We use OGGM v.1.5.3 for the first component of the study – the simulation of reference glaciers – and a slightly updated version, in terms of calibration, which was not an official release, for the global runs (see Sect. ). OGGM is an open-source modeling framework written in Python. It was developed to provide a catchment- to global-scale, modular numerical modeling framework for various study setups of glacier evolution on multiple scales while accounting for glacier geometry and ice dynamics. and the continuously expanding and adapting model documentation at http://docs.oggm.org (last access: 12 March 2025​​​​​​​) explain the model in detail and can be referred to for an in-depth model description. The current study focuses on the application of OGGM's mass balance modeling capabilities rather than the glacier flow.

For each component of our study, we carry out a separate model calibration. It must be noted that for the purpose of our study, the performance of the mass balance model itself is secondary, since only the change in performance when using various forcing products is investigated. The calibrated parameters are held constant for each forcing product, allowing us to assess the impact of the forcing strategy alone, not the impact of calibration.

Due to the importance of the initial state of the climate system (atmosphere and ocean) for decadal prediction, forecast skill often declines with lead time . Lead time here adheres to the definition by the American Meteorological Society: “The length of time between the issuance of a forecast and the occurrence of the phenomena that were predicted”. To assess the lead-time-based skill in the context of our study, we create lead-time-based ensemble means of results in the decadal re-forecast experiment to validate against observations. This results in nine time series of mass balances, 2000–2020, with input from lead times 1–9, respectively. Due to the clipping to hydrological years to match the WGMS measurements, lead time 0 does not exist in component 1. So for a decadal re-forecast initialized in 1990 (always in November), the first full year of simulated values is for the year 1992. In component 2, the first full year of simulated values would be 1991. For the persistence experiment, we also create lead-time-based time series. Here, lead time refers to the forecast length, which is the same time period until the start of the forecasts. An example of lead time 2 persistence forecast would be the forecast period 2000–2001 being the same as the year 1998–1999. In the case of our study period 2000–2020, the lead time 1 persistence forecast uses temperature and precipitation from the time period 1999–2019, and lead time 9 therefore uses values from 1991–2011 for the forecast. In our decadal re-forecast experiment, we create ensemble means of results as they would be utilized in practice. As note, many assessments of re-forecast skill are likely overestimated, as the re-forecasts are informed by observations over the period assessed that would not be available to real forecasts. In order to avoid this as much as possible, we only assess a period that was not used in the drift correction (see Sect. ) and use only lead times that would be available at the beginning of the forecast period. This results in time series for each glacier and each full decade in the period 2000–2020. For an example decade, say 2000–2010, the ensemble mean of results consists of information from all re-forecasts initialized in 1990–2000. This means the ensemble size decreases over time, with only lead time 9 information being available in 2009. Decreasing ensemble size at longer lead times typically increases forecast uncertainty, potentially affecting skill metrics slightly. We use information from all lead times available to maximize ensemble size and, in turn, skill . This approach again reiterates the fact that decadal re-forecasts are multi-annual, rather than strictly for 10 years. In order to compare persistence as it would be used in practice, for decadal mean and cumulative mass balance forecasting, persistence forecasts at lead time 9 are applied.

The mass balance model in OGGM requires monthly climate in the form of reference height (2 m) air temperature and precipitation time series. The default baseline climate forcing, which we use for our persistence experiment, is the gridded Climatic Research Unit Time Series (CRU TS v4.01; ). This coarse (0.5°) dataset is then interpolated to a higher-resolution climatology (CRU CL v2.0 at 10^′ resolution; ) following the anomaly mapping approach described in to acquire climate time series with elevation data, which is not an attribute in the CRU TS. For each glacier, the monthly time series of temperature and precipitation are taken from the grid point closest to the glacier. Temperature is converted using an elevation-based lapse rate of 6.5 K km⁻¹, and precipitation is corrected using the default correction factor of pf=2.5 . While the CRU dataset constitutes our OGGM baseline climate for calibration, OGGM can also be supplied with GCM output that is bias-corrected to the baseline climate, as we do in the decadal re-forecast and GCM historical experiments.

