Hybrid forecasting: blending climate predictions with AI models

Abstract

Hybrid hydroclimatic forecasting systems employ data-driven (statistical or machine learning) methods to harness and integrate a broad variety of predictions from dynamical, physics-based models – such as numerical weather prediction, climate, land, hydrology, and Earth system models – into a final prediction product. They are recognized as a promising way of enhancing the prediction skill of meteorological and hydroclimatic variables and events, including rainfall, temperature, streamflow, floods, droughts, tropical cyclones, or atmospheric rivers. Hybrid forecasting methods are now receiving growing attention due to advances in weather and climate prediction systems at subseasonal to decadal scales, a better appreciation of the strengths of AI, and expanding access to computational resources and methods. Such systems are attractive because they may avoid the need to run a computationally expensive offline land model, can minimize the effect of biases that exist within dynamical outputs, benefit from the strengths of machine learning, and can learn from large datasets, while combining different sources of predictability with varying time horizons. Here we review recent developments in hybrid hydroclimatic forecasting and outline key challenges and opportunities for further research. These include obtaining physically explainable results, assimilating human influences from novel data sources, integrating new ensemble techniques to improve predictive skill, creating seamless prediction schemes that merge short to long lead times, incorporating initial land surface and ocean/ice conditions, acknowledging spatial variability in landscape and atmospheric forcing, and increasing the operational uptake of hybrid prediction schemes.

1 Introduction: defining hybrid forecasting and prediction

This review addresses the growing popularity of hybrid forecasting, an approach that seeks to enhance the predictability of hydroclimatic variables by merging predictions from dynamical physics-based weather or climate simulation models with data-driven models. Dynamical models represent the temporal changes in system properties by using numerical modelling to solve dynamical physical processes. Data-driven models include empirical, statistical, and machine learning (ML) methods (i.e. can be described as artificial intelligence or AI) and can range from simple linear regression to deep neural networks. Recognizing that dynamical and AI models have different strengths, hybrid prediction reflects the deliberate fusing of the two.

Table 1

Examples of different hybrid model structures.

Name	Description
(i) Statistical–dynamical	Statistical–dynamical hybrid models consist of driving or conditioning a data-driven model with dynamical weather, climate, or Earth system model (ESM) predictions e.g.. Both expressions, statistical–dynamical and dynamical–statistical, are used, depending on the focus of the research or the field of study. This approach is also referred to as informed-parameter e.g. or physical–statistical e.g. prediction.
(ii) Serial	A serial structure combines the dynamical and data-driven models sequentially and may include additional models such as a hydrological model. For instance, one could pre-/post-process the output of a dynamical model using a data-driven approach e.g. and use those predictions as input to a conceptual or physics-based model. In , post-processed general circulation model (GCM) forecasts are used to force a monthly rainfall–runoff model. In , weather patterns are identified in an ensemble prediction system and subsequently used to forecast threshold exceedance probabilities of extreme precipitation and flooding.
(iii) Coupled or parallel	In a coupled hybrid structure, the data-driven and dynamical models are combined in parallel. This may involve, for instance, replacing a component of a dynamical model with a data-driven model, e.g. to create a machine-learning-corrected GCM e.g.. Alternatively, it is possible to combine outputs from an ensemble of dynamical and statistical predictions run in parallel e.g.. A data-driven model may also be employed to combine dynamical predictions from both meteorological and hydrological models e.g..

Figure 1

Defining hybrid hydroclimate forecasting and prediction. The term “hydroclimate” refers to a range of variables defined in the text, including streamflow. The top row indicates the traditional dynamical hydroclimate predictions (blue), the middle row is data-driven (DD) predictions (yellow), and the bottom row represents hybrid predictions (red), which combine dynamical and data-driven approaches. In the last row, three examples of a hybrid structure are shown from top to bottom, namely (i) statistical–dynamical (Stat-dyn), (ii) serial, and (iii) coupled, as described in Table . The figure provides simple examples, but other schemes are possible, including, for example, a mix of observations and predictions in the left column.

[Figure omitted. See PDF]

Table 2

Examples of hybrid forecasts of different hydroclimate variables and model types. Each example includes both a data-driven model and a dynamical weather or climate model. Examples are sorted by increasing time horizon. Hybrid model types are defined in Table , and the acronyms are defined in Table .

