eys in Geophysics (2023) 44:1489–1517 1 3 o e pola egions which a e mo e densely sampled by GRACE’s g ound acks (Lu hcke e al. 2006). The es ima ion o mascon pa ame e s can be imp o ed by using as an addi- ional cons ain an expec ed a e age pa e n o co a iances o a iances be ween neigh- bou ing mascons ( aken o ins ance om a hyd ologicalmodel o a p e ious GRACE solu ion) (Wa kins e al. 2015; Sa e e al. 2016). An addi ional po en ial cons ain is o implemen empo al co ela ion in he mascon pa ame e s, aking ad an age o he ac ha many la ge-scale mass changes un old ela i ely slowly and a e hus au oco ela ed in ime. In con as , sphe ical ha monic solu ions a e global in na u e and each mon hly solu ion is usually independen om he nex . No e ha spa ial and/o empo al cons ain s can also be in oduced in sphe ical ha monics, as in Ku enbach e al. (2012) o in Sa e e al. (2012). Fo hyd ological applica ions, key ad an ages o cons ained mascon p oduc s com- pa ed o uncons ained sphe ical ha monics a e ha he o iginal magni udes o he TWS signals a e be e eco e ed and he TWS changes (especially along coas lines) a e be e esol ed spa ially (Scanlon e al. 2016) (also see Fig.3). Mascon p oduc s a e also easie o use in gene al as hey do no need o be spa ially il e ed (smoo hed) du ing pos p ocessing. This is because some (geophysically mo i a ed) spa ial in o ma ion is explici ly guiding he e ie al o he mascon solu ion, hus g ea ly educing he spa ial noise pa e ns. While such cons ain s a e e ec i e in educing he noise, he numbe o obse a ions necessa y o compu e a solu ion s ill places an uppe limi on he achie able maximum spa ial esolu- ion (see he Sec ion2.2 on ‘Sphe ical ha monics’). Thus, while some cen es p o ide mas- cons ha ha e a ela i ely ine spa ial esolu ion, o ins ance a 1° (110 × 110km) g id, he e ec i e spa ial esolu ion emains close o 300 × 300km (Sa e e al. 2016). 2.4 De‑aliasing Tempo al changes in he Ea h’s g a i y ield a e no only happening because o e es ial wa e s o age a ia ions, bu also due o many o he p ocesses. Fo ins ance, he a mos- phe ic and oceanic ci cula ions cause g a i y ield changes a empo al scales o a ew hou s o a ew days (Dobslaw e al. 2013). Because GRACE obse a ions a e sensi i e o hese p ocesses as well, he a iabili y caused by a mosphe ic and oceanic p ocesses is said o be aliased on o he GRACE measu emen s (Fig.4a). In o he wo ds, he g a - i y signal associa ed wi h land hyd ological p ocesses is con ol ed wi h g a i y signals esul ing om highe - equency p ocesses. In o de o isola e he hyd ological e ec s, he high- equency signals need o be es ima ed wi h obse a ion-d i en a mosphe ic eanaly- sis (i.e. wea he models) and hen sub ac ed om he GRACE measu emen s. This p ocess is called de-aliasing. Se e al de-aliasing p oduc s a e a ailable, such as he AOD1B p od- uc om he Ge man GeoFo schungsZen um (GFZ) (Dobslaw e al. 2017). Fo end-use s o GRACE hyd ology da a p oduc s, he choice o he de-aliasing me hod is a ely an issue because his s ep is pe o med du ing he gene a ion o TWS anomaly ields. Howe e , i is wo h knowing ha e o s in he a mosphe ic and oceanic ci cula ion models, oge he wi h spa ial and empo al unde sampling o he g a i y ield changes associa ed wi h hose ci cula ions (which complica es hei emo al) do con ibu e a la ge ac ion o he e o s in e ie ed TWS anomalies (Han e al. 2004; Seo e al. 2008). In addi ion o educing aliasing e o s, de-aliasing also implici ly emo es he con ibu ion o he a mosphe e o mon hly mass changes. 