Data, knowledge and modeling challenges for science-informed management of river deltas

1 Natural Capital Project, Stanford University, Stanford, CA 94305, United States of America 2 The Woods Institute for the Environment, Stanford University, Stanford, CA 94305, United States of America 3 Doerr School of Sustainability, Stanford University, Stanford, CA 94305, United States of America Soil Geography and Landscape group, Wageningen University & Research, Droevendaalsesteeg 3, 6708 PB Wageningen, The Netherlands Department of Civil, Environmental and Architectural Engineering, University of Padova, Via Marzolo 9, 35131 Padova, Italy Department of Subsurface and Groundwater Systems, Deltares Research Institute, Daltonlaan 600, 3584 BK Utrecht, The Netherlands *corresponding author: rschmitt@stanford.edu


Introduction
Global environmental change drastically alters human life and ecosystems in all their domains, but few environments embody consequences of human activities as drastically as river deltas. Major parts of those unique landforms could disappear below rising sea levels by the end of the century, drowning not only ecosystems but also critical areas for food supply 1,2 and human livelihoods [3][4][5] . The great risk faced by deltas is documented by increasingly urgent calls for action by the global scientific community 6-11 over recent years.
Averting potentially disastrous environmental degradation in river deltas will require decisive action across scales and sectors. River deltas are geologically young, depositional landforms created by the interplay of rising sea levels and fluvial sediment deposition. For that reason, river deltas naturally experience land subsidence and shifting coastlines as their unconsolidated sediments compact 12 . Today the processes that created deltas are altered by human activities in many ways (Figure 1 A). Global sea level rise is accelerating 13 , the sediment load of many large rivers is reduced by artificial reservoirs 14-17 and sand mining 18 , and the spreading of the remaining sediment supply across delta landscapes is hindered by dykes and levees 1,9,10,19,20 . Human activities on deltas, e.g., the extraction of underground resources, drainage of shallow soils, and artificial loading further accelerate land subsidence 6,21,22 . Together, those drivers lead to rapid rates of coastal erosion 17 and relative sea level rise (rSLR), which denotes a lowering of the land surface compared to rising sea levels 23 and thus a greater risk of land falling below the ocean surface than from either sea level rise or accelerated subsidence alone.
While the existential risks for coastal livelihoods become more evident, there is a limited recognition for the complex risks originating from a multitude of interconnected drivers on global, regional and local scales. For instance, when addressing the Security Council in February 2023, the UN secretary general emphasized that sea level rise poses a major threat to global peace and security, explicitly mentioning large deltas like the Mekong 24 . Creating awareness and elevating these risks onto the global policy agenda is critical. Yet, it also needs to be acknowledged that in many deltas, where coastal risks are most concentrated, those risks are created not only by rising sea levels, but by the combined effects of global and local drivers that cause rSLR.
Managing risks for coastal livelihoods will require actions across sectors and scales. Reducing greenhouse gas emissions will be critical, as will be limiting fossil fuel extraction, avoiding sediment trapping in dams and reservoirs 1,[25][26][27][28][29] , reducing groundwater overextraction 30,31 , enhancing sedimentation 32 , and conserving or restoring of coastal vegetation. Those exemplary measures highlight the need to manage drivers of land loss in deltas across global, regional, and local scales and all sectors of the water-energy-food nexus (Figure 1 B). Managing rSLR is thus closely linked to climate mitigation and adaptation across scales (Figure 1 C). Sea level rise and the occurrence of hydroclimatic extremes need to be addressed through climate mitigation, while adaptation is required to reduce vulnerability of people and ecosystems 13 in deltas. In a nested manner, climate adaptation for deltas requires to mitigate root causes of rSLR for a delta, e.g., by phasing out groundwater overuse and sand mining, as well as adaptation, e.g., through improved grey-green coastal protection, naturebased solutions, and diversified livelihoods 13 . Yet, important knowledge gaps remain to inform effective measures to reduce rSLR and reduce climate risks in river deltas.
In the face of complexities and interconnections, delta management needs to be informed by science. Curbing rSLR requires understandings current baselines and risks from continued "business as usual" as well as identifying effective adaptive and sustainable management strategies 19,33,34 . While all deltas are built by similar processes, their contemporary diversity is enormous. This diversity brings specific challenges and opportunities for each delta and precludes a one-fits-all approach to delta science and management. What will instead be needed are reliable data and transferable interdisciplinary approaches to inform participatory and adaptive delta management 11 . There have been detailed reviews of global patterns 3,6,22,29,[35][36][37][38] , monitoring techniques 39 , and numerical models 40-42 for specific drivers, and in-depth reviews of the multiple drivers behind rSLR in specific deltas 1,27,[43][44][45] . However, based on reviewing the current state-of-science, we argue that some key knowledge gaps persist that, while implicit in many of the above papers, will need explicit attention of the global scientific community.
Herein we focus specifically on identifying such critical knowledge gaps, rather than exhaustively reviewing models for delta processes. We highlight that the ability to model delta subsurface processes and sediment dynamics is limited compared to the modeling of global and basin-scale processes. This is a major limitation to study local adaptation strategies (including, but not limited to, nature-based solutions like sediment enhancing strategies and protection/restoration of coastal vegetation). Other key gaps include the coupling of basin and delta models and the integration of delta systems in global assessments. Lastly, our review highlights major knowledge disparities between deltas, reducing not only the capacity to manage specific deltas but also to derive a unified understanding of risks and mitigation/adaptation opportunities. As a result, this paper outlines a agenda to close management-relevant knowledge gaps and modeling challenges for the sustainable, science-informed management of river deltas. Figure 1: Sustainable delta management needs to span scales and domains. Deltas are created at the interface of coastal and basin processes, and their future is determined by actions across multiple scales (A). Sustainable management of deltas will require thinking across sectors (e.g., water-energy-food) while considering multiple scales for each sector (local-regional-global) and linkages between sectors (A, B). Sustainable delta management also needs to be embedded in global actions for climate mitigation and adaptation, where basin and local scales offer a wide range in mitigation options (C).

