In the case of short-term hybrid forecasts, which focus on outlook horizons of hours to weeks driven by dynamical meteorological models, hybrid approaches offer the potential to address the challenge of forecasting extreme events, such as floods, from convective rainfall . In these situations, the time taken to transfer data between meteorological and hydrological organizations and the run time of the physics-based models can be restrictive. In contrast, the strengths of ML are the small number of input parameters making the models easy to develop, quick to run, and accurate for short lead time events . In regions where access to hydrological and inundation forecasts is limited, data-driven models offer promising alternatives for flood forecasting e.g. and show the potential to overcome limitations of data scarcity . At 1–7 d lead times, found that ML models outperform MLR (Tables  and ). At the shortest lead times, their hybrid approach worked best when it was driven by observations and the National Oceanic and Atmospheric Administration (NOAA) Global Forecast System (GFS) model output and at longer lead times when driven by a combination of local observations and climate indices. The potential of ML as a means to post-process dynamical forecasts and produce warning scenarios for convective weather is also emerging e.g. but has not yet been widely utilized as input to hydrological models. For hydrologic forecasts, ML is highly successful in assimilating recent observations of streamflow to improve near-term daily forecasts of streamflow and soil moisture . In some cases, machine learning can ingest near-real-time data without the need for backwards methods like data assimilation, since any data stream can be fed directly into the model as input, as long as at least some samples from each input data stream are available during training. It is also possible to perform more traditional types of data assimilation on or with ML models – for example, variational assimilation can be done by leveraging the same partial gradients in the models that are required for backpropagation .

At the subseasonal to decadal timescale, climate model predictions are often used to drive statistical or ML models. A simple example of a hybrid statistical–dynamical model is one that employs the predictions of precipitation or temperature from a climate model as predictors within a regression model, where the predictand can be a hydroclimatic variable such as streamflow magnitude e.g. or flood duration . describe this approach as an informed-parameter approach in which the parameters of the flood distribution can be conditioned on time-varying covariates such as time, climate indices, infrastructure development indices, or land use indices. For example, distributional regression models can be used to predict seasonal discharge. To illustrate the approach, we consider a 9000 km2 catchment that has experienced a rapid expansion of the agricultural land area over the 20th century (Fig. ). Two lumped covariates are employed to predict the seasonal maximum of the mean daily streamflow in each year, namely the basin-averaged total seasonal precipitation and the harvested corn and soybean acreage in the same season. The model employs a two-parameter gamma distribution, and the entire streamflow distribution is computed for each time step. The model is trained over the historical period using climate observations or forecasts, model parameters are extracted, and the streamflow forecast is based on those parameters and the dynamical predictions of the covariates obtained from an ensemble of climate models. Once new observations become available, the model can be retrained, updating the model parameters. A different model can be developed for each season, initialization time (e.g. 0.5, 5.5, and 9.5 months ahead of a given season), and quantile of the predicted discharge distribution. This example shows how a simple statistical model can be used to produce subseasonal to seasonal streamflow forecasts. The skill of such a scheme might be improved by post-processing the ensemble of climate predictions used to drive the model.

Seasonal forecasts of diverse hydroclimatic variables such as SSTs, sea level pressure, or large-scale climate indices have also been used in hybrid models to predict variables such as precipitation and tropical cyclone activity . For instance, atmosphere–ocean teleconnections obtained from the NMME – including the Pacific Decadal Oscillation (PDO), Multi-variate ENSO Index (MEI), and Atlantic Multi-decadal Oscillation (AMO) – were used to successfully predict seasonal precipitation anomalies in the southwestern USA using a statistical Bayesian-based model . Hybrid methods can also be trained on large model ensembles to capture nonlinear interactions between predictor variables. For instance, trained ML models for seasonal precipitation forecasts in the western USA on a large historical climate model ensemble of atmospheric and oceanic conditions (i.e. on thousands of seasons of simulations from the Community Earth System Model Large Ensemble, CESM-LENS). The same trained models were then tested by using observational data over 1980–2020. The resulting ML-based approach performed as well as, if not better than, seasonal NMME forecasts, and the physical processes could be interpreted using ML interpretability plots, highlighting the most important variables influencing a given forecast. For Ireland, found that MLR and ANN models applied to hindcasts of mean sea level pressure from GloSea5 and SEAS5 produced skilful forecasts of the winter (December–February, DJF) and summer (June–August, JJA) precipitation for lead times of up to 4 months, with the ANN outperforming MLR for both seasons and all lead times. A study over the Netherlands using streamflow, precipitation, and evaporation found that the hybrid ML approach outperformed climatological reference forecasts by approximately 60 % and 80 % for streamflow and surface water level, respectively, using various machine learning models . Another study showed that predictions of large-scale indices by NCEP CFSv2 (National Centers for Environmental Prediction Coupled Forecast System model version 2) could be used to successfully predict the frequency of tropical cyclones in the Bay of Bengal using principal component regression .