1496 Su eys in Geophysics (2023) 44:1489–1517 1 3 2.5 De‑s iping andFil e ing A long-s anding issue wi h GRACE da a p ocessing has been he p esence o unphysical no h–sou h-o ien ed s ipes in maps o mass anomalies (e.g., Wou e s e al. 2014). The o igin o hese s ipes lies mainly in he pola con igu a ion o he GRACE o bi s and he along- ack o ien a ion o he wo sa elli es hemsel es, which causes no h–sou h g adi- en s o be much be e obse ed han eas –wes ones. Simula ion s udies ha e shown ha his o bi con igu a ion ends o magni y inaccu acies in he de-aliasing p oduc s, causing s iping in he g a i y solu ions (Seo e al. 2008). Recen wo k by Peidou and Pagia akis (2020) has also shown ha s iping may esul om sub-Nyquis a e ac s caused by la i- udinal o e sampling o he low- equency g a i a ional signal o he geoid. In addi ion o s ipes, measu emen s e o s and noise om many o he sou ces also cause esidual e o s which con amina e he maps o TWS anomalies ob ained om aw GRACE solu ions. a b c Fig. 4 Illus a ion o some o he equen ly encoun e ed concep s in GRACE p ocessing. a Aliasing e e s o he con amina ion o a low- equency signal, he e he hyd ological a iabili y, by an unde sampled high- equency signal, he e idal and non- idal e ec s on he geopo en ial. De-aliasing e e s o he (impe ec ) emo al o aliasing using model es ima es o he high- equency signals. b Simpli ied ep esen a ion o he co ela ed e o s a ec ing he mass anomalies eco e ed by GRACE and he use o il e ing echniques o emo e hem. An unwan ed e ec o il e ing is ha i also a enua es and mixes up he ue geophysical sig- nals, leading o a bias in he e ie ed TWS ampli ude and a leakage o TWS signals be ween neighbou ing egions. c Gene a ion p ocess and usage o he model-based scale ac o s designed o co ec o biases in GRACE TWS when compu ing egional a e ages a a la ge scale 1497 Su eys in Geophysics (2023) 44:1489–1517 1 3 Many app oaches ha e been p oposed o educe s iping pa e ns as well as o he e o s in he mos e icien way. O iginally, la ge-scale (i.e. up o 1000km) Gaussian il e ing was applied o he da a, e ec i ely emo ing he noise, bu wi h he nega i e consequence ha many eal smalle -scale ea u es would be en i ely smoo hed ou (Wou e s e al. 2014). This posed a signi ican challenge because e alua ing he i s GRACE TWS anomalies agains hyd ological models equi ed ha he model da a unde go a compa able il e ing (Schmid e al. 2006). Mo e ad anced echniques ake ad an age o he aniso opy o he s iping pa e ns o op imally emo e he noise while s ill e aining mos o he eal spa ial pa e ns (Swenson and Wah 2006b; Kusche 2007). The objec i e o hese de-s iping and il e ing algo i hms has gene ally been o imp o e g idded GRACE hyd ology p oduc s o egion-speci ic ime se ies ha a e based on sphe ical ha monics and make hem mo e easily compa able o o he model-based o obse a ional da ase s. Fo mascon solu ions, his p oblem is much less p ominen because he a p io i cons ain s used in he solu ions explici ly mi iga e he noise. Thus, i is no necessa y o apply de-s iping o il e ing du - ing mascon pos p ocessing. 2.6 Leakage Due o he unca ion o sphe ical ha monics, he de-s iping, il e ing, and/o cons aining p ocesses, g idded maps o TWS anomalies ha e a e y high deg ee o spa ial au oco ela- ion which is, o a la ge pa , no ep esen a i e o he eal TWS anomaly pa e ns. The spa ial smoo hing and il e ing inhe en o GRACE p ocessing algo i hms means ha he TWS anomaly es ima ed a any gi en g id cell also inco po a es TWS signals occu ing in he neighbou ing egion, ou side he a ea o in e es . The consequence is ha eal TWS anomaly pa e ns may be dis o ed and signal ampli udes will be gene ally damped. In he GRACE communi y, his e ec is usually e e ed o as signal leakage. Figu e4b illus a es i o he gene al case o sphe ical ha monics pos p ocessing. Some au ho s p e e o use he e m leakage o desc ibe he con amina ion by ex e nal signals and use he e m bias o desc ibe signal damping (Klees e al. 2007). O he au ho s use he e m