Values at risk in global deltas
Deltas support important economic activities and ecosystem services. Estimates indicate that global deltas generate economic and ecosystem services in the order of hundreds of billions or even trillions of dollars per year 7,46 . This makes deltas an important part of the global economy and important contributors to global ecosystem services (in total valued between $125 -$145 trillions 47 ).
The value of ecosystem services for individual deltas can be major and has been estimated to be $12 to $47 billion/year for the Mississippi Delta 48 and $10 to $27 billion/year for the Yangtze Delta 49,50 . In purely economic terms, the Mekong Delta covers only 10 % of Vietnam's land area, but studies suggest that the delta contributes around 25 % 51 of the country's GDP of $360 billion 52 . Based on global gridded GDP values 53 , we estimate that the contribution of deltas to the global GDP is around $4.4 trillion or 4.1 % of the global GDP ($107 trillion in 2015), a notable increase from 2.6 % of the global GDP in 1990 ($1.2 trillion of $47 trillion). These findings provide quantitative support for previous estimates 7 and highlight the growing importance of delta landforms for the global economy.
Deltas are created from recent deposits of sediments, thus offering fertile agricultural lands with easy access to freshwater resources 54 . As a result, deltas support significant agricultural production and thus contribute to food security. For instance, it has been estimated that up to 5 % of the global rice production takes place on the Mekong Delta in Vietnam 1 . Other deltas in Asia play similarly important roles, being the location of the region's most productive agricultural areas 2 . Based on global gridded data 55 , we estimate that the value of agricultural production on deltas was around $40 billion in 2010, and thus around 3 % of the total global crop value of $1.25 trillion.
The fate of river deltas is also a key determinant for sustainable human development 56 . Currently, 5.6 % (450 million out of 8 billion) of the world's population live on river deltas and populations along low-lying coastlines and deltas is projected to reach one billion by 2100 57 . Deltaic populations make up the majority of population in a number of countries, notably 33 % of Nigeria's population live on the Niger Delta, and 10 % of Egypt's population live on the Nile Delta 54 . With a population of around 150 million (Figure 2 B), the Ganges-Brahmaputra Delta would fall solidly in the top ten countries of the world by population if it were its own country. Some deltas, mostly in Asia, stand out across indicators (GDP, agricultural production, population, see histograms in Figure 2). Many deltas in Asia (e.g., Pearl, Yangtze, Chao Phraya) are also highly urbanized, leading to an intersection of hazards, exposed socio-economic values, and thus great risks. It is noteworthy that many deltas see rates of growth that outperform the growth in the country where the respective delta is located, highlighting that deltas have been global hotspots of socio-economic growth over the past few decades (see upward triangle markers in Figure 2).
Deltas also provide significant other benefits to global societies that are harder to quantify. In addition to crop production, deltas also contribute to food security through fishing 58,59 , aquaculture 60-63 , and livestock production 64 . Additional ecosystem services are provided through water quality regulation, flood protection, recreation 48 , and habitat provision along the world's major flyways 65,66 . Some deltas are also important hotspots for extracting hydrocarbons 54,67,68 and other mineral resources such as sand 18 or clay. Often those activities have negative impacts on ecosystems and people, e.g., impacting water quality, destroying natural coastal vegetation, and accelerating subsidence and coastal erosion. The fate of livelihoods and ecosystems is closely linked to sustainable human development. Examples range from food security (SDG 2), to sustainable and livable cities (SDG 11: some of the most dynamically growing cities are located on or close to deltas) to life on water and land (SDGs 14 and 15), and many other goals that can only be achieved if there is exposure to natural hazards and rising sea levels is low (e.g., SDG 4: Good education, SDG 9: Industry, Innovation and Infrastructure) 24 . Global trends and models for key drivers of relative sea level rise and land loss The relevant linkages between altered delta processes and human livelihoods are manifest in recent research on global land subsidence, its drivers and magnitude 8,69 and its socio-economic consequences 70,71 . Relative sea level rise (rSLR) is the sum of vertical land motion (VLM), with negative motion meaning land subsidence, which is often but not always accelerated by human activities, and sea level rise (SLR) 23,72 . Rates of rSLR for a river delta can thus be expressed as: Vertical land movement is the cumulative result of many processes, for instance, (1) deep earth-crust dynamics like isostacy and tectonics 73 , (2) shallow natural compaction and peat oxidation 12,74-76 , (3) increased compaction from increased loading (e.g., buildings, linear infrastructure or drainage) 30,77,78 , (4) extraction of underground resources like groundwater 31,79,80 or hydrocarbons [81][82][83] . The natural mechanism of deltas to cope with rSLR is to build elevation through sediment aggradation, both from fluvial and marine sediment deposition and organic accumulation 7,27,84,85 .