Statistical–dynamical approaches can also be deployed for longer horizons, such as decadal streamflow predictions e.g., and data-driven techniques are proving successful for enhancing the skill of the decadal climate predictions, with consequent benefits for climate-linked variables such as streamflow. Decadal forecast skill can be increased by mode-matching, which consists of sub-selecting the individual members from a large climate model ensemble of decadal predictions that best represent the multi-year temporal variability in a relevant large-scale mode of climate variability . Large climate ensembles can be pre-processed to select members which are skilful at a given time, and the improved predictions can then be supplied to a statistical modelling framework to predict seasonal streamflow quantiles .

In the case of coupled hybrid models, a data-driven model and a physics-based model can be run in parallel, sometimes replacing a component of the dynamical model with a data-driven model or combining different types of model predictions. combined the seasonal precipitation predictions from an ensemble of dynamical models (99 members from the NMME) with the precipitation predictions from a statistical model (using copulas to describe the relationship between three large-scale climate indices and precipitation). They used an Expert Advice algorithm to link the dynamical and statistical predictions to obtain improved precipitation predictions over the southwestern USA, as illustrated in Fig. .

Coupled hybrid models can also employ a data-driven model to combine other types of dynamical predictions in parallel, such as dynamical meteorological and hydrological predictions. In southern Switzerland, five ML models were trained to predict monthly total hydropower production by combining precipitation, temperature, radiation, and wind speed forecasts from a dynamical meteorological model with runoff from a conceptual hydrological model . Day of the week and holiday information were provided to the ML models as additional information to further enhance the prediction.

A third example of a coupled hybrid approach is when data-driven models are employed during the dynamical climate model simulations to correct model biases e.g.. A RF model coupled to an atmospheric model (FV3GFS) can correct temperature, specific humidity, and horizontal winds at each time step, bringing the coupled model in line with observations. This was shown to reduce annual mean precipitation biases by around 20 %, with particular improvements in the simulation of rainfall over high mountains . A similar approach was used by to nudge the output of a low-resolution climate model towards the coarsened output of a high-resolution climate model.

Recent work has demonstrated the ability of ML models to outperform traditional hydrological models e.g.. In one of the most comprehensive studies to date, compared 13 locally and globally calibrated models (including ML, lumped, and gridded models) in terms of their ability to simulate streamflow, actual evapotranspiration, surface soil moisture, and snow water equivalent in the Great Lakes region. They found that the ML model outperformed the traditional hydrological models in all experiments. This finding extends to ungauged catchments. found that an out-of-sample LSTM performed better than the calibrated SAC-SMA (the conceptual model used by the U.S. River Forecast Centers) and the NWM, which is less calibrated. found that RFs worked best at regionalizing the parameters of the GR6J conceptual model for low-flow prediction in ungauged Irish catchments. Such work has shown the potential of hybrid methods to address the long-standing hydrological challenge of prediction in ungauged basins e.g.. The next step is to move from simulation to prediction.