Predictand	Data-driven model	Dynamical model	Hybrid type	Time horizon	Citation
River stage and inundation	LSTM	ECMWF HRES	Stat-dyn	1–6 $\mathrm{d}$
Daily streamflow	BNN, SVR, GP, MLR	NOAA GFS	Stat-dyn	1–7 $\mathrm{d}$
Precipitation	RF	FV3GFS	Coupled	1–10 $\mathrm{d}$
Precipitation extremes andflooding	Probability of exceedingthresholds	UKMO GloSea5, ECMWF	Serial	15 $\mathrm{d}$
Biweekly temperature andprecipitation	PLSR	CFSv2	Serial	2–3 and 3–4 weeks
Seasonal streamflow	PCR and CCA	CFSv2 and ECHAM4.5	Stat-dyn	1 month
Monthly reservoir inflow	RF, GBM, ELM,M5 cubist, elastic net	FLOR	Stat-dyn	1 month
Drought – seasonal SPI	Dynamic-LSTM	ECMWF SEAS5	Stat-dyn	3 months
Seasonal tropical stormfrequency	MLR	UKMO GloSea5	Stat-dyn	3 months
Seasonal rainfall	ANN, MLR	UKMO GloSea5, ECMWF SEAS5	Stat-dyn	1–4 months
Drought	Bayesian model based oncopula functions	NMME (eight models)	Coupled	3–5 months
Accumulated seasonalreservoir inflow	SVR, GP, LSTM, NLANN, DL	CMCC	Serial $+$ stat-dyn	1–6 months
River discharge and surfacewater levels	MLR, LR, DT, RF, LSTM	ECMWF SEAS5; EFAShydrological forecasts	Stat-dyn	1–7 months
Hurricane frequency andintensity	GAMLSS	NMME (six models)	Stat-dyn	1–9 months
Seasonal runoff	PCR	NMME (seven models);ECWMF SEAS4	Stat-dyn	4–9 months
Hurricane frequency	Statistical emulator of dynamical atmospheric model	GFDL–CM2.1; NCEP–CFS	Stat-dyn	1–10 months
Seasonal streamflow	GAMLSS	NMME (eight models)	Stat-dyn	1–10 months
Monthly streamflow	FoGSS, CBaM	POAMA-M2.4	Serial	1–11 months
Seasonal flood magnitude	GAMLSS	5/8 CMIP5/6 GCMs	Stat-dyn.	2–5 years
Seasonal flood counts	Poisson regression	9/14 CMIP5 GCMs	Stat-dyn	1–10 years
Daily streamflow	TCNN (and others)	4 GCMs from LOCA (CMIP5)	Serial $+$ stat-dyn	Decades
Flood magnitude	LSTM ($+$5 GHMs)	5 GCMs from ISIMIP-FT (CMIP5–6)	Serial	Decades
Daily streamflow	DNN-PCE	10 GCMs (CMIP5)	Serial	Decades

While challenging to identify distinct categories, given the flexibility and diversity of hybrid methods, three principal types of hybrid model structure may be discerned (Fig. ; Table ). These include (i) statistical–dynamical models that typically drive a statistical or ML model (data driven) with dynamical weather or climate model outputs from numerical weather prediction (NWP) models or Earth system models (ESMs). The statistical–dynamical structure is the most common type of hybrid model in the literature (Table ). (ii) Serial models combine data-driven and dynamical models sequentially and may include additional types of models, such as a hydrological model. (iii) Coupled or parallel approaches combine data-driven and dynamical models in parallel. The coupled approach is more commonly employed in operational settings, where ML is increasingly being used to upgrade components within existing modelling schemes. We do not provide a prescriptive definition of hybrid forecasting, as it exists along a continuum from loosely to fully hybrid e.g. and may include a wide range of models and big data, such as Earth observations (EOs).