Most of these processes are not isolated but interconnected across domains and scales. For instance, understanding the impact of dams on deltas requires to take a regional perspective on human needs for energy and food, a basin-scale perspective on sediment transport processes 25, [86][87][88] , and a local perspective on channel, floodplain and coastal processes in deltas 10,19 . Additionally understanding is required on deltaic surface-subsurface process as, for example, increased sediment deposition drives compaction of underlying sediments 89 , in turn altering surface dynamics.
The most fundamental challenge for modeling rSLR is that accurate information on land surface elevation is hard to obtain for deltas. While global DEMs are now widely available, their remotesensing derived elevation data are still prone to vertical errors in the order of several meters, significantly more than the average elevation of many deltas. For instance an analysis of ground elevation measurements for the Mekong delta revealed that the average elevation of the delta is around 0.8 m above local sea level, significantly less than the 2.6 m average elevation previously erroneously assessed from widely used global DEMs 90 . Such a difference has major consequences when assessing what is at risk for different levels of rSLR. A recent study on the Ayeyarwady delta revealed similar large discrepancies between different global DEM and local control data 91 . On a global scale, attempts are being made to improve existing global DEMs for the coastal zones, for example using machine-learning 92,93 or interpolating space-borne LiDAR data (I.e. ICEsat 2) for the coastal zone 94 . Such products allow improved modeling of coastal and delta products than "raw" DEMs but they should be validated using local groundtruth data, as large discrepancies may still occur 90,91 , and need to be updated periodically to reflect latest developments in land subsidence 31 .
Discovering opportunities to curb rSLR will not only rely on better data, but also on new types of numerical modeling approaches. Numerical models are no panacea for solving complex real-world problems 95 but models, ideally informed by in-situ data 96 , can be useful to study hazards, exposure, vulnerability, and thus risks 33 from continued "business as usual" (Figure 3 A, B). Models are also critical to explore future adaptation in a way that reduces risk for deltas and avoids exceeding societal and biophysical limits for adaptation. Another application is to use numerical models to solve trade-off problems, e.g., between hydropower development and sediment supply to deltas 87,88,97 , or to optimize green-grey infrastructure portfolios 98 . Many challenges faced by deltas are typical "wicked" 95 problems without a single "win-win" solution. Thus, iterative and participatory 99 modelbased explorations of the many dimensions of threats and management opportunities are essential to mitigated and adapt to climate risk 100 .
In this review, we focus on some key drivers that have been identified as dominant forces behind anthropic rSLR and delta elevation change in many of the world's largest deltas. Those drivers are (from larger to smaller scales): (1) global sea level rise 13,101 , (2) changes in sediment supply from contribution basins 14,15,25,102,103 , (3) accelerated land subsidence due to the extraction of underground resources such as groundwater and hydrocarbons 31,43,104 , (4) altered sediment dynamics on the delta surface 32,105-107 . The following sections will discuss the current state of knowledge for those four drivers, with an additional section on socio-economic dynamics. Each section will provide a brief overview over what is known about each driver from empirical observations or modeling studies and then discuss our ability to model each drivers' impact on rSLR in future management applications. Global sea level rise Global sea levels have risen by around 1.5 mm per year since 1900 108,109 with a notable increase in rates post-2000. Total sea level rise is the compound effect of as a result of baristatic and thermosteric sea level rise. Baristatic sea level rise results from changes in ocean mass as the cumulative effect of decreasing water storage in glaciers and polar ice mass (and to a smaller degree from groundwater depletion), counteracted by increased storage of water in artificial reservoirs. Thermosteric sea level rise refers to the thermal expansion of oceans in a warming climate 110 . Of the total, baristatic sea level rise has contributed most to observed sea level rise, with the exception of the mid-20 th century when a rapid rise in dam storage counteracted losses in global ice mass 108 .
Sea level rise is spatially heterogenous, with variability within 111 and between the world's major oceans basins 108 and between coasts and offshore oceans 112 . This spatial heterogeneity is driven by gravitational differences, currents and spatially heterogenous thermal expansion. Notably, satellite observations seem to indicate that coastal sea-level rise is most quickly accelerating in South Asia 112 (comparing 1973-1982 and 1993-2000 periods) and thus in a region where many large deltas are located (Figure 4), and more on the northern than in the southern hemisphere 113 . Model estimates for off-shore sea levels indicate greatest increases in the South Pacific, around the coasts of North America, Northern Europe and the poles 13 . In addition, ice loss may exacerbate regional sea level rise in certain hotspots 114 , notably also the east Pacific Ocean with large deltas like the Mekong, Red and Pearl River deltas. Past and future sea level rise contributes to rSLR in global deltas and expose populations and infrastructure to extreme events 7,46 such as hurricanes and typhoons. Obtaining realistic ranges of sea level rise is critical as a boundary condition for modeling any type of delta management.