Hybrid models combining ML and climate predictions also tend to outperform the raw dynamical forecasts from climate models. , for instance, developed a hybrid drought-forecasting model of the 3-month Standardized Precipitation Index (SPI). They used RF models to post-process ECMWF SEAS5 predictions of geopotential height, sea level pressure, and air temperature and supplied the output to an LSTM model to predict the 3-month SPI. They found that the SPI predictions from these hybrid models outperformed the predictions of SPI obtained from the raw model outputs. For prediction purposes, hybrid models have the advantage of being able to minimize biases that exist within GCM outputs or that might be otherwise introduced within a hydrological modelling chain. By training a hybrid model directly on the climate model forecasts, rather than on observations, the biases are automatically accounted for within the model e.g.. This approach is similar to that of model output statistics (MOSs) long used by the weather forecasting community and in seasonal hydrological predictions . For instance, if a climate model tends to overpredict winter rainfall, then this bias is accounted for directly in the streamflow predictions, given that the model is trained using the same winter rainfall forecasts (assuming a constant bias).

Hybrid models may benefit from a wide range of statistical advances for enhancing the skill of hydroclimate predictions. Since a hybrid system is based on a data-driven model, it is straightforward to incorporate statistical upgrades, such as ensembling the outputs of multiple climate or Earth system models . One such example is the addition of an error model onto Ensemble Streamflow Prediction (ESP) forecasts to enable prediction in ephemeral rivers . In a hybrid system, one may easily integrate the predictions from multi-model ensembles with over 50 or 100 model members as covariates . Increasing the number and diversity of climate models included within a hydrological predictive model enhances confidence in the hydrological model spread. By blending multi-model ensembles intelligently, one can further reduce uncertainty. In a hybrid system, for instance, one can incorporate time-varying weights for the dynamical predictions, such as Bayesian updating, which varies the model weight per month and lead time . ML models especially can learn space–time variable input weighting directly . Similarly, many post-processing methods can be applied to weather and climate inputs or the hydrological outputs to enhance skill .

One under-researched but promising aspect of hybrid models is their ability to combine different sources of predictability over a continuum of time horizons. Hybrid models can easily make use of different predictors chosen on a sound physical basis (such as climate indices, precipitation, air pressure, and snowfall) without explicitly describing the processes and equations. This makes it much easier to explore information from new sources and improve models and has the potential to widen information access to climate-affected populations. Including additional inputs can also produce marked improvements in model quality. used seven weather regime indices (based on the 500 hPa geopotential height) with a Gaussian process ML model to post-process subseasonal hydrological forecasts, alongside runoff, soil moisture, baseflow, and snowmelt in Switzerland. The results showed that the additional input of weather regime indices improved the forecast skill, especially in the mountainous catchments and over longer lead times, where skill was difficult to improve without any additional information. The conceptual hydrological model would not have been able to take weather regime indices as input, but by including them in the post-processing ML model as part of the hybrid set-up, it was possible to explore the connection between large-scale weather regimes and local hydrological conditions to improve the forecast skill.

As multiple predictor variables can be included within a statistical or ML model, it is feasible to combine predictors that have very different time-varying impacts, such as reservoir management decisions or initial hydrological conditions impacting the short term, versus annual-to-multi-decadal climate oscillations for longer-term predictability. For instance, present a reservoir inflow forecasting framework combining a suite of different ML models (including gradient-boosting machine, random forests, and elastic net) with climate model outputs from the FLOR model for reservoirs in the Upper Colorado River basin. They also included soil moisture and evaporation to represent antecedent conditions, which significantly improved the forecasts of reservoir inflow. used a dataset of > 3000 basins across the USA and found that basins with small and medium reservoirs behaved differently from the reference basins but could be well simulated by a LSTM model with input attributes describing basin-lumped reservoir statistics.

Large-scale climate indices or modes can also be combined with other predictors. For instance, predicted seasonal precipitation using large-scale climate indices, namely the PDO, the MEI, and the AMO, computed from outputs of the 99 ensemble members of the NMME. The approach enhanced the skill of the seasonal forecasts by 5 %–60 % in comparison with the raw NMME precipitation forecasts, especially for negative rainfall anomalies. Similarly, forecasted daily streamflow in a river catchment 1–7 d ahead by employing weather forecasts from the NOAA GFS model within a variety of machine learning models. They combined observations with the model outputs and a range of large-scale climate indices representing ENSO, the Pacific–North American teleconnection pattern (PNA), the Arctic Oscillation (AO), and the North Atlantic Oscillation (NAO). Last, used forecasts of the intraseasonal oscillation (ISO), an important mode of subseasonal predictability for seasonal rainfall, to force a Bayesian hierarchical model predicting subseasonal precipitation during the boreal summer monsoon season in different regions of China.