Traditional workflows in which a physics-based or conceptual land/hydrology model generates the final forecast product are still the most commonly used operational forecasting systems worldwide. Physics-based models are based on a spatially distributed representation of known physical laws through mathematical equations and numerical solutions e.g., while conceptual models simplify the representation of physical processes, often using empirical relationships e.g.. There is a long history of the development and application of standalone dynamical land surface and catchment hydrology models of varying complexity (from conceptual to physically explicit) for operational forecasting. Process-based hydrological modelling approaches may either be spatially distributed (gridded) or lumped (catchment averaged). Examples include the hourly conceptual rainfall–runoff GR4H (Génie Rural à 4 paramétres Horaires) model used by the Bureau of Meteorology in Australia , the conceptual reservoir-based HSAMI model implemented by Hydro-Québec , or the conceptual Sacramento Soil Moisture Accounting (SAC-SMA) model of the Community Hydrologic Prediction System of the U.S. National Weather Service . In operational systems, the hydrological model is typically forced with NWP-based forecast meteorology, as in the case of the U.S. National Water Model (; see , for a report on the science-driven operational application of several end-to-end ensemble hydrometeorological forecasting systems). Outputs from coupled atmosphere–ocean–land GCMs may be used over longer time horizons, as is the case with the European and Global Flood Awareness Systems, EFAS and GloFAS . These approaches are considered to be more physically interpretable than black box statistical methods. However, the large computational demand and variable skill of many traditional forecasting approaches still persists , and their calibration still requires substantial effort relative to most data-driven models (see Sect. ).

In contrast with traditional forecast workflows, data-driven prediction has historically relied more on observed data than dynamical climate model predictions, building empirical relationships between, for example, streamflow and precipitation , using time lag relationships between upstream and downstream flow, or stochastic autoregression approaches, like autoregressive moving average models . In such data-driven models, the hydroclimatological predictands can be regressed on a range of covariates, such as observed precipitation/temperature records, static variables (e.g. elevation, slope, and geology), initial hydrologic conditions, or large-scale predictors such as sea surface temperatures (SSTs), surface air temperature, geopotential height, meridional wind, sea ice extent, or modes of climate variability such as the El Niño–Southern Oscillation ENSO; e.g.. Broadly speaking, the strength of statistical models lies in their simplicity, speed, ease of use, and comparable skill to dynamical methods when there are sufficient observations for model training. However, data-driven models are sometimes thought to be less able to extrapolate to extreme outlier values that have not been seen in the historical record or unable to reflect shifts in the relationship between the predictand and predictors. Others have raised the risk of artificial skill in cases where predictors are selected preferentially based on the correlation with the predictand and are not fully cross-validated e.g.. Data-driven models may also be difficult to optimize for multi-variate, high-dimensional output fields, which are simulated intrinsically by dynamical models. Recent studies focusing on more complex data-driven techniques such as deep learning have suggested that some of these limitations can be overcome, such as the extrapolation to extreme or unforeseen conditions , to new (untrained) catchments , and to poorly gauged large regions . Nevertheless, the inclusion of physical constraints could further elevate the prediction robustness in data-sparse situations . Research is required to understand the hydroclimatological conditions to which new ML and DL models are able to extrapolate from the training set and their performance as they are extrapolated in space.

Hybrid forecasts benefit from combining the ability of physical models to predict and explain large-scale phenomena (i.e. through NWPs or climate model predictions) with the ability of data-driven models to efficiently estimate the characteristics of events from observed data and account for bias or anomalies in the data. Many current examples of hybrid prediction build on traditional forecast workflows by using an ML algorithm in sequence with or alongside a conceptual or physics-based hydrological model (; Fig. ). Some notable examples of operational hybrid prediction include the objective consensus climate forecast (i.e. derived objectively from multiple models) at the U.S. Climate Prediction Center, which uses ensemble regression e.g. to combine multiple dynamical and statistical forecasts into one. The International Research Institute for Climate and Society (IRI) has a multi-model-calibrated prediction based on three Subseasonal Experiment (SubX) models . The UK Met Office uses a tool called Decider, which assigns medium-range precipitation forecast ensemble members to a set of 30 probabilistic weather patterns and then feeds several downstream forecasting applications, such as for coastal flooding and fluvial flooding . Last, the Google flood forecasting model (https://sites.research.google/floods/, last access: 6 May 2023) produces operational, public-facing forecasts of water levels up to 6 $\mathrm{d}$ ahead , using ML models forced with operational, real-time weather forecasts from the ECMWF Atmospheric Model high-resolution 10 $\mathrm{d}$ forecast (ECMWF HRES) as inputs. Broadly speaking, many hydroclimate projection systems are now hybrid, as per the serial definition in Table , because some kind of statistical processing is applied to generate a final information product from an ensemble of climate model outputs. Dynamical modelling centres often lack the resources or scope to tailor outputs to particular stakeholder needs (adding value with data-driven methods), leading to the implementation of such processing by the end-users themselves. These predictions are not always visible as hybrid activity but are operational nonetheless. These examples show the general evolution of the field from traditional forecasting toward hybrid prediction.