By 2100, sea levels are expected to rise up to 0.84 m on global average compared to the year 2000 and even optimistic climate futures result in at least 0.43 m of sea level rise 13 . Those estimates are derived using global circulation models for different socio-economic pathways (SSPs) that cover relevant ocean and ice-sheet processes 13 ( Figure 4). Additionally, different statistic and mechanistic approaches can be used to estimate combined effects of rising average sea levels and increasing extreme events such as storm surges and similar. Each of those processes adds considerable uncertainty 115 . IPCC's 2019 special report on Oceans and the Cryosphere thus indicates only medium confidence in sea level rise estimates, while solicitations of expert opinions indicate greater expected rates of SLR 116 . Projections of future sea level rise are freely available and can be used to constrain assessments for specific deltas (e.g., 117,118 ).  13 , overlaid with centroids of the world's major river deltas 229 . Modeling changing sediment supply Sediment supply from river basins to deltas is controlled (1) by how much sediment is supplied from hillslopes to rivers and (2) by the capacity of river networks to convey sediment to downstream deltas 119 . These two overarching processes are the result of many spatially heterogenous drivers that are altered by human activities. Land use and climate change can increase or decrease erosion rates and thus how much sediment is supplied to rivers, while dams and reservoirs trap sediment in their impoundment and thus reduce sediment conveyance in rivers 120 (Figure 1 A). Additionally, dams modify river discharge regimes and thus the transport capacity of downstream rivers, i.e., how much of the remaining sediment can be transported downstream 121 . If the transport capacity after dam construction exceeds the remaining sediment supply, dammed rivers can erode sediment from riverbeds and banks, which increases sediment transport. Yet this effect is only temporary until sediment stores are depleted and results in significant negative impacts, e.g., on instream habitat and infrastructure 122,123 . Mining of sand and other aggregates can lead to significant sediment starvation 124,125 particularly when rivers are both impacted by dams and mining activities. In downstream deltas this results in deepening of the channels, leading to tidal amplification and consequently increased flooding 126 , salinity intrusion 127 , and coastal erosion 17,128 .
Erosion from hillslopes and sediment supply to rivers can be modelled on basin scales with a variety of tools. The full range of erosion and sediment transport models is reviewed elsewhere 40 and we hence only introduce some typical example of different model types. On the one hand, the Universal Soil Loss Equation 129 , USLE, and its various derivatives 40 , are now deployed on continental and even global scales to model erosion rates under environmental change scenarios with high resolution 130,131 . USLE enables to explicitly model the impact of landuse and climate patterns on erosion rates, and can be easily coupled to connectivity models that describe sediment delivery from hillslopes to rivers 132 . Yet, USLE and similar erosion models have two major limitations when it comes to estimating sediment delivery from basins to river deltas. Firstly, USLE has been developed and parameterized to represent sheet and rill erosion only and thus omitting processes such as gullying, mass movements or glacial erosion. Secondly, erosion rates can be a proxy for sediment delivery to deltas, but typically a significant fraction of eroded sediment is deposited in channels and floodplains before it reaches the ocean 119 . On the other hand, regression models such as BQART aim 15 to estimate sediment export from a river basin based on a number of covariates aggregated on a basin-level (e.g., total glaciation, trapping efficiency of reservoirs and human footprints for the entire contributing basin of a delta) 14-16,102 . Thus, BQART and similar models implicitly account for deposition. Being lumped to a catchment scale, BQART does not allow to estimate where sediment originates in a catchment. Despite their limitations, progress has been made to integrate both approaches into explicit sediment routing schemes 133,134 or catchment models (e.g., SWAT 135,136 ), so that modeling hillslope erosion and sediment deliveries to deltas is now feasible with a number of publicly available models.
Modeling the transport of multiple grain sizes remains a challenge. Most approaches discussed above only consider for the transport of suspended sediment, without considering for the movement of coarser grain sizes (e.g., sand or gravel). Even if suspended sediment makes up the majority in of total sediment in large rivers 137 not considering for other fractions of sediment is a limitation. Coarser sediment fractions contribute over proportionately to building stable coastlines and will also be more impacted by human interventions such as dams and sand mining 138 . To address this gap, new models such as the CASCADE model 139 allow to quantify the transport of multiple grain sizes for longer river reaches 140 or entire basins 141,142,139,[143][144][145][146]88 . Those models are probably best described as "process related models" as they leverage approaches from graph theory 147 , combined with empirical sediment transport equations, and a simplified handling of hydrology (and more recently, morphodynamics) to estimate the impacts of all sediment fractions on a network scale. Results can then be used to quantify impacts of sediment delivery to deltas and opportunities to mitigate those impacts 146 . Yet, bed load observations to calibrate modes are even more scarce than observations of total sediment load and are mostly available for rivers in developed countries only.
2D or 3D models for river morphodynamics are designed to explicitly account for the abovementioned complexities. Yet, they are typically prohibitively data and resource intensive to be useful on the systems scales which are required for delta management. Data and computational demands are particularly prohibitive for use in large river basins or for water management applications that might require evaluating many different decision alternatives 40 . Thus, studies using morphodynamic models to evaluate and minimize impacts of dams on river sediment budgets are typically limited to small river sections and individual dams 148,149 .
A last challenge lies in modeling the impacts of dams on sediment delivery to deltas. In many settings, dams are the most significant disturbance of river sediment budgets. How much sediment will be trapped in dams will depend on where they are located and how they are designed and operated. Particularly the last part is challenging to represent, as future dam operation and economic implications of sediment flushing or sluicing will depend greatly on the demand and prices for hydropower. So far, most studies using water resources and distributed hydrologic models to optimize the passage of sediment through dams and towards deltas 150-152 rely on very simplified representations of sediment transport processes in reservoirs and approaches for optimizing the siting of dams often represent sediment transport to downstream deltas in a highly stylized manner 88,97,153,154 .
There is thus the need to refine and integrate models for the different aspects of sediment supply to deltas. Yet, most relevant processes can already be modelled in a way that allows to study human impacts on sediment supply from a system scale perspective, represent the impact of management actions, and analyze future scenarios. With that regard, the capacity to model basin-scale processes and the resulting sediment supply to deltas is much greater than the capacity to model processes on a delta scale.