In the decadal re-forecast experiment, OGGM is driven with a multi-model, multi-member retrospective ensemble of monthly temperature and precipitation re-forecasts from the DCPP component A, which provides re-forecasts. We use decadal realizations from the “Flexible Global Ocean-Atmosphere-Land System Model” (FGOALS; ), the “Norwegian Climate Prediction Model” (NorCPM; ) and the “Model for Interdisciplinary Research on Climate version 6” (MIROC6; ). We use the r1i1p1f1-r1i1p1f10 realization of all models where available. The DCPP-A decadal re-forecasts are initialized each year in the period 1960–2010, the first forecast year being 1961. The processing of the decadal data is explained below, in Sect. .

In the GCM historical experiment, we drive OGGM with temperature and precipitation from the historical iteration and projections of the same three GCMs, obtained from CMIP6 archived model output: FGOALS, NorCPM and MIROC6 (see Table ). The end of the historical simulation is in 2014, and data from 2015–2020 are provided by projection runs, leading to 11 full decades in the period 2000–2020. As the number of available data becomes larger because of the different shared socio-economic pathways (SSPs), the choice is to select certain SSPs or to introduce a discrepancy in ensemble size if using all CMIP6 SSPs. We realize that neither option facilitates perfect comparison with the decadal re-forecast and persistence experiment. However, the benefit of comparison with projections outweighs these concerns, as initialized forecast vs. projections represents the most realistic future use case. To preserve ensemble size, SSP2-4.5 was chosen as the projection for comparison, as it represents a medium pathway of future greenhouse gas emissions. From FGOALS runs, not enough SSP2-4.5 realizations were available at the time of the study, so SSP1-2.6, SSP2-4.5 and SSP5-8.5 time series were used. As these scenarios do not diverge significantly during 2015–2020, we still consider these results comparable.

In the pre-processing for this experiment, the time series are bias-corrected and downscaled to the glacier scale using a variation of the delta method . Here, we take GCM anomalies relative to the 1961–1990 GCM mean for temperature and apply these to the CRU TS 4.01 1961–1990 means. The correction is applied monthly and ensures that the mean and standard deviation are preserved during the bias correction period for temperature. Precipitation is corrected with a multiplicative factor and preserves only the mean. This is the standard method of processing GCM data for projection studies (e.g., ) and is the reason we use it as an evaluation procedure for the decadal re-forecasts.

In order to drive OGGM with the re-forecasts, each member is downscaled to the glacier scale using a statistical method applied with baseline climate CRU . Decadal re-forecasts experience a bias referred to as drift because they start from an initialized state constrained by observations, which is inconsistent with the model's dynamics . The drift is lead time dependent because, with time progressing, the model drifts away more from the initial state towards a state more consistent with the model's climatology, which can lead to significant error . The re-forecasts have to be bias-corrected to counter this error. Our correction adheres to recommendations in , who recommend an overarching bias correction method, regardless of the initialization type of the forecast. The reasons behind these recommendations are discussed in depth in, for example, , and . We assume that the bias contained in each member is model dependent and lead time dependent. Because of the assumption that the bias is different at and dependent on each lead time, subtracting a mean drift per member would lead to over-compensation at some lead times and residual drift at others. For this reason, we create lead-time-based climatologies per model, meaning one climatology over 1971–2000 which contains all lead times 1 year from the re-forecasts, one which contains all lead times 2 years from the re-forecasts and so on. These are then used to create anomalies relative to the baseline climate. For each model, each member is bias-corrected according to 2dt=Tt′‾-CRUcl‾,3Tm,t,y′=Tm,t,y-dt, in which dt is the average model bias or drift at each lead time t, calculated relative to the baseline climate input CRU. CRU_cl is the CRU monthly climatology averaged over 1971–2000 . Tt′ is the model climatology at lead time t calculated by averaging the lead time t re-forecasts of all ensemble members of one model falling into the period 1971–2000. Tm,t,y is the raw re-forecast, of member m at lead time t for year y. Tm,t,y′ is the bias-corrected re-forecast of member m at lead time t for year y.