Given the diversity of potential inputs to hybrid forecasting systems, exploratory data analysis to identify correlations between hydrologic variables and climate patterns over different time horizons is an important step during model development. employed ML to identify the most relevant large-scale climate indices for daily streamflow forecasting. They provided an overview of studies that have employed large-scale climate indices and climate variables (such as sea level pressure, sea surface temperature, and specific and relative humidity) within ML models for daily, monthly, and seasonal streamflow modelling. Beyond the use of pre-defined climate indices, it is possible to identify tailored, site-specific climate indices from big data and incorporate them in the modelling chain. For instance, described a method that avoids relying on standard climate indices and instead suggests that the most relevant climate indices in a given location are effectively unknown (they are hidden) and can be estimated directly from observations. The authors used a Bayesian hierarchical model for flood occurrence, with hidden climate indices treated as latent variables. They identified the hidden climate indices and then showed their correlation with atmospheric climate variables (geopotential height, zonal westerly wind, and also more distant teleconnections using convective available potential energy and meridional wind). These indices explain the occurrence of flood-rich and flood-poor periods in the historical record. Such an approach could be employed using climate model outputs to develop skilful hybrid forecasts.

Related to the different time horizons of the predictors is also the ability to design hybrid forecasting systems which dynamically update when new information (e.g. observations or climate hindcasts) becomes available. For instance, a statistical model can be updated iteratively over time to track the evolution of nonstationary predictor–predictand relationships. Such approaches incorporate new observations as they become available and update the model parameters e.g.. developed a data assimilation approach for LSTM models that leverages tensor network gradients to assimilate real-time observation data. To date, very little has been published using such methods.

One perceived challenge of hybrid approaches is the requirement for large numbers of training data to constrain models compared with physics-based or conceptual models. Previously, it was felt that the information requirement of data-driven approaches might hinder their applicability in catchments with limited data (e.g. ungauged basins). Although this might have been true in the past, the increasing availability of large-scale hydroclimatic datasets, such as remote sensing data, is turning this potential challenge into a new opportunity. A data-driven model can be trained on the same data as a conceptual model and will tend to outperform physics-based models, on average and even more so with large datasets; see. This advantage is partly due to the fact that data-driven models are unconstrained by mass and energy balance rules that force process models to compensate for erroneous inputs, which data-driven models can instead optimize against. Data-driven models learn process relationships and model structures rather than enforce prescribed ones, which may make them more flexible and generalizable. Large training datasets tend to be useful for ML but less so for physics-based models, for these reasons. The ability to leverage large datasets effectively is a strength of ML and in particular for ungauged basins, where several studies have shown that ML models tend to have higher accuracy, on average, than physics-based models calibrated in gauged basins e.g.. There is, in fact, a data synergy effect, where data of greater diversity lead to better models, according to a systematic study of LSTM models for either streamflow or soil moisture . With conceptual and process-based models, accuracy can be lost when performing regional (as opposed to basin-specific) calibration, and the lack of calibration data typically results in poor-quality predictions (training on longer periods leads to superior results; see ). In contrast, with hybrid models, strong performance can be achieved when training the models on global datasets, and accuracy is gained when performing regional calibration.

Since long (50 year +) hydroclimatic time series data are not available everywhere , methods are required that can draw on pooled multi-site approaches with similar catchment and climate characteristics . For instance, show a comparison using pooled vs. unpooled data for streamflow estimation and found that the former was better, even for gauged catchments, and allowed for prediction in ungauged catchments. There are, however, few studies combining LSTM methods with climate model forecasts for long-term (subseasonal to decadal) prediction, especially in ungauged catchments. Such models may start to emerge with the growing availability of observational training datasets, such as the national CAMELS datasets available for the USA, United Kingdom, Chile, Brazil, Australia, and soon France and Switzerland; e.g. and international Caravan streamflow dataset . However, real-time data are currently still difficult to access for developing predictive models.