Table 3

Modelling acronyms referred to in the paper. The top section includes data-driven models and approaches; the bottom section includes other acronyms used.

Acronym	Full name
ANN	Artificial neural network
BAMLSS	Bayesian additive models for location, scale, and shape
BMA	Bayesian model averaging
BNN	Bayesian neural network
CBaM	Calibration, bridging, and merging
CCA	Canonical correlation analysis
DL	Deep learning
DLNN	Deep learning neural network
DNN-PCE	Deep neural network-based polynomial chaos expansion
DT	Decision tree
ELM	Extreme learning machine
FoGSS	Forecast-guided stochastic scenarios
GAMLSS	Generalized additive models for location, scale, and shape
GAN	Generative adversarial network
GBM	Gradient-boosting machine
GP	Gaussian process
LR	Lasso regression
LSTM	Long short-term memory
ML	Machine learning
MLR	Multiple linear regression
NLANN	Nonlinear autoregressive neural network
PCR	Principal component regression
PLSR	Partial least squares regression
RF	Random forest
SVM	Support vector machine
SVR	Support vector regression
TCNN	Temporal convolutional neural network
CMCC	Euro-Mediterranean Center on Climate Change
CMIP5 and 6	Coupled Model Intercomparison Project phases 5 and 6
ECMWF	European Centre for Medium-Range Weather Forecasts
ECMWF SEAS5	Seasonal Forecast System version 5
FLOR	Forecast-oriented Low Ocean Resolution model
FV3GFS	Finite-Volume Cubed-Sphere Global Forecast System (global atmospheric model)
GCM	Global climate model
GFDL-CM2.1	Geophysical Fluid Dynamics Laboratory Coupled Model
GHM	Global hydrological model
ISIMIP	Inter-Sectoral Impact Model Intercomparison Project
LOCA	Localized Constructed Analogue
PREVAH	PREcipitation–Runoff–EVApotranspiration HRU-related model
RCP8.5	Representative Concentration Pathway 8.5 (high-emission warming scenario)
UKMO GloSea5	UK Met Office Global Seasonal Forecasting System version 5

Figure 2

Example of a seasonal hybrid forecasting system for maximum summer discharge at one stream gauge, using seasonal climate forecasts from eight climate models (94 members) of the NMME to drive a distributional regression model of streamflow. The maximum summer discharge is the largest of the 92 daily values in the summer (June–August, JJA) period. The time series shows the model fit (1980–2000) and forecast (2001–2015) against the observations of maximum summer daily streamflow (grey circles). Initialization times are 0.5, 5.5, and 9.5 months ahead of the summer season. For example, the initialization in June uses climate forecasts with a 0.5-month lead for June, 1.5-month lead for July, and 2.5-month lead for August to compute the summer streamflow, while the initialization in September includes forecasts initialized 9.5, 10.5, and 11.5 months ahead in the previous year. Adapted from .

[Figure omitted. See PDF]

The diversity of approaches for hybrid forecasting and prediction is evident from the sample of studies listed in Table . The scope of hybrid models can vary widely, encompassing different forecast units (e.g. hourly or seasonal mean forecasts), lead times from the next hour to next decade; e.g., and geographical domains (from point to street level; from a single river catchment through to global approaches). Hybrid models have been applied to predict a variety of hydrometeorological variables, including extreme heat and precipitation , seasonal climate variables , tropical cyclones/hurricanes , streamflow , flooding , drought , sea level , and reservoir levels , over a range of timescales (Table ). Certain other examples discussed in this review are not fully hybrid (e.g. ML models that are not driven by weather/ESM predictions) but serve to illustrate the possibilities of future hybrid systems. Many types of data-driven models have been used (Tables  and ), including simple regression methods, principal components, distributional regression frameworks, such as the generalized additive models for location, scale, and shape (GAMLSS), and various types of deep learning approaches, including artificial neural networks (ANNs) and long short-term memory (LSTM) models. The atmospheric and climate models employed for hybrid forecasting can range from single models to large multi-model ensembles. For example, there are the North American Multi-Model Ensemble NMME; and the Copernicus Climate Change Service (C3S) seasonal forecasting systems over subseasonal to seasonal timescales or the Coupled Model Intercomparison Project (e.g. CMIP5–6) over decadal timescales. The dynamical predictors may include various model outputs such as meteorological forecasts with lead times of up to 14 $\mathrm{d}$, initialized climate predictions with subseasonal to decadal lead times, subseasonal runoff predictions, and/or land surface or ocean state fields from the reanalyses used to initialize the climate system. Predictors are not only selected based on their ability to enhance hybrid forecast skill, such as traditional hydroclimate variables (e.g. precipitation, temperature, and evapotranspiration) but also large-scale climate indices and teleconnections e.g.. Hybrid hydroclimatic forecasts and predictions have numerous operational and strategic applications, including water resources planning, reservoir inflow management , surface water flooding , flood risk mitigation, navigation , and agricultural crop forecasting .