leakage o desc ibe bo h e ec s (Swenson and Wah 2002). Signal bias and leakage a e p oblema ic o hyd ological applica ions which a emp o isola e he TWS anomalies occu ing wi hin a speci ic egion like a wa e shed o a la ge aqui e . I is e en wo se when damped TWS changes a e combined o compa ed wi h luxes in a wa e budge analysis. Va ious app oaches ha e been p oposed o add ess his issue, which a ec s sphe ical ha monic solu ions mo e han mascon solu ions. I he egion o in e es is p ecisely de ined, a speci ically op imized a e aging ke nel (o unc ion) can be used o minimize he con amina ion by TWS signals ha a e loca ed ou side o he egion o in e es (Swenson and Wah 2002). These a e aging ke nels a e also used o cal- cula e he expec ed signal a enua ion and es ima e a mul iplica i e co ec ion ac o which is used o es o e (o escale) he signal ampli ude (Velicogna and Wah 2006; Rodell e al. 2009), hus mi iga ing signal bias ( hough no leakage). In some cases, hyd ological model da a may also be used o es ima e and emo e he leakage con ibu ion o TWS signals ou side o he a ea o in e es (Swenson and Wah 2007). Fo he case o signal leakage ac oss coas lines (i.e. be ween land and ocean mass changes), speci ic app oaches ha e been de eloped o u he educe leakage and be e sepa a e he land and ocean mass con- ibu ions (Chen e al. 2015; Wiese e al. 2016; T egoning e al. 2022). Howe e , leakage and bias co ec ion echniques a e in gene al oo cumbe some o implemen o hyd olo- gis s, glaciogis s, o o he end-use s who a e no amilia wi h GRACE da a p ocessing 1504 Su eys in Geophysics (2023) 44:1489–1517 1 3 no ed in Eq.1 co esponds o he di e ence be ween he s a and he end o he conside ed ime pe iod. Howe e , GRACE ne e p o ides such ins an aneous es ima es o TWS, only empo al a e ages aken o e he whole ime pe iod (Fig.6a). As a esul , di e en ia ing mon hly GRACE da a only p o ides an app oxima e es ima e o dTWS∕d (Rodell e al. 2004; Swenson and Wah 2006a). This can be easily demons a ed o a ious di e ence ope a o s and syn he ic ‘ oy’ model da a (Fig.6b). Swenson and Wah (2006a) o iginally e alua ed he accu acy o he backwa ds di e - ence app oxima ion using hyd ological model da a: As demons a ed in Swenson and Wah (2006a) and as illus a ed in Fig.6b, app oxi- ma ion e o s o a gi en mon h can be e y la ge, ex eme alues a e gene ally unde es i- ma ed and may also be empo ally shi ed. Use s should e y ca e ully ake hese app oxi- ma ion e o s in o accoun when de i ing any conclusions abou wa e balance closu e o phase shi s be ween wa e s o age and wa e luxes on a mon hly basis. Because GRACE obse a ions also con ain noise, compu ing cen ed di e ences has been epo ed o p o- ide a mo e obus and less noisy app oxima ion o dTWS∕d as compa ed o o wa ds o backwa ds di e ences (Lande e e al. 2010; Long e al. 2014; Pascolini-Campbell e al. 2020). This means compu ing he di e ence be ween he nex and he p eceding mon hs and di iding ha by he ime di e ence. No e ha his in oduces some smoo hing in he es ima e o dTWS∕d (see Fig.6b). (3) dTWS d ≈ TWSA −TWSA − 1 Δ Fig. 6 a Illus a i e TWS anomaly ime se ies gene a ed wi h a simpli ied hyd ological model. b Wa e budge closu e a mon hly scale be ween he mon hly sum o wa e luxes (g een), and mon hly TWS changes es ima ed wi h di e en app oaches: backwa ds di e ences o mon hly TWS a e ages (blue), cen- ed di e ences o mon hly TWS a e ages (o ange), and he ac ual mon hly s o age change calcula ed om he daily TWS ime se ies (black) 1505 Su eys in Geophysics (2023) 44:1489–1517 1 3 The mos impo an akeaway he e is ha compu ing a de i a i e o mon hly TWS o ob ain mon hly TWS changes ( Δ TWS, o ΔTWSAm ) does no p o ide a necessa ily accu- a e es ima e o dTWS∕d o use in Eq.1 (Rodell e al. 