One way to circumvent the lack of observational training data and the low predictability of GCMs is by integrating a range of other types of predictors in hybrid models. This may include sources of remotely sensed measurements such as snow, soil moisture, land cover, surface water extent, water storage, or evapotranspiration to provide better information about the initial states e.g.. There are many different global datasets now available that can be drawn on using cloud-based geospatial analysis platforms such as the Google Earth Engine, as was the case for the creation of an open-source community streamflow dataset . Overall, the forecasting landscape is becoming increasingly complex, with a growing number of forecasting systems and datasets potentially overwhelming users. Hybrid forecasting could help to address this challenge, with hybrid workflows providing a set of tools and data that forecasters could mix and match to address their own forecasting needs.

A key advantage of statistical or hybrid methods is their speed and computational efficiency. For instance, the calibration of the GloFAS system with an Evolutionary Algorithm (EA) in 2018 required approximately 6 h to calibrate each one of thousands of streamflow stations on a 12-core PC, depending on the number of generations needed before the improvement criterion was met . Training deep learning (DL) models is now orders of magnitude cheaper in terms of the computational expense. For example, it took about 10 h in 2021 to train an ensemble of long short-term memory (LSTM) networks on a single NVIDIA V100 graphics processing unit (GPU) using 2 decades of daily data from 518 basins in the CAMELS-GB dataset (; i.e. about 70 s per basin). This means that training a high-quality DL model for hundreds of basins is feasible using a standard workstation (or even a GPU-enabled laptop with sufficient memory), while calibrating a conceptual or process-based model over hundreds of basins requires either months of runtime or a high-performance computer (HPC) facility. The training time depends on the computing power, number of locations and volume of data involved, compiler, and optimization. While deep learning methods such as LSTMs can take several hours to train e.g., they have the significant advantage that one model is trained on multiple sites (although the fitted model can then be fine-tuned to a specific site). A differentiable ML-based parameter learning scheme can be trained on satellite-based soil moisture observations for the entire continental USA with one GPU in under 1 h, but the conventional approach would take a cluster machine of 100 central processing units (CPUs) 2–3 d to calibrate the model .

This efficiency has advantages for water managers. In a traditional setting with limited computational resources, water managers need to quickly run different scenarios . For instance, the UK Met Office Flood Forecasting Centre will produce a reasonable worst case and a best estimate based on the most likely scenario (see ) ahead of a flood event . Using all available deterministic and ensemble forecast products alongside expert assessment from the chief forecaster, they will decide what the reasonable worst case is likely to be. These outputs are used to inform the flood guidance statement and the Environment Agency then uses these scenarios to run their catchment models . The speed of data-driven approaches in comparison with these more traditional, physics-based modelling approaches could prove beneficial for users wishing to run multiple scenarios quickly. Hybrid methods may shorten the traditional forecasting approach by going end to end, potentially skipping out some of the intermediary steps in a conventional modelling chain, such as downscaling, bias correction, and hydrological modelling. This offers significant potential for applications where the run time of physically based models limits the ability to provide forecasts with a useful lead time for action – such as forecasts of pluvial floods or flash floods.

The efficiency of hybrid models may also be helpful in generating faster research cycles for model improvements (i.e. setting up an upgraded system and releasing hindcasts for testing) relative to traditional approaches. Model upgrades for dynamical systems usually take a very long time because the model has to be recalibrated and a set of x (e.g. 30) years of hindcast data must be produced to quantify the impact of the changes to the system.

Last, hybrid systems can be used to develop customized climate services. For instance, use data-driven methods to predict seasonal reservoir inflows for hydropower plants. The information is made easily accessible online to support decision-makers in hydropower production. Such approaches can be designed to be replicated globally as a climate service, provided there are suitable data for training, and by developing transferable rule sets. p. 8239 also highlight the importance of operational convenience and the advantages of combining the convenience of stochastic scenarios with the skill of a modern forecasting system. Their method enhances the precipitation forecasts necessary for streamflow forecasting through post-processing – by reducing the biases, correcting the reliability, and maximizing the forecast signal.