Lead-time-dependent bias correction is a fundamental step used in decadal forecasting, as is mean bias correction in future projections for impact modeling. Because the aim of our study is to compare the standard methodologies commonly applied in the respective fields, the GCM historical data are processed as they would typically be in glacier modeling (e.g., ; and many more), and the re-forecasts are processed according to the recommendations mentioned above. It must be added that the drift correction, following the lead time (the length of time between the issuance of a forecast and the occurrence of the phenomena that were predicted), does not apply to the GCM historical experiment, where we have only one simulation per realization.

We first focus on individual years, assessing how skill changes with lead time. To quantify model skill, we calculate the mean absolute error (MAE) and the Pearson correlation coefficient (r) for each lead-time-based ensemble mean, with the results displayed in Fig. . The decadal re-forecast experiment shows consistent performance, with an MAE of 0.64 m w.e. at lead time 1 and a slightly lower value of 0.63 m w.e. at lead time 4, before increasing slightly to 0.65 m w.e. by lead time 9. Pearson correlation coefficients decrease from 0.14 at lead time 1 to 0.07 at lead time 9, reflecting the inherent difficulty of simulating individual annual mass balance values. For the persistence experiment, MAE increases from 0.69 m w.e. at lead time 1 to 0.72 m w.e. at lead time 9, with greater variability in correlation compared to the decadal re-forecast forcing. By contrast, results from the GCM historical experiment, which does not depend on lead time, show constant skill. As there is no application of lead time to the GCM historical experiment, its results (MAE = 0.66 m w.e., r=0.01) are plotted as a constant to compare the skill score magnitude. Overall, skill is low when simulating individual years, which is expected and in line with other studies using OGGM for this set of reference glaciers. One example is , who yield an MAE of 0.60 m w.e. with baseline climate CRU over the time period from 1917 until the RGI outline date per glacier (often early 2000s). Simulating single-year mass balances is not the focus of this study; however, the results show that already on the single-year level, forcing OGGM with decadal re-forecasts outperforms the persistence and the GCM historical experiments, which both show higher errors and lower correlations.

Next, we compare mean and cumulative mass balance over full decades, as illustrated in Fig.  and Table . To quantify model skill, we look at the mean error (ME), which is the average difference between observed and simulated values (sometimes called “mean bias”); the mean absolute error (MAE); and the Pearson correlation coefficient. In the time period 2000–2020, we have 11 full decades for which the mean and cumulative mass balance are calculated per glacier. The full decades, which have significant overlap, are still compared separately and depicted in Fig. 2 to show how the choice of decade can considerably impact skill statistics. For example, in the decadal re-forecast experiment, the decade 2001–2011 has a mean model error of -0.022 m w.e., whereas the decade 2002–2012 has a mean model error of 0.11 m w.e.

Observed mean mass balance for the decade 2000–2010 is -0.79 m w.e. Simulations using reanalysis data (CRU), which provide a benchmark for comparison, yield a mean error (ME) of -0.037 m w.e. and an MAE of 0.23 m w.e. Decadal re-forecasts produce comparable results, with an ME of 0.091 m w.e. and an MAE of 0.27 m w.e., while persistence forecasts display a larger ME of -0.16 m w.e. and an MAE of 0.39 m w.e. The GCM historical experiment shows slightly better performance than persistence, with an ME of -0.0059 m w.e. and an MAE of 0.29 m w.e. Correlation coefficients are moderate to high, with decadal re-forecasts achieving the highest correlation (r=0.64), followed by GCM historical (r=0.61) and persistence (r=0.58).