Accelerated compaction and land subsidence
Most deltas will naturally subside because sediment compacts under its own weight 12,155 and because of downward tectonic and isostatic movements 156 . Yet the rates of subsidence are often significantly increased by human activities and unsustainable use of natural subsurface resources is a leading driver of rSLR in many large river deltas 31, 79,80,157,158 . When fluids are extracted from porous subsurface layers compaction ensues as the overburden compresses lower sedimentary layers, resulting eventually in land subsidence 37, 159 . Subsidence related to groundwater pumping for urban use and irrigation can lead to subsidence rates which exceed rates for SLR by an order of magnitude 8,159,160 . Additional shallow subsidence can be triggered when drainage leads to lowering of the surface water table, resulting in shallow compaction and volume loss following oxidation of soil organic material and peats 35,161,162 .
Satellite-based estimates of subsidence in the Mekong Delta, where the phenomenon has been relatively well studied, range from 10 -40 mm/yr between 2006-2010 79 and up to 60 mm/yr between 2014-2019 163 with contemporary rates associated to groundwater pumping alone modeled to be on average around 11 -16 mm/yr 79,80 , with continued acceleration into the future as groundwater extraction keeps increasing 31 . In other deltas, rates of subsidence in areas with known major groundwater extraction can reach similar rates, e.g., localized up to 18 mm/yr in the Ganges-Brahmaputra Delta 104 , and up to 9.8 mm 164 over parts of the Nile Delta. Typically, rates are highest around cities 79,159,165 , and particularly cities in Asia 69,166 , which greatly increases potential socioeconomic impacts of land subsidence. Where deltas hold reserves of hydrocarbon such as oil and gas, such as in the Niger 83,167 or Mississippi Delta 82,168 , hydrocarbon extraction can further accelerate land subsidence.
Land subsidence, especially in unconsolidated deltaic settings, is the cumulative result of various subsurface processes acting at different depths, time scales and spatial extents 6,169 . As a result, land subsidence can be highly spatio-temporally variable, which makes modeling and projecting it not straightforward and current models tend to focus on a single driver or process only. As human induced subsidence, predominantly because of the overextraction of groundwater 31,160 , is responsible for the majority of subsidence in deltas, proper modeling and accurately predicting these anthropogenically driven processes is critical for delta management.
Modeling future overuse of groundwater and extraction-induced accelerated delta subsidence remains a major challenge. Firstly, contemporary data on groundwater extraction in deltas is sparse and when available comes with large uncertainties. Consequently, estimating rates of future groundwater extraction are even more challenging. Groundwater is primarily used for irrigated agriculture 36 and extraction rates depend on crop decisions and surface water availability, which could be derived from global agrohydrologic models 170,171 . Yet, many widely used agrohydrologic models also operate on relatively coarse resolutions (typically 10 -50 km at the equator), which would reduce even a large delta, such as the Mekong Delta to only a few pixels and hide fine-scale spatial patterns and dynamics 172 . Current extraction estimates from such global models are shown to be several factors off (up to 4 times higher or lower) compared to locally validated datasets 173 for several major deltas. A new generation of scalable hydrologic models might help overcome those limitations in the near future (e.g. a high-resolution implementation of the widely used PCR-GLOBWB model 174 ).
Models to translate groundwater depletion rates and other drivers into rates of subsidence vary widely in their complexity and their data demand, as well in how well they represent different processes ( Figure 5). One extreme are complex 3D aquifer system models 22 which require a detailed understanding of sub-surface hydrogeological layering, hydromechanical properties and extraction rates (i.e. history, depth, amount). While the required data will be challenging to obtain in many deltas, the potential of such complex models is their ability to provide process-based, non-linear projections of future spatial patterns of land subsidence in response to resource extraction 31 . Some studies which have deployed such models are, e.g., Ye et al. (2016) 176  "Back of the envelope" calculations 27,179 represent the other extreme in terms of model complexity. Such approaches can yield results for accelerated subsidence and future elevation change in the right order-of-magnitude and will be feasible for most global deltas (Figure 5 B). However, such "back of the envelop" approaches omit the significant spatial and temporal heterogeneity in sub-subsurface processes that control subsidence, feedbacks with sedimentation, and resulting complex patterns of land subsidence and land loss 19 . This is particularly relevant because even small errors in projected rates of subsidence will result in major differences when projected until the mid or the end of the century. In a setting where land is often only few meters above the sea level, a cumulative error of 50 cm, or 0.5 cm/yr over 100 years, would lead to major differences in estimated land loss.  80 but require significant amounts of input and validation data, as well as expertise. . Simple "delta plain" models 27 (B) are a spatial expansions of delta sediment budgets 29, 179 . Such models are useful to translate vertical rates of subsidence into spatial approximations of land loss without considering dynamic feedbacks between processes (panel A modified from Minderhoud et al. 80 , panel B modified from Schmitt et al. 27 ).