One important challenge of hybrid models is the need to produce physically plausible or explainable forecasts in unseen extreme conditions such as severe floods, droughts, intense heatwaves, and tropical storms. This is particularly important as new weather records are being set in different parts of the world, and models must produce credible predictions under extreme forcing conditions. Although it has sometimes been suggested that data-driven models might be less suited to extrapolation to out-of-sample conditions than physics-based models due to the lack of physical understanding e.g., recent work tackled the question of whether modern LSTMs could predict events larger than those seen in the training data for a particular catchment. The authors found that the LSTM could predict unseen streamflow extremes and did this better than the physics-based models that were used in the study . It is now increasingly recognized that one of the advantages of data-driven models is their flexibility, allowing them to find unexpected patterns in the data. Thus, there are emerging synergies between data-driven and physics-based approaches, since the former can enhance the performance of the latter, e.g. by learning the parameterizations required for the physical models from large datasets or analysing the patterns of error from the physical models .

One emerging route for hybrid models is to employ physics-guided or theory-guided ML designs that explicitly observe the law of conservation of mass. Such approaches seek to integrate physical knowledge within the data-driven models to take advantage of the strengths of both. For instance, created an LSTM architecture that obeys conservation laws, and these laws can also be used to guide physical interpretation of model outcomes. Although there have been considerable methodological advances in interpreting neural networks e.g., physics-guided ML approaches (also referred to as physics-informed, physics-aware, or theory-guided approaches) still require further development. As alluded to earlier, the presence of data errors in observed hydroclimate records means that an unconstrained ML performs better than a physics-guided ML model because of the ability to learn and account for data errors , including heteroscedastic and nonstationary data errors .

Another new development is differentiable, learnable, physics-based models that can not only approach the performance of ML models but also output internal physical variables such as evapotranspiration and soil moisture . first demonstrated the ability of connected neural networks to provide physical parameter sets to process-based models. They showed the efficiency and generalizability of this paradigm for untrained variables, spatial extrapolation, and interpretability. In data-sparse regions, this approach can even produce better daily metrics and future trends than LSTM and can be used to improve flood routing . These models seek to combine the power of both ML and physics and have the potential to alleviate data demand, extrapolate better in space and for more extreme conditions, and be constrained by multi-variate observations to enable better forecasts. Furthermore, they provide a systematic pathway for asking scientific questions and obtaining answers from big data.

Explainability is sometimes useful to help develop trust in model predictions. Forecasting agencies frequently engage in a form of story-telling, both for internal and external communication. One reason for providing explainable predictions is that, when the forecasts evolve for a given variable, such as spring runoff, users often wish to understand why (i.e.  what has changed in the predictors or other factors to explain the change in the predictions). One way to achieve explainability is by providing storylines or narratives around the hybrid forecasts which demonstrate the geophysical credibility of the results. Differentiable modelling can also provide diverse physical variable outputs, trained or untrained, which help develop a narrative . showed how hydroclimatic storylines can be produced for clients to make the forecast interpretable in terms of understandable geophysical processes. They used pragmatic methods such as popular votes for the candidate predictors cast by a genetic algorithm. The approach revealed how the values of predictors such as antecedent flow and snow water equivalent could help explain the ensemble-mean-predicted volume. However, there are also limitations to such approaches. Although narratives may help with stakeholder acceptance of hybrid forecasting systems, they can also form a constraint on the forecasting approach, by enforcing consistency of a given prediction method.

Another emerging challenge is assimilating human influences on the water cycle to obtain better predictions of hydroclimate variables, especially droughts . Limited data exist on human impacts such as water storage, groundwater depletion, irrigation, land cover changes, and water transfers. Therefore, how can human decisions, such as the management of reservoir levels or flow abstraction, be integrated within hydrological forecasts? This question is especially relevant over longer timescales, and for hydrological forecasting in general, as access to such data is limited (e.g. only very limited information on reservoir operations is included in GloFAS). One option is to develop proxies to detect and model human influence. For instance, census information on the number of households has be used to extend UK urbanization records . Population density data have also been used as a proxy for urbanization, to assess the extent to which seasonal streamflow predictability might benefit from anthropogenic predictors such as land cover change alongside seasonal climate forecasts . supplied a dynamic reservoir index alongside climate indices to predict historical annual maximum peak discharge in Spanish rivers. In a large-scale study it was found that reservoir operations could be implicitly simulated by ML approaches that learn from past operations . Last, information on the day of the week and on local festivities has been used successfully as a proxy for difference in energy demand . Such proxies might also inform a hybrid system on hydro-peaking in rivers downstream of dams.