2004; Swenson and Wah 2006a). I daily es ima es o wa e luxes (i.e. o P-ET-R) a e a ailable, i becomes possible o mo e accu a ely compa e GRACE mon hly TWS da a agains wa e luxes (Rodell e al. 2004). In he ollowing, we p o ide equa ions ha can suppo such a o mal compa ison be ween wa e luxes and mon hly GRACE da a. Fi s , TWS is de ined as he a e age TWS calcula ed o e a whole mon h m which includes se e al days d = [1,…, n]: Because GRACE can only p o ide anomalies wi h espec o some unknown long- e m TWS a e age, wha is ac ually measu ed is a TWS anomaly (TWSA): TWSd is he absolu e wa e s o age on a gi en day o he mon h. (This absolu equan i y canno be de i ed om GRACE obse a ions, as he sa elli es a e a ec ed by all mass, no jus wa e mass.) Neglec ing la e al wa e edis ibu ion, TWSd can be de ined as he accu- mula ion o he wa e luxes since he s a o he mon h, plus he TWS amoun which was al eady he e jus be o e he mon h s a ed (Rodell e al. 2004; Swenson and Wah 2006a). Fo ins ance, wi h Pi, ETi, and Ri exp essing daily sums, Replacing TWSd in Eq.6 wi h he abo e exp ession yields he ollowing This equa ion shows ha he GRACE TWS anomaly o a gi en mon h is ela ed o he mean o he cumula i e sums o he wa e luxes o each day o he mon h, plus wo unknown o se s. These o se s con enien ly cancel ou wi h di e en ia ion. Fo ins ance, using Eq.8 and compu ing he backwa ds di e ence be ween wo consecu i e GRACE mon hs m12 and m34, which s a a days n1 and n3, and end a days n2 and n4, espec i ely, we ob ain (neglec ing measu emen e o s): whe e Δ is he ime di e ence be ween he middle poin s o he wo mon hs. This o mu- la ion co esponds o he di e ence in he unning means o he lux accumula ions (Rodell (4) dTWS d ≈ TWSA +1 −TWSA −1 2Δ (5) TWS m= 1 n n ∑ d=1 TWS d (6) TWSA m=TWSm−TWS = 1 n n ∑ d=1 TWSd−TWS (7) TWS d= [d ∑ i= 1 Pi−ETi−Ri ] +TWSd= 0 (8) TWSA m= 1 n n ∑ d= 1 [d ∑ i= 1 Pi−ETi−Ri ] +TWSd=0− TWS (9) dTWS A d = TWSA m34 −TWSA m12 Δ = 1 (n4−n3+1)∑n4 d=n3[∑d i=n1 Pi−ETi−Ri]−1 (n2−n1+1)∑n2 d=n1[∑d i=n1 Pi−ETi−Ri ] Δ 1506 Su eys in Geophysics (2023) 44:1489–1517 1 3 e al. 2011). P o ided daily es ima es o P, ET, and R, a e a ailable, TWSA di e ences can be o mally compa ed o wa e lux a iables using Eq.9. 3.6 Agg ega ing e o s When in e p e ing use -le el g idded GRACE da a, i is bes o assume ha neighbou ing pixels a e no independen o each o he . This needs o be aken in o accoun when compu - ing e o es ima es o he TWS a e age a he basin scale o egion scale (Be ing on and Robinson 2003). When compu ing an a e age o e an a ea con aining i=[1, …,n] pixels, he agg ega ed e o a iance 𝜎2 is ob ained as he sum o he a iance–co a iance ma ix o all he (g id poin le el) e o s. whe e w is he weigh assigned o each g id poin ( o an a i hme ic a e age, w=1∕n ) and 𝜌i , j is he co ela ion be ween he e o s (no be ween he TWS ime se ies) a he g id le el. Tha co ela ion is assumed o decay exponen ially as a unc ion o he (sphe ical) dis ance be ween g id poin s Di , j , wi h a a e ha is condi ioned by he so-called de-co - ela ion leng h ( l ) o he e o . (No e ha his iso opic app oach neglec s he no h–sou h e o s uc u e induced by s ipes.) The GRC Tellus Land webpage1 ecommends o use l=300 km o he measu emen e o and l=100 km o he leakage e o . I also p o ides a pseudo-code o implemen ing his equa ion. The o al e o is usually es ima ed in quad a u e (i.e. assuming he measu emen and leakage e o s a e independen ): 𝜎2 o al =𝜎 2 measu emen +𝜎 2 leakage Fo he 3° JPL mascons, assuming ha he measu emen e o s be ween mascons a e independen , he abo e o mula ion can be adap ed o 𝜌i,j=1 i g id poin s i and j belong o he same mascon and 𝜌i , j=0 o he wise ( o he measu emen e o s only). O he app oaches o de e mine egional unce ain ies om mascon p oduc s a e discussed in Loomis e al. (2019). 