opportunities and challenges, as exemplified for the Mekong Delta. High resolution 3D models of subsurface processes (A) enable detailed spatiotemporal estimates of land subsidence as a result of groundwater overuse
Delta-scale processes and nature-based solutions Sediment deposition on deltas is not only reduced because of changes in sediment supply, but also because of modifications of lateral connectivity between river channels and delta floodplains. A natural delta is built by the gradual spreading of sediment on the delta surface by floods, and by avulsion events that drastically change patterns of sediment distribution 42 . Floods and avulsions can have catastrophic impacts on human lives and livelihoods 10,42,180 . Hard engineering in the form of dykes and levees was therefore deployed in many deltas to reduce the impact of floods on agriculture, settlements and infrastructure; and river control structures were built to control avulsions 10,19,181 . Today, those infrastructures impede the natural flow of sediment across delta plains and thus the processes that would fuel natural aggradation 4,76,106,128,182-187 . Rethinking those linear infrastructures and allowing for natural sediment spills can contribute to maintaining and restoring delta land 20,32,188,189 . Modeling lateral connectivity becomes particularly relevant when sediment supply is much lower than under natural conditions, and decisionmakers need to decide where artificial splays of available sediment resources would lead to the greatest benefits in terms of land building 32 .
Modeling delta evolution and feedbacks between sediment and accretion is common in landscape evolution studies but less for management applications. As reviewed in, e.g., Edmonds et al. and Liang et al. (ref. 41,190 ), models for sediment distribution on delta surfaces range from full 3D models that explicitly describe the hydrodynamic processes behind the routing of water and sediment (e.g., Delft 3D), to reduced complexity models (RCMs) [190][191][192] in 2D, and simplified 1 D models of delta crosssectional profiles 41 . Similar to what is described above for subsidence, even simple back-of-theenvelope calculations can yield some insights into how different levels of sediment splaying can contribute to aggregation 27,29,193 . One important process that all of the above models lack is postdepositional compaction of newly deposited sediments, a relevant 12 aspect which is only recently included in fully coupled 3D geo-mechanical models 194 .
As discussed for fluvial sediment transport, the accuracy of full-complexity, three-dimensional delta evolution models entails significant computational and data needs and specialized skills. Where data and resources are available, such models can yield detailed insights into interactions between surface water flows, sediment splays, and even groundwater dynamics 195 . Reduced complexity models can yield insights into questions with implications for delta management as well, e.g., into feedbacks between delta vegetation 196 and tectonics 197 . Yet, reviewing citations for, e.g., ref 190 , reveals that even simplified 2D models of sediment dynamics are still predominantly used for studies of landscape evolution, rather than for management applications.
Modeling and managing the lateral exchange of sediment between channels and delta floodplains is not only a modeling but also a data challenge, particularly when it comes to water infrastructure. Modeling sediment spreading across a delta surface will need to consider for infrastructure location, design and operation. Yet, data on dykes and levee locations and the operation of associated floodgates are rare. Crowd-sourced data sets from, e.g., Open Street Maps, contain detailed maps of water infrastructure but lack information on their design and operation. The new OpenDELVE 198 aims to provide a global platform for continued, community-driven mapping of such infrastructure, but still misses many smaller infrastructures that are crucial for spatio-temporal sediment dynamics ( Figure 6).
Nature-based solutions in deltas and coastal zones, e.g., protection or restoration of Mangroves, dunes, and marshlands, have received considerable attention in recent years 13,199 but their dependence on sediment is widely overlooked. Indeed, the benefits of such nature based solutions are compelling. By maintaining a soft coastline with, e.g., mangroves elevation may naturally grow with rising sea levels while providing a wide range of additional benefits for livelihoods and biodiversity, while more human-controlled interventions like sediment enhancing strategies can do the same in other parts of a delta 32 . Most nature-based solutions in deltas are dependent on trapping sediment and are thus unlikely to thrive and to provide desired benefits in erosional, sedimentstarved environments 200,201 . Current models of coastal vulnerability can highlight where natural vegetation could contribute most to protect coastlines 202 , but do not include factors that control if vegetation can be restored or conserved under environmental pressures (e.g., sediment starvation, sea level rise, more extreme weather events). Linkages between sediment supply, coastal sediment transport, and vegetation dynamics could be explored using hydrodynamic models 203 . So far, such approaches are not commonly used in delta modeling or management, risking overlooking potentials and risks for deploying nature-based solutions at scale. Figure 6: Modeling and managing human impacts on lateral sediment connectivity will require significant additional data. The openDELvE 198 data set is the first to globally map levees and polders. Yet, the example of the Mekong Delta highlights that there is significant additional water infrastructure, such as canals and floodgates (from Open Street Map), which has been crowdmapped in great detail (see zoomed panel). Dykes and levees are present along many of those canals 106,186 , yet this information is not commonly available.

Socio-economic dynamics and feedbacks
The future management of deltas and thus their resilience to change will depend on complex feedbacks across biophysical and socio-economic domains 19,42,182,204,205 . Questions like "where will people live?", "how will people make a living?" or "to how frequent and severe events will people be exposed?" are relevant question for managing sinking and shrinking deltas. Answering those questions, but also developing relevant plans for delta management, will require an understanding of how local livelihoods will respond to global pressures, and how those together will impact the biophysical resilience of a delta.
For instance, projecting future rates and modeling impacts of saltwater intrusions requires considering a multitude of drivers. Related processes include rising sea levels, groundwater overuse, unsustainable irrigation practices, and modifications of distributary channels 38, 126,127 . From that starting point, a number of adaptation scenarios are possible leading to considerably different delta futures. For instance, farmers might abandon land and migrate to cities (as already observed, e.g., in the Mekong and Ganges-Brahmaputra Delta), which would lead to a lower population density in rural parts of deltas. Such a population shift opens opportunities for soft path adaptation, like implementing sedimentation enhancing strategies 20,86 , but increasing pressure on resources in urban centers. Increasing salinization of freshwater might also motivate construction of levees, increased pumping of deeper groundwater, or switching to less sustainable food systems (e.g., from rice to shrimp farming) and thus to practices with negative feedbacks on subsidence and land loss.