The lack of accurate predictions of future human activities at the catchment scale is also a major limitation for hydrological forecasting over longer timescales. Here, the increasing coverage and resolution of satellite data may help to provide relevant inputs to hybrid forecasting models such as future predictions of land use change e.g.. Emerging satellite altimetry products (e.g. SWOT) may enable a better understanding of reservoir operations, which can be used to constrain hydrological forecasts. Similarly, ML could potentially be used to translate major socioeconomic drivers into land cover change. Overall, we suggest that the main bottleneck to integrating human activities in hybrid forecasting systems is not the model algorithms, which can be adapted to any potential predictors, but rather the lack of consistent historical and future time series data on these activities. Unfortunately, this is likely to be a vexing challenge for automated representation. In many reservoir systems, for instance, operations are determined through unpredictable human interactions and negotiations and may depend on time-varying legal, institutional, ecological, and economic factors, such as agricultural markets influencing irrigation practice, or fisheries health directing environmental releases.

Dynamical forecasts and predictions tend to have low skill over long lead times. The skill of short-term hydroclimatological forecasts is constrained by the skill of meteorological forecasts, which is currently in the range of 3 to 10 d ahead but has been advancing by about 1 d per decade, such that “today's 6 d forecast is as accurate as the 5 d forecast 10 years ago” p. 47. Low flows may have skill up to 20 d in the case of and even longer in other cases, especially with good information on initial conditions and/or the memory effect of catchment storage. Seasonal climate forecasts also have low predictive skill beyond a couple of months, while both seasonal and decadal predictions suffer from the underestimation of atmospheric circulation in climate models, a phenomenon known as the signal-to-noise paradox e.g..

One of the advantages of hybrid predictions is that the data-driven methods can be used to enhance predictive skill of the dynamical meteorological or climate forecasts. For instance, decadal predictions are skilful over multi-year forecast periods but have too much uncertainty to provide useful information on interannual variability. Although the CMIP5–6 models can skilfully reproduce certain large-scale circulation patterns, the magnitude of teleconnections tends to be underestimated. Statistical approaches such as NAO-matching attempt to resolve this by selecting members based on their ability to reproduce climate indices and their teleconnections . Such methods have been employed to enhance decadal streamflow prediction and condition seasonal hydrological forecasts . However, further work is still needed to interpret multi-year forecasts to provide actionable information. Given a skilful multi-year forecast, it should be possible to estimate the increased flood or drought risk (for instance) in each year of the forecast period. Data-driven techniques may aid in future developments by trying to draw out the climate model members that perform well in given months or lead times e.g..

The utility of hybrid models for seamless hydroclimatic prediction systems spanning weeks to decades is an open research question (Fig. ). There is a growing need for reliable long-term predictions of climate change impacts on the risk of floods and droughts over the coming decades (i.e. 1–40 years ahead), yet reliable information does not exist over such timescales. The lack of seamless climate information is explained by the fact that different scientific weather and climate products have been developed for different applications. Short-term predictions (fewer than 5 years ahead) tend to rely more on correct initial conditions, while long-term predictions and projections (> 10 years ahead) rely more on correct external forcings such as greenhouse gases .

One way to provide longer-term climate impacts information over the coming decades is to constrain uninitialized climate model projections (e.g. climate simulations for the RCP4.5 or RCP8.5 scenarios) using initialized decadal predictions (such as the CMIP6 decadal hindcasts), which tend to better reflect observed climate variability. developed a method that does this by selecting the climate projections that best match the mean of the decadal predictions over the next 10 years. They showed that the constrained ensemble, which consisted of uninitialized projections for the upcoming 50 years, had higher skill than the full projection ensemble, even after the 10-year period, once decadal prediction information was no longer available. A hybrid system for enhanced prediction of hydroclimatic impacts (e.g. flood risk) could integrate the outputs of such a constrained ensemble.