4 Applica ions o GRACE inHyd ology andClima e Science This sec ion p o ides only a b ie o e iew o some o he mos common applica ions o space-based e es ial wa e s o age obse a ions o eshwa e esou ces. Fo a mo e comple e pe spec i e, we also sugges he e iews by F appa and Ramillien (2018) and Chen e al. (2016) o g oundwa e moni o ing, Rodell e al. (2018) o long- e m ends in eshwa e esou ces, Gi o o and Rodell (2019) o ex emes in e es ial wa e s o age, Humph ey e al. (2016) o a clima ological summa y, Li e al. (2019) o da a assimila- ion in o nume ical hyd ological models, Tapley e al. (2019) o clima e change impac s (10) 𝜎 2= n ∑ i=1 n ∑ j=1 wi𝜎i⋅wj𝜎j⋅𝜌i, j (11) 𝜌i , j =e −(Di,j) 2 2l2 1 h ps:// g ace. jpl. nasa. go / da a/ ge - da a/ mon h ly- mass- g ids- land/. 1507 Su eys in Geophysics (2023) 44:1489–1517 1 3 de ec ion wi h GRACE, and Chen e al. (2022) o a b oade e iew including GRACE Follow-On. 4.1 Budge Residual App oaches Because TWS is linked o o he componen s o he wa e cycle (Eq.1 and 2), i can be used in combina ion wi h o he well-obse ed componen s in o de o es ima e ano he (less well-obse ed) e m as he esidual o he budge equa ion. Fo ins ance, using Eq.2, i is possible o es ima e g oundwa e s o age changes as ΔGW = ΔTWS – ΔSM – ΔSWE – ΔSW – ΔLI – ΔBW, p o ided eliable es ima es o all he o he componen s a e a ailable. Fo ins ance, Rodell e al. (2007) applied his app oach o es ima e g ound- wa e changes in he Mississippi basin using GRACE TWS obse a ions, as well as hyd o- logical model es ima es o soil mois u e and snow wa e equi alen (o he componen s we e su icien ly small o be neglec ed). These basin-scale es ima es we e hen compa ed agains insi u g oundwa e well obse a ions. This ype o app oach has been success- ully epea ed o moni o seasonal as well as long- e m g oundwa e changes o e many di e en egions and aqui e s o he wo ld (Yeh e al. 2006; Rodell e al. 2009; Famiglie i e al. 2011; Shamsudduha e al. 2012; Feng e al. 2013; Richey e al. 2015a), and equi es a ca e ul conside a ion o he e o p opaga ion. Indeed, because ΔGW is es ima ed as he esidual o he o he e ms, i also accumula es es ima ion e o s om all hese a iables. In combina ion wi h o he da a, GRACE-based g oundwa e a ia ions can be used o iden- i y unsus ainable deple ion o wa e esou ces (Richey e al. 2015b). Ano he ype o budge app oach is o in e Eq.1 in o de o es ima e wa e luxes in a way ha gi es p ope conside a ion o he pa icula na u e o GRACE measu emen s (see Sec . 3.5 In eg a ion wi h he wa e budge ). Because e apo anspi a ion is a gu- ably one o he mos ill-obse ed wa e cycle a iables, he e is g ea in e es in ob aining la ge-scale es ima es using a combina ion o GRACE TWS, p ecipi a ion, and uno da a (Rodell e al. 2004; Swenson and Wah 2006a; Long e al. 2014). Recen ly, his app oach has been used o e alua e model-based e apo anspi a ion o e he Amazon basin (Swann and Ko en 2017), and U.S. basins (Pascolini-Campbell e al. 2020). O he au ho s ha e used he same app oach o es ima e o he componen s o he wa e balance equa ion. Fo ins ance, Beh angi e al. (2017) o Gi o o e al. (2021) ha e used GRACE da a o con- s ain o imp o e p ecipi a ion es ima es, wi h he mos success o snow all. F eshwa e discha ge has also been es ima ed om GRACE using a budge app oach o ins ance in Syed e al. (2005) o in Famiglie i e al. (2009). 