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Stochastic Watershed Models (SWMs) are emerging tools in hydrologic modeling used to propagate uncertainty into model predictions by adding samples of model error to deterministic simulations. One of the most promising uses of SWMs is uncertainty propagation for hydrologic simulations under climate change. However, a core challenge is that the historical predictive uncertainty may not correctly characterize the error distribution under future climate. For example, the frequency of physical processes (e.g., snow accumulation and melt) may change under climate change, and so too may the frequency of errors associated with those processes. In this work, we explore for the first time non‐stationarity in hydrologic model errors under climate change in an idealized experimental design. We fit one hydrologic model to historical observations, and then fit a second model to the simulations of the first, treating the first model as the true hydrologic system. We then force both models with climate change impacted meteorology and investigate changes to the error distribution between the models. We develop a hybrid machine learning method that maps model state variables to predictive errors, allowing for non‐stationary error distributions based on changes in the frequency of model states. We find that this procedure provides an internally consistent methodology to overcome stationarity assumptions in error modeling and offers an important advance for implementing SWMs under climate change. We test this method on three hydrologically distinct watersheds in California (Feather River, Sacramento River, Calaveras River), finding that the hybrid model performs best in larger and less flashy basins. Key Points We document non‐stationarity of hydrologic model errors under plausible climate change in an idealized experimental design We leverage state variable—model error relationships to develop a hybrid machine learning based error model The hybrid model exhibits promise in predicting out‐of‐sample and non‐stationary error properties

1. In the context of ongoing climatic warming, forest landscapes face increasing risk of conversion to non-forest vegetation through alteration of their fire regimes and their post-fire recovery dynamics. However, this pressure could be amplified or dampened, depending on how fire-driven changes to vegetation feed back to alter the extent or behaviour of subsequent fires. 2. Here we develop a mathematical model to formalize understanding of how firevegetation feedbacks and the time to forest recovery following high-severity (i.e. stand-replacing) fire affect the extent and stability of forest cover across landscapes facing altered fire regimes. We evaluate responses to increasing burn rates while varying the direction (negative vs. positive) of fire-vegetation feedbacks under a continuum of values for feedback strength and post-fire recovery time. In doing so, we determine how interactions among these variables produce thresholds and tipping points in landscape responses to changing fire regimes. 3. Where the early-seral vegetation was less fire-prone than older forests, negative feedbacks limited the reductions in forest cover in response to higher fire frequency or slower forest recovery. By contrast, positive feedbacks (more flammable early-seral vegetation) produced a tipping point beyond which increases in burn rates or a slowing of forest recovery drove extensive forest loss. 4. With negative feedbacks, the rates of forest loss and expansion in response to variation in fire frequency were similar. However, where feedbacks were positive, the conversion from predominantly forested to non-forested conditions in response to increasing fire frequency was faster than the re-expansion of forest cover following a return to the initial burn rate. Strengthening the positive feedbacks increased this asymmetry. 5. Synthesis. Our analyses elucidate how fire-vegetation feedbacks and post-fire recovery rates interact to affect the trajectories and rates of landscape response to altered fire regimes. We illustrate the vulnerability of ecosystems with positive fire-vegetation feedbacks to climate change-driven increases in fire activity, especially where post-fire recovery is slow. Although negative feedbacks initially provide resistance to forest loss with increasing burn rates, this resistance is eventually overwhelmed with sufficient increases to burn rates relative to recovery times.