No single model can capture all those complexities or provide a one-fits-all solution for all deltas. Yet it is a major knowledge gap that global estimates of coastal population growth and future land use do not consider for the fact that even under a baseline of sea level rise (i.e., without accelerated subsidence) significant parts of global deltas might fall below sea level in this century. Even broad level information on such feedbacks between rSLR could be extremely useful to constrain future exposure and thus adaptation options (e.g., retreat, protect, accommodate, ecosystem-based adaptions 13 ). Resolving those problems for coastal systems will required more attention for how global and local changes propagate across domains (water, energy, food climate).

The global state of deltas
Models in the above discussed domains will be critical tools to develop management strategies that address critical risks for deltas. Yet, both modeling and management needs to be informed by data (Figure 7), ideally building on some local knowledge on key drivers and what is at risk. However, there are major disparities in what is known and what is unknown with regard to drivers of rSLR across the world's major deltas, and across drivers. To illustrate this point, we reviewed papers that discuss major drivers of rSLR for several of the world's most productive deltas (Figure 2), selected to represent a wide range of geographies and states of knowledge (Mekong, Ganges-Brahmaputra, Mississippi, Nile, Niger). We focus on delta and basin specific drivers discussed above, namely sediment supply, accelerated subsidence related to groundwater overuse, lateral connectivity, and socio-economic dynamics. We do not include sea level rise in this delta-scale review because its magnitude and uncertainties are reviewed in detail elsewhere 13 .
For each delta, we compiled the peer-reviewed literature available for each driver (mostly post-2010) through a literature search on Web of Science. From our review, we determine if drivers are subject to an increasing trend (getting worse), a decreasing trend (getting better), or no trend (respectively no agreement between studies). We also reviewed the confidence in these trends, assigning a "high confidence" level when there were >5 studies, "medium confidence" when there were 3 or 4 studies, and low confidence if there were <3 studies. We also distinguish if the results are based on local data, on location specific models, or on global models and data (Figure 7).
There are clear differences in what is known and not known between drivers and between different deltas. In terms of drivers, sediment supply is best studied while sediment dynamics on deltas and socio-economic feedbacks are in general poorly understood an. There is high confidence in decreasing sediment supply for e.g., the Mekong and Mississippi, medium confidence for the Nile and Ganges Brahmaputra, and limited confidence for the Niger (based on global data 25 ). There is high confidence in rates of accelerated subsidence for the Mekong and Mississippi, and some evidence for the Ganges Brahmaputra, Niger and Nile deltas. Only for the Mekong, Ganges Brahmaputra, and Mississippi deltas sediment dynamics are well enough studied to infer a trend with confidence. Studies on more complex feedbacks between socio-economic and biophysical factors are only available for the Mekong and Mississippi. In terms of geographic trends, many drivers are as well or even better studied for the Mekong delta than for Mississippi delta, which has been studied for decades longer. African deltas (Niger, Nile) stand out with regard to how little they are studied.
Concerningly, not only is evidence scarce but the available evidence points to worsening trends in nearly all drivers for nearly all considered deltas. This is notable for sediment supply, which is decreasing for all deltas, except for the Ganges-Brahmaputra where past trends seem decreasing 206 , but future trends could be increasing or decreasing 25,207 as a function of scenarios of upstream dam construction. The only other example for a delta where we found some ambiguity was the Mississippi Delta, where many studies indicate worsening trends and lock ins into non-sustainable conditions 208 for people and some key sectors 209 , while other sectors have some adaptation capacity 210 , and opportunities for socio-economic adaptation are being studied 211,212 .  87,145,231-235 , b: refs. 31,32,79,80,163,236,237 , c: refs. 106,186,216-218,238 , d: refs. 60,62,239,239-241 , e: refs. 25,206,207,242,243 , f: refs. 43,104,243-245 , g: refs. 245,246 , h: ref. 247 , i: refs. 193,248-252 , j: refs. 253-257 , k: refs. 20,258-262 , l: refs. 208-212,263 , m: refs. 264-267 , n: refs. 164,264 , o: ref. 25 , p: refs. 83,268-271 . Conclusion: The state of delta modeling and priorities for the future Global deltas are unique in terms of values and services that they provide to societies. River deltas are also uniquely endangered by drivers that are interconnected across sectors and spatio-temporal scales. From our review we identify four key shortcomings in terms of models and data and thus priorities for future research and model development. Those priorities are (1) modeling of delta-scale processes and the integrating models across scales and domains, (2) coupling of such integrated models with state-of-the-art frameworks for decision analysis, (3) closing major knowledge disparities between deltas, and (4) consolidation of existing knowledge about global deltas and integrating the fate of deltas in global assessments.