4.2 Moni o ing Ex emes Unlike p ecipi a ion-based o me eo ological d ough indices, GRACE di ec ly obse es changes in a ailable eshwa e esou ces, hus p o iding pa icula ly use ul in o ma ion o hyd ological d ough moni o ing. Many di e en cha ac e is ics o la ge-scale hyd o- logical d ough s such as du a ion, peak magni ude, se e i y, o spa ial ex en ha e been in es iga ed wi h GRACE da a. A la ge numbe o d ough indices o me ics ha can be used quan i y hese cha ac e is ics a a egional o global scale has been p oposed in p e ious s udies (Thomas e al. 2014; Zhao e al. 2017; Kusche e al. 2016). Regionally, excep ional d ough s which occu ed du ing he GRACE eco d ha e been well s udied and epo ed. GRACE has p o ided a space-based pe spec i e o hese d ough s, o en in he con ex o p e-exis ing eshwa e sca ci y and unsus ainable g oundwa e abs ac ions, 1508 Su eys in Geophysics (2023) 44:1489–1517 1 3 such as in Cali o nia (Famiglie i 2014), he Colo ado basin (Cas le e al. 2014), Texas (Long e al. 2013), No hwes e n China (Cao e al. 2015), o he Tig is-Euph a es egion (Voss e al. 2013). Many o hese d ough s ha e also been s udied om he pe spec i e o decadal clima e a iabili y and oscilla ions like he El Niño Sou he n Oscilla ion (ENSO), o ins ance o e he Yang ze i e basin (Zhang e al. 2015), in A gen ina (Chen e al. 2010b), he Amazon basin (F appa e al. 2012; Chaudha i e al. 2019), o a he global scale (Fo oo an e al. 2019). In ac , mos o he in e -annual a iabili y in GRACE TWS changes can be ela ed o clima e indices such as ENSO (Ni e al. 2017; P e e e al. 2021). GRACE obse a ions a e also ou inely assimila ed in o hyd ological models in o de o p oduce con inuous maps o d ough indica o s (Houbo g e al. 2012; Li e al. 2019) and d ough o ecas s (Ge i ana e al. 2020). Mo e ecen ly, GRACE obse a ions ha e been inc easingly used as an ancilla y da ase o quan i y d ough impac s on e es ial ecosys- ems. Fo ins ance, GRACE da a has been used o s udy he esponse o he Amazonian o es o he excep ional 2015–2016 d ough (Yang e al. 2018; Gloo e al. 2018) o he ole o g oundwa e in bu e ing he impac o hea wa es on ege a ion (Mu e al. 2021). Vege a ion also modula es he con ibu ion o he di e en wa e s o es o he o al TWS a iabili y (T au mann e al. 2022). A he global and egional scales, GRACE-based e - es ial wa e s o age a ia ions a e associa ed wi h anomalies in ca bon seques a ion by e es ial ecosys ems ha a e isible in a mosphe ic CO2 concen a ions (Humph ey e al. 2018; Bas os e al. 2020). Besides moni o ing d ough s, e es ial wa e s o age obse a ions a e also use ul o moni o lood po en ial. Because he isk o la ge loods is inc eased in he p esence o sa u a ed soils and illed wa e s o es, GRACE obse a ions can be used o p edic he like- lihood o loods a se e al mon hs’ lead ime (Reage and Famiglie i 2009; Reage e al. 2014). Al hough hey a e ypically mo e sho -li ed han d ough s, and hus mo e di i- cul o cap u e in mon hly GRACE solu ions, majo loods can also be diagnosed in he GRACE eco d. Fo ins ance, Chen e al. (2010a) s udied he TWS anomalies associa ed wi h he excep ional 2009 Amazon lood. O e he Tonlé Sap basin, in Cambodia, Tangda- m ongsub e al. (2016) could de i e a ema kably obus ela ionship be ween TWS anom- alies and inunda ed ex en based on MODIS. S ill, he e a e signi ican ly ewe s udies using GRACE o moni o loods (compa ed o d ough s), mainly because o hei limi ed spa ial and empo al ex en , which is poo ly cap u ed by he mon hly and coa se esolu ion GRACE obse a ions. Thus, o loods, i makes mos sense o assimila e GRACE da a in o hyd ological models wi h he aim o imp o ing lood wa ning sys ems in combina ion wi h o he highe - esolu ion da a (Reage e al. 2015). 