This study evaluates the uncertainties of turbulent flux calculation using eddy covariance (EC) and wavelet analysis (WA) methods. First, a non‐stationary data set is concocted by adding periodic waves and random perturbations which mimic the large eddies, turbulent intermittency, and asymmetry into an observational stationary data set, and the theoretical “true” fluxes are used to quantitatively evaluate the accuracy of these methods. Results show that EC and Morlet‐wavelet generate biases ranging 50%–100% of the “true” values at different non‐stationarity grades, whereas the Mexican hat (Mexhat) wavelet has a bias of about half of them. Furthermore, there is a high correlation of the Mexhat‐derived fluxes to the benchmark values, the regression slopes of the values of these two can be improved to almost 1 by adding a correction coefficient. The results suggest the potential of using the Mexhat‐wavelet method to calculate turbulent fluxes with high accuracy under non‐stationary conditions. Plain Language Summary Eddy covariance (EC) method is the well‐accepted technique to calculate turbulent flux under stationary conditions. However, the observational turbulence data sometimes show non‐stationarity, and in this case, the EC method is not applicable and wavelet analysis (WA) is frequently used. However, because turbulent fluxes are calculated values, and there are no true flux measurements, the accuracy of WA‐calculated fluxes remains unknown. In this study, we constructed a non‐stationary data set and used their theoretical true values to evaluate the accuracy of EC and WA methods in flux calculation under non‐stationary conditions. It is found that EC and Morlet‐wavelet bias 50%–100% of the true values at different non‐stationarity grades, while the Mexican hat (Mexhat) wavelet has the bias about half of them. Besides, there is a high correlation of the Mexhat‐derived fluxes to the true values, and Mexhat‐derived fluxes can be corrected to near true values by adding a correction coefficient. Therefore, the Mexhat‐wavelet method has the potential to be used to calculate turbulent fluxes under non‐stationary conditions. Key Points A method to concoct non‐stationary data series is proposed Eddy covariance and wavelet analysis methods underestimate turbulent momentum flux under non‐stationary condition by about 50% Mexican hat wavelet method has the potential to accurately calculate flux of non‐stationary turbulence after correction

Identifying the demographic parameters (e.g., reproduction, survival, dispersal) that most influence population dynamics can increase conservation effectiveness and enhance ecological understanding. Life table response experiments (LTRE) aim to decompose the effects of change in parameters on past demographic outcomes (e.g., population growth rates). But the vast majority of LTREs and other retrospective population analyses have focused on decomposing asymptotic population growth rates, which do not account for the dynamic interplay between population structure and vital rates that shape realized population growth rates (λt = Nt+1/Nt) in time-varying environments. We provide an empirical means to overcome these shortcomings by merging recently developed \"transient life-table response experiments\" with integrated population models (IPMs). IPMs allow for the estimation of latent population structure and other demographic parameters that are required for transient LTRE analysis, and Bayesian versions additionally allow for complete error propagation from the estimation of demographic parameters to derivations of realized population growth rates and perturbation analyses of growth rates. By integrating available monitoring data for Lesser Scaup over 60 yr, and conducting transient LTREs on IPM estimates, we found that the contribution of juvenile female survival to long-term variation in realized population growth rates was 1.6 and 3.7 times larger than that of adult female survival and fecundity, respectively. But a persistent long-term decline in fecundity explained 92% of the decline in abundance between 1983 and 2006. In contrast, an improvement in adult female survival drove the modest recovery in Lesser Scaup abundance since 2006, indicating that the most important demographic drivers of Lesser Scaup population dynamics are temporally dynamic. In addition to resolving uncertainty about Lesser Scaup population dynamics, the merger of IPMs with transient LTREs will strengthen our understanding of demography for many species as we aim to conserve biodiversity during an era of non-stationary global change.