This paper provides an overview of recent developments and ongoing challenges in hybrid hydroclimatic forecasting. We seek to highlight the benefits of employing hybrid methods alongside or within traditional forecasting systems. Accordingly, in Sect. , we provide several in-depth examples of different approaches to hybrid hydroclimatic forecasting. In Sect. , we discuss the key strengths of hybrid models, followed by ongoing challenges and future research opportunities in Sect. . We close with some concluding remarks in Sect. .

2 Hybrid forecasting examples

Here we provide examples of the statistical–dynamical, serial, and coupled approaches outlined in Fig.  and Table .

2.1 Statistical–dynamical hybrid forecasts

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 $\mathrm{d}$ 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 ${\mathrm{km}}^{\mathrm{2}}$ 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 .

2.2 Serial hybrid forecasts

2.2.1 Serial pre- and post-processing of hydroclimate predictions using data-driven approaches

Hybrid approaches often include pre-/post-processing of inputs and outputs at different stages of the predictive model. Pre-processing refers to techniques for enhancing the signal and removing the systematic biases of the data inputs, such as the dynamical climate simulations, while post-processing refers to techniques for refining and correcting model outputs. Depending on the point of reference, the same technique can be considered to be either pre- or post-processing. These techniques are often used as a routine add-on to traditional forecasting systems (e.g. driving a hydrological model with pre-processed climate predictions), and here we focus principally on approaches that go beyond the traditional set-up. The strength of hybrid approaches lies in their ability to incorporate such corrections directly within hybrid modelling frameworks.

Hybrid models often include a data-driven component which downscales low-resolution climate model simulations to reduce bias and make the outputs more skilful at the local scale. For instance, generative adversarial networks (GANs) have been used to spatially downscale precipitation forecasts to capture the complex joint distributions between precipitation and initial climate conditions from climate simulations. At the decadal timescale, linear and kernel regression can be used to enhance climate predictions . Random forest (RF) models can be trained to map the low-resolution climate model predictions to high-resolution values . Regardless of the algorithm used, once the mapping from low-resolution to high-resolution values has been learnt, data-driven models can be applied to a much larger number of model simulations to produce an ensemble of high-resolution outputs at a much lower computational cost than running a dynamical model at an equivalent resolution. Another example is the use of data-driven methods to reduce the degrees of freedom in data, for instance, through discrete or empirical wavelet transforms .

Data-driven approaches can also be applied directly to post-process the hydrological forecasts. deployed an ERRIS (error reduction and representation in stages) model to directly correct errors in streamflow prediction up to 168 $\mathrm{h}$ ahead (i.e. maximum lead time of 7 $\mathrm{d}$). Such approaches can be especially beneficial for longer forecast horizons. For instance, a Gaussian process (GP) model was trained to post-process weekly tercile forecasts of runoff and soil moisture from a Swiss conceptual hydrological model PREVAH (PREcipitation–Runoff–EVApotranspiration HRU-related model) and showed improvements in the forecast skill up to 4 weeks ahead . developed a daily Multi-Temporal Hydrological Residual Error (MuTHRE) statistical model to seamlessly transform daily streamflow forecasts to timescales ranging from daily, weekly, and fortnightly to monthly. This one-model-for-all-scales approach is a novel take on the potential of the hybrid forecasting system. LSTMs can also be used to post-process outputs from physics-based models, such as long-term streamflow projections and streamflow simulations to make them more realistic. implemented a physics-informed approach to post-process the streamflow projections from GCMs, GHMs, and the Catchment-based Macro-scale Floodplain (CaMa-Flood) model. The LSTMs were trained to learn a relationship between simulated streamflow (from the physics-based model GHMs–CaMa-Flood), basin-averaged daily precipitation, temperature, wind speed, and observed streamflow. The LSTM model can thus be perceived as a post-processor which aims to constrain (i.e. reduce the uncertainty of) the streamflow simulations from the physics-based model. This post-processing approach improved the simulations for the reference period and was then successfully applied to project streamflow over the future period. However, the authors concede that this LSTM-based post-processor is still subject to the same limitations as other post-processing methods, such as the assumption of stationarity in the parameters of the post-processing method. similarly employed an LSTM to post-process the outputs from the physics-based U.S. National Water Model (NWM). They implemented two variants of the post-processing method alongside an LSTM forced with atmospheric inputs only (i.e. without any NWM inputs). The authors showed that the routing scheme and the land surface component of the NWM introduced timing and mass balance errors in the simulations. Thus, in some cases, it would be preferable to simply use an LSTM model that can simulate streamflow from atmospheric forcings only (without any NWM inputs) to avoid propagating errors from the NWM to the streamflow prediction.

