The prediction of flow duration curves (FDCs) in ungauged basins remains an important task for hydrologists given the practical relevance of FDCs for water management and infrastructure design. Predicting FDCs in ungauged basins typically requires spatial interpolation of statistical or model parameters. This task is complicated if climate becomes non-stationary, as the prediction challenge now also requires extrapolation through time. In this context, process-based models for FDCs that mechanistically link the streamflow distribution to climate and landscape factors may have an advantage over purely statistical methods to predict FDCs. This study compares a stochastic (process-based) and statistical method for FDC prediction in both stationary and non-stationary contexts, using Nepal as a case study. Under contemporary conditions, both models perform well in predicting FDCs, with Nash-Sutcliffe coefficients above 0.80 in 75 % of the tested catchments. The main drivers of uncertainty differ between the models: parameter interpolation was the main source of error for the statistical model, while violations of the assumptions of the process-based model represented the main source of its error. The process-based approach performed better than the statistical approach in numerical simulations with non-stationary climate drivers. The predictions of the statistical method under non-stationary rainfall conditions were poor if (i) local runoff coefficients were not accurately determined from the gauge network, or (ii) streamflow variability was strongly affected by changes in rainfall. A Monte Carlo analysis shows that the streamflow regimes in catchments characterized by frequent wet-season runoff and a rapid, strongly non-linear hydrologic response are particularly sensitive to changes in rainfall statistics. In these cases, process-based prediction approaches are favored over statistical models.

We introduce topological restricted maximum likelihood (TopREML) as a method to predict runoff signatures in ungauged basins. The approach is based on the use of linear mixed models with spatially correlated random effects. The nested nature of streamflow networks is taken into account by using water balance considerations to constrain the covariance structure of runoff and to account for the stronger spatial correlation between flow-connected basins. The restricted maximum likelihood (REML) framework generates the best linear unbiased predictor (BLUP) of both the predicted variable and the associated prediction uncertainty, even when incorporating observable covariates into the model. The method was successfully tested in cross-validation analyses on mean streamflow and runoff frequency in Nepal (sparsely gauged) and Austria (densely gauged), where it matched the performance of comparable methods in the prediction of the considered runoff signature, while significantly outperforming them in the prediction of the associated modeling uncertainty. The ability of TopREML to combine deterministic and stochastic information to generate BLUPs of the prediction variable and its uncertainty makes it a particularly versatile method that can readily be applied in both densely gauged basins, where it takes advantage of spatial covariance information, and data-scarce regions, where it can rely on covariates, which are increasingly observable via remote-sensing technology.

Globally, many different kinds of water resources management issues call for policy- and infrastructure-based responses. Yet responsible decision-making about water resources management raises a fundamental challenge for hydrologists: making predictions about water resources on decadal- to century-long timescales. Obtaining insight into hydrologic futures over 100 yr timescales forces researchers to address internal and exogenous changes in the properties of hydrologic systems. To do this, new hydrologic research must identify, describe and model feedbacks between water and other changing, coupled environmental subsystems. These models must be constrained to yield useful insights, despite the many likely sources of uncertainty in their predictions. Chief among these uncertainties are the impacts of the increasing role of human intervention in the global water cycle - a defining challenge for hydrology in the Anthropocene. Here we present a research agenda that proposes a suite of strategies to address these challenges from the perspectives of hydrologic science research. The research agenda focuses on the development of co-evolutionary hydrologic modeling to explore coupling across systems, and to address the implications of this coupling on the long-time behavior of the coupled systems. Three research directions support the development of these models: hydrologic reconstruction, comparative hydrology and model-data learning. These strategies focus on understanding hydrologic processes and feedbacks over long timescales, across many locations, and through strategic coupling of observational and model data in specific systems. We highlight the value of use-inspired and team-based science that is motivated by real-world hydrologic problems but targets improvements in fundamental understanding to support decision-making and management. Fully realizing the potential of this approach will ultimately require detailed integration of social science and physical science understanding of water systems, and is a priority for the developing field of sociohydrology.

Vegetation cover in dry regions is a key variable in determining desertification. Soils exposed to rainfall by desertification can form physical crusts that reduce infiltration, exacerbating water stress on the remaining vegetation. Paradoxically, field studies show that crust removal is associated with plant mortality in desert systems, while artificial biological crusts can improve plant regeneration. Here it is shown how physical crusts can act as either drivers of or buffers against desertification depending on their environmental context. The behavior of crusts is first explored using a simplified theory for water movement on a uniform, partly vegetated slope subject to stationary hydrologic conditions. Numerical model runs supplemented with field data from a semiarid Long-Term Ecological Research site are then applied to represent more realistic environmental conditions. When vegetation cover is significant, crusts can drive desertification, but this process is potentially self-limiting. For low vegetation cover, crusts mitigate against desertification by providing water subsidy to plant communities through a runoff-runon mechanism.