Beyond the use of uninitialized projections by themselves (covering the whole 1–50-year period), temporally concatenating a bias-corrected time series of decadal climate predictions and climate projections is also possible. assessed different types of bias correction and found that the variance inflation (VINF) method could reduce inconsistencies between the decadal- and century-scale time series, especially for central quantiles of the climate time series (close to the multi-model ensemble median). However, the method could not eliminate all inconsistencies, notably those for extreme quantiles. A seamless hybrid method would therefore be more difficult to generate for hydroclimate extremes such as floods and droughts. However, these two papers open the way for novel research on the merging of decadal predictions and uninitialized projections as input to seamless prediction schemes for hydroclimate impacts using hybrid ML-based approaches.

The data employed in many hybrid hydrological models are often lumped, i.e. spatially averaged at the catchment scale, ignoring spatial variability in landscape and atmospheric forcing. Lumped models are challenging for the prediction of hydroclimate in complex environments such as snow-dominated watersheds, which may have karst conduits, or the spatiotemporal variation in snow accumulation and snowmelt processes. However, new approaches exist to overcome this limitation in statistical/machine learning models. For instance, developed a convolutional LSTM, termed convLSTM, which is able to capture spatiotemporal correlations, considering both the input and the prediction target as spatiotemporal sequences. One example is the use of past and future radar maps as input and output; such spatiotemporal sequences have high dimensionality and, until recently, could not be included in hydroclimate prediction schemes. Similarly, developed a spatial variability aware neural network, termed SVANN-E, in which the architecture of the neural network varied spatially across geographic locations. They evaluated the approach using high-resolution imagery for wetland mapping. Such novel spatiotemporal prediction approaches are just starting to be used for hydroclimate prediction. used a hybrid approach to predict streamflow in a watershed with spatially variable karst carbonate bedrock. They combined a spatially distributed snow model with a deep learning karst model based on convLSTM, which simulated the effect of surface and subsurface properties on the streamflow. This approach allowed the authors to better include the spatial variability in the input variables to their prediction scheme.

Hybrid approaches for hydroclimate prediction over subseasonal to decadal lead times face several challenges to their continued uptake by various communities. One issue that is critical to making hybrid schemes more widely accepted is determining whether the improvement in forecast skill obtained by building a hybrid model is worth the extra effort. In other words, it can be difficult to determine a priori how much added value can be obtained without first developing the hybrid model and benchmarking the results against a more traditional approach. Despite a commitment to developing the use of ML within operational hydrology e.g., close co-operation is needed between the hydrology, forecasting, and ML communities to explore their potential either alone or in hybrid frameworks , build trust , communicate skill , and overcome barriers to operational uptake . The benchmarking study of provided a detailed intercomparison of modelling approaches over the Great Lakes region (USA and Canada), suggesting that the effort related to ML is justifiable. However, this work was for retrospective simulation, rather than forecasting (for which there are more steps needed), and research is still needed to assess ML's potential for improving prediction skill, particularly over seasonal to decadal horizons, for which studies are lacking. In the hybrid set-up of , for instance, which required the development of both an ML and a conceptual model for three gauges in southern Australia, the authors found that the hybrid model was more skilful than either the conceptual or the data-driven models alone. However, the increase in skill was only marginal for one of the three study locations. They concluded that for this given station, the extra time and effort required to implement the hybrid model was not worth the small gains. Implementing an operational hybrid framework for hydroclimatic forecasting often requires extensive time and expertise, given that two completely different types of models must be developed in parallel. These requirements would also likely require a shift in the expertise of the organization in addition to an upgrade in the computing architecture in the case of GPU-requiring hybrid and data-driven approaches. Overall, the operational uptake of hybrid models is expected to be faster in cases where there is no existing forecasting capability (requiring modification) or where complex physical processes make traditional approaches challenging.