Data-driven models can enhance the signal of predictors by generating an ensemble (by pooling) of different climate model predictions . A common approach to incorporating an ensemble of climate model predictions (within a statistical, ML, or hydrological model) is to assume that predictions from each ensemble member are equally likely. However, owing to varying model skill, and a lack of independence amongst some models, the assumption of equal likelihood can be compromised. Hence, hybrid forecasting can be used to combine ensembles in more intelligent ways by accounting for the varying information content of the ensemble members. Statistical ensembling/post-processing of climate model ensemble outputs can improve forecast skill at relatively low computational cost. For instance, applied a deep neural network to ensemble predictions to improve the forecast skill and reduce the computational requirements of the forecast system. applied Bayesian model averaging (BMA) to weight models according to their skill at reproducing observations. They show that the weighted ensemble average skill for the contiguous United States exceeds that of the conventional ensemble average, with better constrained uncertainty estimates. Bayesian updating can also be applied to enhance the skill of a multi-model ensemble of GCMs, such as the NMME for different seasons or lead times e.g.. Bayesian updating provides the best results when the raw GCM predictions have high skill to begin with, such as SST-based ENSO forecasts . Post-processing hydrological forecasts (instead of climate forecasts) is another application of BMA. demonstrated how such an approach can be deployed to improve the skill of a conceptual runoff forecast by pooling four separate runoff forecasts forced with different lead times (24, 72, 120, and 240 $\mathrm{h}$) and ensemble members (1, 1, 16, and 51, respectively) in a Swiss catchment.

Figure 3

Example of a coupled hybrid system for predicting seasonal precipitation several months ahead. (a) Ensemble of precipitation predictions from a dynamical multi-model ensemble such as the NMME. The ribbon indicates the full distribution of model members, and the dark line indicates the mean prediction. (b) Ensemble of statistical precipitation predictions. (c) Both ensembles are overlaid. (d) The two ensembles are blended using a data-driven approach, such as an Expert Advice algorithm, which assigns weights to the different ensemble members based on their performance during training and computes the weighted average prediction. The resulting ensemble mean (orange line) outperforms that of the separate dynamical and statistical predictions. Adapted from .

[Figure omitted. See PDF]

2.2.2 Serial hybrid forecasts that include a hydrological model

Hybrid forecasting systems that include a conceptual hydrological model try to combine the strengths of data-driven and conceptual models, driven with dynamical predictions. For instance, used a combination of historical observations and downscaled dynamical forecasts of rainfall and potential evapotranspiration in southern Australia from POAMA (Predictive Ocean Atmosphere Model for Australia) to drive the conceptual rainfall–runoff model GR4J . The simulated soil moisture from GR4J was separately used to drive a Bayesian ANN model to predict streamflow (hybrid approach). They showed that the hybrid model performed better than either the GR4J model or the Bayesian neural network alone. A number of studies have coupled conceptual models and data-driven models but without necessarily integrating dynamical weather or climate predictions (this would be the next step in developing a hybrid forecasting system). Both and replaced the routing component of the GR4J model with an ANN to predict streamflow in catchments in France, the USA, and the Republic of Türkiye. These studies concluded that the hybrid model was superior to a purely ML model. Other conceptual hydrological models have also been used in hybrid frameworks. For example, used two conceptual models, HBV and NRECA , to provide inputs to support vector machines (SVMs) and an adaptive neuro-fuzzy inference system (ANFIS), to build seven variants of hybrid models. They tested and compared the hybrids and the individual models (HBV, NRECA, SVMs, and ANFIS) on four subbasins of the Pemali–Comal River basin, Indonesia, and again found the hybrid models performed best in terms of RMSE, $R^{\mathrm{2}}$, and MAE. Other studies on hybrid modelling using the HBV model include and . They both used different variables computed by HBV (e.g. soil moisture and snowmelt) as inputs to ANNs. outline that, in most hybrid modelling frameworks, variables computed by the conceptual model are used as inputs to a data-driven model, which necessarily increases computation time. They also note that although there could potentially be interactions between the parameters of the conceptual models and those of the data-driven model, those interactions often go unaccounted for because the two models are calibrated separately. In the context of monthly rainfall–runoff modelling, they proposed to address these two common shortcomings of hybrid models by coupling the two models and performing their calibration jointly.