We face a new era in the assessment of multiple natural hazards whose statistics are becoming alarmingly non‐stationary due to ubiquitous long‐term changes in climate. One particular case is tsunami hazard affected by climate‐change‐driven sea level rise (SLR). A traditional tsunami hazard assessment approach where SLR is omitted or included as a constant sea‐level offset in a probabilistic calculation may misrepresent the impacts of climate‐change. In this paper, a general method called non‐stationary probabilistic tsunami hazard assessment (nPTHA), is developed to include the long‐term time‐varying changes in mean sea level. The nPTHA is based on a non‐stationary Poisson process model, which takes advantage of the independence of arrivals within non‐overlapping time‐intervals to specify a temporally varying hazard mean recurrence rate, affected by SLR. The nPTHA is applied to the South China Sea (SCS) for tsunamis generated by earthquakes in the Manila Subduction Zone. The method provides unique and comprehensive results for inundation hazard, combining tsunami and SLR at a specific location over a given exposure time. The results show that in the SCS, SLR has a significant impact when its amplitude is comparable to that of tsunamis with moderate probability of exceedance. The SLR and its associated uncertainty produce an impact on nPTHA results comparable to that caused by the uncertainty in the earthquake recurrence model. These findings are site‐specific and must be analyzed for different regions. The proposed methodology, however, is sufficiently general to include other non‐stationary phenomena and can be exploited for other hazards affected by SLR. Plain Language Summary Assessing natural hazards that are made worse by climate change cannot use previous methods that assume that the average behavior is a good representation of the hazard. Here we show the effect of climate‐change‐driven sea level rise (SLR) on tsunami hazard, where the continuously increasing SLR cannot be represented by an average value. Higher sea levels produce several changes in the tsunami behavior, including an increase in the maximum tsunami water level and in the speed the tsunami propagates. We introduce a new method which incorporates the long‐term time‐varying changes in mean sea level. The method can be applied to other coastal hazards, such as storm surge and waves. The new method is applied to port cities in the South China Sea (SCS) for tsunamis generated by earthquakes in the Manila Subduction Zone. We determine the probability of flooding urban areas within 50 and 100 years. The hazard in SCS is significantly impacted by SLR when it rises by an amount comparable to the tsunami height for a tsunami with moderate likelihood. The effect is comparable to that caused by the estimated uncertainty in recurrence interval of the causative earthquake. These results, though, are site‐specific. Key Points The impact of sea level rise (SLR) on probabilistic tsunami hazard assessment (PTHA) depends on the exposure time and the relative magnitude of both phenomena For the probabilistic tsunami hazard assessment (PTHA) in South China Sea, the sea level rise (SLR) is as important as the uncertainty of the earthquake recurrence model Sea level rise (SLR) can change the tsunami propagation properties so probabilistic tsunami hazard assessment (PTHA) must include nonlinear effects in the tsunami behavior and inundation level

In this paper, some general theory is presented for locally stationary processes based on the stationary approximation and the stationary derivative. Laws of large numbers, central limit theorems as well as deterministic and stochastic bias expansions are proved for processes obeying an expansion in terms of the stationary approximation and derivative. In addition it is shown that this applies to some general nonlinear non-stationary Markov-models. In addition the results are applied to derive the asymptotic properties of maximum likelihood estimates of parameter curves in such models.

Predictions of groundwater fluctuations in space and time are important for sustainable water resource management. Infiltration variability on monthly to decadal timescales leads to fluctuations in the water tables and thus groundwater resources. However, connections between global-scale climate variability and infiltration patterns and groundwater are often poorly understood because the relationships between groundwater conditions and infiltration tend to be highly nonlinear. In addition, understanding is further hampered because many groundwater records are incomplete and groundwater tables are often anthropogenically influenced, which makes identifying the effects of infiltration variability difficult. Previous studies that have evaluated how infiltration variability controls groundwater are based on a limited number of point measurements. Here, we present a global assessment of how infiltration variability is expected to affect groundwater tables. We use an analytical solution derived from Richards' equation to model water level responses to idealized periodic infiltration variability with periods that range from months to decades, to approximate both the effects of short-term and long-term climate variability and thus infiltration patterns. Our global-scale assessment reveals why infiltration variability would lead to periodicity in groundwater recharge in particular regions. The vadose zone strongly dampens short-term (seasonal and shorter) variations in infiltration fluxes throughout most of Earth's land surface, while infiltration cycles exceeding 1 year would yield transient recharge, except in more arid regions. Our results may help forecasting long-term groundwater tables and could support improving groundwater resource management.