In terms of cumulative decadal mass balance, error patterns are similar. Decadal re-forecasts achieve an ME of -0.39 m w.e. and an MAE of 1.33 m w.e., while persistence experiments have an ME of -0.96 m w.e. and an MAE of 1.62 m w.e., reflecting the difficulty of using persistence forecasts for warming-sensitive variables like glacier mass balance. GCM historical simulations show comparable results to decadal re-forecasts, with an ME of -0.27 m w.e. and an MAE of 1.58 m w.e.

To gauge the statistical significance of the differences between experiments, we carry out a two-tailed t test (significance level 0.05) on the set of individual glaciers. The samples for these tests are the 279 glacier-specific values of decadal mean and cumulative mass balance for each forcing type. For decadal re-forecasts and GCM historical experiments, these values are ensemble means, whereas for the persistence forecast, a single-member simulation is used. For the decadal mean mass balance, the difference between the decadal re-forecast and persistence experiment is statistically significant, as is the difference between the persistence and GCM historical experiment. However, there is no significant difference between the decadal re-forecast and GCM historical experiments. For the cumulative mean mass balance, there are no statistically significant differences amongst the experiments. We also perform a binomial test, assessing improved skill by specifically evaluating reductions in mean absolute error for the decadal re-forecast relative to persistence or historical forcing. This shows that out of the 279 glaciers we analyze, 174 showed improved skill using decadal re-forecasts for decadal mean mass balance and 186 showed improved skill for cumulative mass balance. Using a binomial significance, this suggests that the overall improvement from using decadal re-forecasts is significant at the 5 % level. We note that the t test and binomial test can yield different interpretations because they test different aspects of statistical significance. The t test compares the mean differences between forecast methods across the entire set of glaciers, assessing whether differences in the average performance are statistically distinguishable given the spread in the dataset. By contrast, the binomial test assesses significance based only on the count of glaciers showing improved performance (in terms of lower mean absolute error) when comparing one forecast method directly with another, irrespective of the magnitude of improvement.

Thus, while in some cases, the t test does not indicate a statistically significant difference, due to variability across glaciers and the relatively small magnitude of improvement on average, the binomial test can indicate statistical significance simply because more glaciers improve under one approach compared to another than would be expected by chance alone. Both tests provide complementary perspectives: the t test assesses the robustness of the average improvement magnitude across glaciers, whereas the binomial test evaluates consistency in improvement across individual glaciers.

The persistence experiment shows a notable overestimation of mass balance, particularly at longer lead times. This is evident in Fig. , where persistence forecasts systematically deviate from the observed values due to a lag in warming trends. This highlights the limitations of persistence-based methods for forecasting glacier mass balance on decadal timescales, where warming trends have significant influence, as is the case with glacier mass balance.

The skill differences between the experiments are further quantified in Table . Here for the reference glaciers, forcing with decadal re-forecasts outperforms forcing with persistence forecasts or historical GCM data, even though the absolute improvements in skill are small and statistically not significant between the decadal re-forecast and GCM historical experiments, for individual glaciers. Pearson correlation coefficients between simulated and observed values are generally in the same range for all three experiments, with the highest correlations for the decadal re-forecast experiment. All Pearson correlations are moderate – up to 0.64 for the decadal re-forecast experiment – for mean decadal mass balance and high – up to 0.85 – for cumulative decadal mass balance. Comparison these correlations to the low degree of correlation when simulating individual years emphasizes how the skill of our experiments lies primarily in simulating multi-annual averaged or cumulative mass balances, filtering out inter-annual noise. This is in line with similar approaches, where skill is found through the integration of fluxes over time, such as in seasonal snow accumulation .

We also note here that in the decadal re-forecast experiment, the multi-model ensemble mean of results yields higher skill than single-model ensembles. Comparing the multi-model ensemble mean of results to observations of mean decadal mass balance vs. single-model ensemble means of results (N=3) compared to observations yields a decrease in MAE of 11 % (vs. FGOALS), 8 % (vs. NorCPM) and 6 % (vs. MIROC6), respectively. This aligns with our expectations from the literature due to an increase in ensemble size and associated error cancellation and the separate forecast systems adding signal to the multi-model ensemble . Other studies applying multi-model ensembles in impact models, such as , also come to the conclusion that a multi-model ensemble generally gives the best performance, which is why we do not explore single-model ensemble performance further.