4.3 Syne gies wi hHyd ological andClima e Models GRACE obse a ions may be used in combina ion wi h nume ical models in a a ie y o ways. He e, we will co e wo b oad ca ego ies. Fi s , GRACE obse a ions o TWS anomalies can be used as an independen benchma k o e alua e o compa e a collec ion o hyd ological and clima e models. Second, GRACE da a can also be assimila ed in o a nume ical model. In his case, some in o ma ion de i ed om GRACE is ans e ed o he model, wi h he goal o imp o ing i . Classically, his can be done ei he by uning he model pa ame e s so ha he model ou pu bes i s wi h GRACE da a (model calib a ion), o by o ce ully adap ing he model s a e (and po en ially b eaking he mass o ene gy bal- ance) so ha he model is b ough close o he obse a ions (da a assimila ion). Se e al examples o hese di e en applica ions can be ound in he li e a u e. 1509 Su eys in Geophysics (2023) 44:1489–1517 1 3 Va ious in e na ionally used model benchma king ools ely on GRACE da a o pe o m model in e compa isons. Fo ins ance he In e na ional Land Model Benchma king sys em (ILAMB) is used o e alua e land su ace and hyd ological models (Collie e al. 2018), and he Ea h Sys em Model E alua ion Tool (ESMValTool) (Ey ing e al. 2016b) is used o e alua e global coupled clima e models pa icipa ing in he Coupled Model In e compa i- son P ojec (CMIP) (Ey ing e al. 2016a). Compa isons be ween GRACE and hyd ological models has shown ha many models end o p oduce a peak seasonal TWS ha occu s oo ea ly compa ed o GRACE obse a ions, po en ially ela ed o a gene al unde es ima ion o he o e all wa e s o age capaci y (Schellekens e al. 2017). Limi a ions in he ep esen a- ion o TWS be ween he di e en models (inclusion o su ace and g ound wa e s o es, modelling o g oundwa e abs ac ions), as well as unce ain ies in he me eo ological o cing, may also explain some o he di e ences wi h GRACE obse a ions. Consis en wi h hese indings, land su ace and hyd ological models we e ound o lack in e -annual a iabili y compa ed o GRACE, especially o e semi-a id and opical egions, a si ua- ion which u he impac s he ep esen a ion o he ca bon cycle in hese models (Hum- ph ey e al. 2018). Models we e also shown o unde es ima e he magni ude o long- e m TWS ends compa ed o GRACE da a (Scanlon e al. 2018; Yang e al. 2020). In a ecen s udy, Jensen e al. (2019) compa ed he long- e m ends in GRACE TWS agains clima e change induced ends in wa e s o age as simula ed by coupled clima e models o e he las cen u y. Pa ly due o he di icul y o de i ing obus ends om he sho GRACE eco d, hey ound limi ed ag eemen , excep in egions wi h s ong p ojec ed d ying ends such as he Medi e anean basin and he Sou hwes e n Uni ed S a es. This limi ed ag ee- men also occu sbecause a subs an ial ac ion o he nega i e TWS ends obse ed om GRACE globally is ela ed o g oundwa e abs ac ions a he han o clima ic changes (An e al. 2021). In addi ion o model e alua ions, GRACE is also ou inely used o calib a ion and/o da a assimila ion in o hyd ological models. Model pa ame e iza ion exe cises in ol ing GRACE TWS include o example he wo k by Lo e al. (2010) who used GRACE da a o calib a e g oundwa e pa ame e s o he Communi y Land Model (CLM) o by Swenson and Law ence (2015) who de i ed an op imal soil hickness map also o CLM. We h e  al. (2009) used basin-scale GRACE obse a ions o calib a e he Wa e GAP Global Hyd ology Model (WGHM) and ound ha he model pa ame e s which we e he mos sensi i e o TWS as a model cons ain we e highly dependen on clima e egions and he ela i e impo ance o he di e en hyd ological p ocesses (snowmel , e apo anspi a ion, loodplain dynamics). In addi ion o s udies ocusing on he calib a ion o model pa ame- e s, a la ge numbe o s udies ha e also used da a assimila ion echniques, such as Ensem- ble Kalman il e s, wi h he goal imp o ing he model’s ep esen a ion o wa e s o es and luxes o e he pe iod whe e GRACE da a is a ailable, wi hou a emp ing o imp o e model physics o pa ame e s. In his case, assimila ion o GRACE in o nume ical models can also be iewed as a (model-dependen ) way o bo h downscaling and disagg ega ing TWS obse a ions in o cons i u ing indi idual wa e