Drought and pluvial extremes are defined as deviations from typical climatology; however, background climatology can shift over time in a non‐stationary climate, impacting interpretations of extremes. This study evaluated trends in meteorological drought and pluvial extremes by merging tree‐ring reconstructions, observations, and climate‐model simulations spanning 850–2100 CE across North America to determine whether modern and projected future precipitation lies outside the range of natural climate variability. Our results found widespread and spatially consistent exacerbation of drought and pluvial extremes, especially summer drought and winter pluvials, with drying in the west and south, wetting trends in the northeast, and intensification of both extremes across the east and north. Our study suggests that climate change has already shifted precipitation climatology beyond pre‐Industrial climatology and is projected to further intensify ongoing shifts. Plain Language Summary Managing water resources has become challenging due to the effect of human‐caused climate change on precipitation. This study examines trends in droughts and pluvials from the distant past (850 CE) to the projected future (2100 CE) to determine whether precipitation extremes in the modern, Industrial era and future are beyond what is typical of natural climate variability in North America. Trends were generated by merging information from tree rings, observations, and climate models using a novel statistical approach. Results indicate the widespread intensification of both drought and pluvials–especially summer drought and winter pluvials during the modern and future periods. Spatially, southern and western regions of North America are becoming drier, while the northeast is getting wetter, and central areas of North America show a wider range between drought and pluvial years. Our study suggests that anthropogenic climate change has already modified drought and pluvial extremes beyond natural, pre‐Industrial conditions and these ongoing trends are projected to intensify through the future. Key Points This study models seasonal drought and pluvial trends, merging reconstructions, observations, and projections from 850 to 2100 CE Results show widespread exacerbation of both extremes with overall drying (wetting) in southern (northeastern) North America Modern drought and pluvial distributions are outside pre‐Industrial (1850) conditions, and exhibiting substantial shifts in some regions

Reliable seasonal flood forecasting is vital for managing reservoirs and disaster response. This study investigates whether probabilistic forecasts of seasonal floods can be improved by integrating spectrally transformed hydroclimatic variables. We apply the Wavelet System Prediction (WASP) method to enhance climate covariates within a Generalized Extreme Value (GEV) model. Using streamflow observations from 649 European catchments, we compare forecasts using raw and spectrally transformed covariates. Results show that the transformation significantly improves forecast skill, measured by the Ranked Probability Skill Score (RPSS), especially at longer lead times. The most notable gains are observed in Northern and Western Europe, including the UK and Norway. The proposed hybrid WASP‐GEV forecasting framework, integrating spectral transformation, significantly enhanced seasonal flood forecast skills with up to 3 months of lead time. These findings highlight the potential of advanced data transformation techniques to improve hydroclimatic extreme forecasts, benefiting water resource management in a changing climate.

The relationship between the performance of individuals and the surrounding environment is fundamental in ecology and evolutionary biology. Assessing how abiotic and biotic environmental factors influence demographic processes is necessary to understand and predict population dynamics, as well as species distributions and abundances. We searched the literature for studies that have linked abiotic and biotic environmental factors to vital rates and, using structured demographic models, population growth rates of plants. We found 136 studies that had examined the environmental drivers of plant demography. The number of studies has been increasing rapidly in recent years. Based on the reviewed studies, we identify and discuss several major gaps in our knowledge of environmentally driven demography of plants. We argue that some drivers may have been underexplored and that the full potential of spatially and temporally replicated studies may not have been realized. We also stress the need to employ relevant statistical methods and experiments to correctly identify drivers. Moreover, assessments of the relationship between drivers and vital rates need to consider interactive, nonlinear and indirect effects, as well as effects of intraspecific density dependence. Synthesis. Much progress has already been made by using structured population models to link the performance of individuals to the surrounding environment. However, by improving the design and analyses of future studies, we can substantially increase our ability to predict changes in plant population dynamics, abundances and distributions in response to changes in specific environmental drivers. Future environmentally explicit demographic models should also address how genetic changes prompted by selection imposed by environmental changes will alter population trajectories in the face of continued environmental change and investigate the reciprocal feedback between plants and their biotic drivers.