2.3 Coupled or parallel hybrid models

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.

Figure 4

Strengths, challenges, and opportunities of hybrid hydroclimate prediction systems, as discussed in Sects.  and .

[Figure omitted. See PDF]

3 Strengths of hybrid forecasting

Hybrid methods offer various strengths, as summarized in Fig. . These strengths include the higher performance of ML models (in terms of bias and error minimization) and the ability to easily blend outputs from climate multi-model ensembles, integrate large datasets, and combine multiple sources of predictability, as well as improved speed and operational convenience. These strengths are discussed in more detail below.

3.1 ML model performance and bias minimization

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 .

3.2 Combining local and remote sources of predictability with varying time horizons

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 $\mathrm{hPa}$ 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 $\mathrm{d}$ 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.

3.3 Integrating large datasets

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.

3.4 Speed and operational convenience

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 $\mathrm{h}$ 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 $\mathrm{h}$ 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 $\mathrm{s}$ 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 $\mathrm{d}$ 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.

4 Key challenges and opportunities of hybrid forecasting

Beside the strengths of hybrid methods, there are challenges and research priorities to be tackled. As hybrid forecasts and predictions rely on data-driven models, they inevitably inherit some of the limitations of these techniques. Frequently cited limitations of ML models include the requirement for large datasets and issues associated with the curse of dimensionality, namely data sparsity (i.e. when there are too few data points relative to the number of dimensions), multi-collinearity of the variables, multiple testing (leading to an increased number of false positives), and overfitting . There is also the difficulty of obtaining physically plausible results for previously unseen extremes that are larger than those seen in the observational record; however, new research suggests that ML models may provide results that are more physically plausible than physics-based and conceptual models when data are biased . Further challenges for improving the skill of hybrid models include data assimilation, physics-guided ML designs, assimilation of human influences, model optimization, ensembling, and hybridization, where models are merged with other methods including simulations and physical models; e.g.. While some of the difficulties associated with large sample sizes apply less for seasonal to decadal hybrid forecasting, where the sample sizes can be much smaller (often near 100 values) than the sample sizes for shorter ranges (thousands or more), the small sample sizes present a challenge for model training. Thus, a range of different challenges may apply, depending on the forecasting horizon and data required.

4.1 Obtaining physically realistic results

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.

4.2 Assimilating human influences

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.

4.3 Developing predictive skill

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 $\mathrm{d}$ ahead but has been advancing by about 1 d per decade, such that “today's 6 $\mathrm{d}$ forecast is as accurate as the 5 $\mathrm{d}$ forecast 10 years ago” p. 47. Low flows may have skill up to 20 $\mathrm{d}$ 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..

Figure 5

Hybrid models could be a promising route for seamlessly linking initialized predictions from seasonal and decadal forecasts to scenario-based projections across timescales. Different ML-based bias correction approaches could be explored for merging or concatenating the covariate time series (e.g. ) before using them to drive a hybrid hydroclimate prediction model (e.g. for streamflow). Such an approach is likely to be more challenging for extremes such as floods and droughts and remains an open research question.

[Figure omitted. See PDF]

4.4 Seamless forecasting: merging forecasts, predictions, and projections

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.

4.5 Incorporating spatial variability

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.

4.6 Interpretability, usability, and uptake of hybrid forecasts

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.

5 Conclusions and remaining research areas in hybrid forecasting

Hybrid forecasting is emerging as a powerful enhancement to traditional hydroclimatic forecasting techniques, but important questions remain regarding their place in the pantheon of methods. We lay out some of the most important research possibilities. First are questions about the evaluation of hybrid methods. How well do dynamical-statistical methods perform when compared with more traditional, operational approaches? What benchmarks should be used? How reliable are these models, and over what lead times can they be trusted? As far as we are aware, there have been very few papers (if any) comparing the skill of hybrid models with operational systems. One systematic comparison of 13 different models (including machine-learning-based, basin-wise, subbasin-based, and gridded models) revealed the superiority of the data-driven LSTM-lumped model in all experiments e.g., suggesting that hybrid LSTM-based prediction systems would be a promising route for daily simulation and potentially for applications such as forecasting.