s o es (i.e. soil mois u e, g oundwa- e , e c.) (S ampoulis e al. 2019). The impac o da a assimila ion on he pe o mance o hyd ological models has gene ally been epo ed o be posi i e. Fo ins ance, Zai chik e al. (2008) ound ha assimila ion o GRACE TWS led o highe model skill when compa ed o insi u g oundwa e , Li e al. (2012) ob ained imp o emen s in uno es ima es in mos cases, Tangdam ongsub e al. (2015) ound imp o ed pe o mance agains insi u g ound- wa e bu only sligh imp o emen o s eam low, and Kuma e al. (2016) ob ained a be - e pe o mance o g oundwa e bu egionally a iable impac s in e ms o i e discha ge and e apo anspi a ion. In cases whe e an h opogenic p ocesses play an impo an ole, 1510 Su eys in Geophysics (2023) 44:1489–1517 1 3 bu a e no ep esen ed in he model (e.g., g oundwa e use and/o i iga ion), assimila - ing GRACE da a can ac ually lead o a signi ican dec ease in model pe o mance (Gi o o e al. 2017). Assimila ing GRACE da a in o nume ical models also poses some c i ical (and no ully esol ed) echnical challenges because o i s qui e coa se spa ial esolu ion and mon hly sampling (Eicke e al. 2014). In addi ion, he peculia , spa ially co ela ed, e o s uc u es o GRACE da a also need o be aken in o accoun by he da a assimila ion me hods (Schumache e al. 2016; Khaki e al. 2017). Finally, assimila ing only GRACE TWS da a in o a hyd ological model may also lead o a deg ada ion in pe o mance o some o he a iables. Thus, he assimila ion o GRACE simul aneously wi h se e al o he emo ely sensed wa e a iables, such as mic owa e-based soil mois u e o lake al ime y cons i u es one o he logical nex s eps (e.g., an Dijk e al. 2014; Tian e al. 2017; Khaki e al. 2019). Acknowledgemen s V.H. acknowledges inancial suppo om he Swiss Na ional Science Founda ion (g an no. P4P4P2_194464). Da a sou ces a e accessible as lis ed in Table1 o men ioned in he main ex . V.H. was esponsible o  he concep ualiza ion, li e a u e sea ch, igu es (excep Fig.2), and ini ial d a . M.R. and A.E. con ibu ed o he main ex and comple ed he li e a u e sea ch. We hank To s en Maye - Gü a Technische Uni e si ä G az o gi ing us pe mission o use Fig.2. We hank D . Julia P e e a Magellium o cons uc i e commen s and sugges ions on he manusc ip . Funding Open access unding p o ided by Swiss Fede al Ins i u e o Technology Zu ich. Decla a ions Con lic o in e es The au ho s ha e no compe ing in e es s o decla e ha a e ele an o he con en o his a icle. Open Access This a icle is licensed unde a C ea i e Commons A ibu ion 4.0 In e na ional License, which pe mi s use, sha ing, adap a ion, dis ibu ion and ep oduc ion in any medium o o ma , as long as you gi e app op ia e c edi o he o iginal au ho (s) and he sou ce, p o ide a link o he C ea i e Com- mons licence, and indica e i changes we e made. The images o o he hi d pa y ma e ial in his a icle a e included in he a icle’s C ea i e Commons licence, unless indica ed o he wise in a c edi line o he ma e ial. I ma e ial is no included in he a icle’s C ea i e Commons licence and you in ended use is no pe mi ed by s a u o y egula ion o exceeds he pe mi ed use, you will need o ob ain pe mission di ec ly om he copy igh holde . To iew a copy o his licence, isi h p:// c ea i eco mmons. o g/ licen ses/ by/4. 0/. Re e ences Abelen S, Sei z F (2013) Rela ing sa elli e g a ime y da a o global soil mois u e p oduc s ia da a ha - moniza ion and co ela ion analysis. Remo e Sens En i on 136:89–98. h ps:// doi. o g/ 10. 1016/j. se. 2013. 04. 012 An L, Wang J, Huang J, Pokh el Y, Hugonne R, Wada Y, Cáce es D, Mülle Schmied H, Song C, Be hie E, Yu H, Zhang G (2021) Di e gen Causes o Te es ial Wa e S o age Decline Be ween D ylands and Humid Regions Globally. 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