Numerical models are critical for quantifying complex and interrelated processes (Figure 1), for identifying challenges and management opportunities, for resolving conflicts between sectors, and for identifying pathways for sustainable delta management (Figure 3). We thus reviewed the current state of modeling with regard to four key drivers of subsidence, relative sea level rise, coastal erosion, and thus land loss. We find that regional sea level rise in response to global warming can be relatively well modeled and is included in well-tested earth systems models, with some of the greatest uncertainties associated to certain tipping points, such as the melting of major artic ice caps. Modeling sediment supply from upstream contributing basins is an area that has seen many innovations over the past decade. Today, several process-related frameworks are freely available that are applicable on systems scales. Suspended load of rivers can now be monitored using remote sensing and sediment transport models now commonly integrate some key human drivers, e.g., landuse change and the location and operation of dams. Some of the greatest uncertainties related to sediment transport concern the transport of bed load, sand mining [213][214][215] , and in general the poor availability of sediment data, which hinders effective model calibration and determining a reliable baseline. The capacity to model accelerated subsidence is, with few exceptions, very limited. However, rates of subsidence can be tracked using the latest generation of space-born radar sensors. Moving from remote sensed observations towards process-based modelling of land subsidence is crucial to 1) disentangle the subsidence signal into different drivers and processes, and 2) properly simulate the spatio-temporal heterogeneity of deltaic subsidence, enabling highly relevant non-linear scenario projections. However, this is hindered by the need for subsurface data that can only be obtained insitu and the simultaneous need for understanding socio-economic drivers such as groundwater use. Lateral connectivity and sediment dynamics on delta floodplains also remain understudied. While there are some examples of detailed models of channel-floodplain sediment exchange 216-219 , those models remain a notable exception. Yet, remote sensing can be used to monitor channel-floodplain sediment exchanges and could be leveraged more widely 220,221 . Only very recently a new generation of numerical models is being developed that can account for post-depositional sediment compaction and consequent delta elevation change. Future efforts are needed to link these to morphodynamic sedimentation models to resolve process feedbacks and connect deltaic surface to subsurface processes. Modeling abilities are most limited when it comes to processes on a delta scale, namely accelerated subsidence and sedimentation dynamics. There are successful examples for how those processes can be modelled for management or research applications 31,194 , but efforts are needed to develop modeling frameworks that are generalizable and modular to account for delta-specific differences in data and resource availability.
Secondly, new models that integrate biotic and abiotic delta and basin processes are needed to represent the fate of deltas in decision making frameworks and for sensitivity analyses. Delta management would be an ideal use case for approaches for robust and adaptive decision making 33,222 , e.g. to design effective portfolios of grey-green infrastructure interventions and associated policies 187 across delta and basin scales. Yet, there are only few examples that integrate rSLR as objective in basin-scale planning, and those examples are based on simplifying and implicit representations of sedimentation and accelerated subsidence 87 . In turn, there are only few studies that consider basin management in the evaluation of local mitigation and adaptation 203 , e.g., through nature-based solutions. There are also opportunities to couple integrated, cross-scale modeling frameworks to state-of-the-art tools for sensitivity analysis 223 to identify critical sources of uncertainty (see also next paragraph). Common to all those applications is the need for models that are computationally efficient. Thus, future basin-delta modeling frameworks need to strike a balance between process representation, data needs, and computational demand.
Thirdly, there is a blatant knowledge disparity between deltas, which not only hinders the management of specific deltas but also the identification of global drivers, trends, and management responses. For instance, few deltas have data or studies available to establish a reliable baseline of current elevation and trends of rSLR over the past decades. The lack of information is likely not a result of lacking threats and pressures, but rather results from limited capacity in local institutions and weak links between local researchers and the global research community. It should be noted that some studies 224 already aimed at comparing vulnerability across deltas in a more standardized manner (including some data-poor deltas) and future global assessment could build on previous efforts. Likely, a nested approach would be most effective, firstly aiming to consolidate knowledge for individual deltas 225,226 , and secondly aiming to synthesize across deltas.
Knowledge limitations for individual deltas can be overcome, as is demonstrated by the Mekong Delta. Within the past decade, the Mekong Delta has gone from being basically unstudied to being the best studied delta in the Global South, including many studies from local scholars. Local scholarship is also critical to train new scientists, engineers, and decision makers who can further contribute to bridging knowledge and management gaps in the future. We do not know how many resources went into these research and capacity building efforts for the Mekong, yet the expenditures were likely extremely small compared to what is at risk.
Fourthly, overlooking the fate of deltas in global assessment studies risks overlooking significant climate risks as well as opportunities for adaptation. So far, delta-scale studies incorporate downscaled results and scenarios from global assessments. Yet, results from delta-scale studies are rarely upscaled to understand feedbacks between land loss in deltas and global patterns of, e.g., migration, food supply, and trade, and thus issues for which deltas are of outstanding importance (see section 0). It is also a limitation that sea level rise is integrated as core hazard in the IPCC assessments while land subsidence, a driver that exceeds sea level rise as driver of relative elevation loss in many deltas, is not. Thus, calls have been made for an International Panel on Land Subsidence (IPLS) (www.IPLSubsidence.org) to bridge different research communities working on coastal vertical land motion and elevation dynamics, consolidate knowledge, identify knowns and unknowns and their respective importance; and design a consistent framework to integrate coastal land subsidence into rSLR projections.
Numerical models are no panacea in the efforts to mitigate the existential threats faced by many deltas. Yet, policy initiative such as the 2022 COP27 highlight the need for knowledge and the role of "best available science" to reduce climate risk 227 . Meanwhile efforts by, for example, UNESCO's Land Subsidence International Initiative (LaSII) 228 , the Global Delta Alliance (http://www.deltaalliance.org), or the Cities40 (https://www.c40.org) aim to make hazard posed by land subsidence and sea level rise more visible and catalyze global action 8 . This need for knowledge is embodied for global deltas, where reliable and transparent data and numerical models will be critical to inform decision-making processes, navigate trade-offs, and provide long-term strategies that span sectors and scales to avoid catastrophic environmental degradation in the next decades.