Second are questions about the potential for seamless prediction. To what extent can hybrid approaches be employed to meld historical trends, near-term, and decadal predictions of hydroclimate variables from atmospheric forecasts, climate model predictions, and projections? How would such a system be used operationally? Seamless hybrid prediction may provide better insights into long-term hydroclimatic trends, but merging across timescales can lead to inconsistencies in the time series (i.e. jumps or step changes) between, for example, decadal climate predictions and the climate projections . Third are questions about using data-driven models to detect and attribute the drivers of hydrologic change , and then integrating such knowledge within a predictive framework. How can data-driven approaches be employed to understand the relative contributions of different predictors, including human impacts such as the effects of reservoir regulation on streamflow ? To what extent can hybrid models uncover hidden large-scale climatic or anthropogenic drivers of change ?

An important step forward would be the development of consistent global datasets of climate hindcasts at various timescales at the catchment level. Similar datasets developed for large sample hydrological analyses, such as CAMELS e.g. and Caravan , have driven rapid progress in ML methods for simulating daily streamflow using observed climate inputs. Such datasets drive progress towards operational hybrid systems by making it easier for model developers to train and test potential methods in a pseudo-operational context. Moreover, they could integrate consistent estimates of other potential drivers – including streamflow signatures and local characteristics related to topography, geology, and land cover (as in the CAMELS datasets) – enabling forecasters to understand the contribution of different drivers to streamflow predictability across timescales.

Finally, there are questions about the acceptance and viability of hybrid models in operational contexts, given the dominance, familiarity with, and deep embedding of physics-based forecasting and prediction methods . In what ways could hybrid approaches complement, support, or replace conventional physically based systems? The pace of change in such settings is often constrained by practicalities, institutional resistance , or the requirement for decision-relevant evidence of skill. Acceptance might be advanced by systematically comparing the outputs from hybrid models with operational models under identical forcings to assess the physical interpretation of model results e.g.. To convince operational forecasters that hybrid models may add value alongside more traditional approaches requires rigorous benchmarking by the community alongside established approaches. It may also require more extensive changes to the education and preparation of the workforce that is needed to staff operational centres.

There are several possible paths forward. One of these frames hybrid models not as replacing current operational systems but as a complementary tool, extension, or enhancement, helping on different levels and likely within existing systems. Another path forward is to recognize the difference in skill between hybrid models vs. traditional models and to start to develop future replacements for current operational models. These replacements should be based fundamentally on data-driven (ML, DL, and even AI) principles but with the ability to incorporate elements of traditional hydrological and climate science where these are beneficial. Furthermore, hybrid models could be developed to estimate both impacts and mitigation measures based on past events. All of these approaches make sense for different reasons and in different scenarios, and various agencies and organizations are pursuing both these and other strategies for incorporating data-driven methods into operational workflows. Overall, the utility of hybrid models is not only for enhancing forecasting and prediction but also for allowing deeper interrogation of diverse data, revealing sometimes hidden or obscure hydroclimatological processes.

Data availability

No data sets were used in this article.

Author contributions

LJS conceptualized the paper and wrote the original draft. LJS, LA, and AYC produced the visualizations. LA, MB, AYC, SM, CM, GN, GS, CS, LS, GV, RLW, AW, and MZ contributed to the conceptualization of ideas and to the writing and editing of the manuscript.

Competing interests

At least one of the (co-)authors is a member of the editorial board of Hydrology and Earth System Sciences. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.

Disclaimer

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Acknowledgements

We wish to thank two anonymous reviewers for their insightful comments that helped improve the work.

Financial support

This research has been supported by the UK Research and Innovation (grant nos. MR/V022008/1 and NE/S015728/1), the Swiss Federal Institute for Forest, Snow and Landscape Research (MaLeFix; Extremes), the Canada First Research Excellence Fund (Global Water Futures programme), the U.S. Army Corps of Engineers (USACE Institute for Water Resources), and the Science Foundation Ireland (grant no. SFI/17/CDA/4783).

Review statement

This paper was edited by Nadav Peleg and reviewed by two anonymous referees.