For all global land-terminating glaciers, we compare results of mean decadal mass balance in all experiments. To assess skill, 2000–2010 and 2010–2020 results are validated against the global geodetic mass balance dataset by . Because the time period 2000–2020 is covered by both validation datasets, a separate comparison of the two is provided in Sect. .

Comparing 2000–2010 decadal re-forecast skill scores to the persistence and GCM historical experiments, improvement in skill is slight (Table ). Over the decade 2000–2010, decadal re-forecasts yield a 23 % and 18 % reduction in mean absolute error (MAE) relative to persistence and GCM historical forcing, respectively. Over this period, the MAE for the decadal re-forecast experiment was 0.28 m w.e., compared to 0.35 m w.e. for persistence forecasts and 0.33 m w.e. for the GCM historical experiment. The Pearson correlation coefficients similarly favor re-forecasts, potentially indicating higher overall skill on a global scale. Performing a two-tailed t test (significance level 0.05) on the collection of glaciers shows that while the difference between the persistence experiment and the two other experiments is significant, the difference between the decadal re-forecast and GCM historical experiments is not.

Between the different glaciated regions of the world – RGI regions (see Fig. ) – there is considerable variation in skill. Indicated in the histograms in Fig.  are the regional mean absolute errors for 2000–2010, which vary considerably. The decadal re-forecast experiment achieves good agreement (regional mean difference ≤ 0.1 m w.e.) in 10 of 18 regions, reasonable agreement (difference 0.1–0.3 m w.e.) in 7 regions and mediocre agreement (difference ≥ 0.3 m w.e.) in 1 region. Variability in MAE is larger for the persistence and GCM historical experiments, with notable overestimation of mass balance due to lagging warming trends in persistence forecasts. The persistence experiment generally performs worse for regions sensitive to rapid warming, such as Greenland and Iceland, highlighting the limitations of static forecasts in a warming climate. Overall, the differences between experiments all lie within 1 standard deviation of the mean, for the simulations as well as within the mean error of observations . All 2000–2010 observed values and their uncertainty, as well as all simulated values per experiment, are included in Table .

The 2010–2020 results are slightly different than for the 2000–2010 period in that the persistence experiment outperforms the decadal re-forecast experiment in terms of the overall skill score. The mean absolute error for the decadal re-forecast experiment is 0.28, while persistence mean absolute error is 0.24, with Pearson correlation coefficients of 0.69 and 0.77, respectively. In terms of the goodness of fit per region however, the decadal re-forecast experiment slightly outperforms the persistence experiment, with 11 of 18 regions showing a good fit (defined as a difference between regional means ≤ 0.1 m w.e.). Of the 18 regions, 5 show a reasonable fit (difference between regional means 0.1–0.3 m w.e.) and 2 show a mediocre fit (difference between regional means ≥ 0.3 m w.e.). The persistence experiment shows 8 regions with good fit, 8 regions with reasonable fit and two regions with mediocre fit. The exact goodness-of-fit numbers, including the observations and observational uncertainty, can be found in Table .

The fact that the persistence experiment performs markedly better for this decade than for the previous one, while skill scores and goodness of fit are similar for the decadal re-forecast experiment, lies in the calibration. As explained in Sect. , the calibration and validation periods are the same. Because of the nature of persistence forecasts, the forcing data for the 2000–2010 period originated from 1990–2000 and were not used in calibration. For the period 2010–2020, however, both the climate data for the persistence forecast (2000–2010) and the forecasted decade were part of the calibration, resulting in a bias of 0 for the full time period of 2000–2020. To assess the effect of this, we run another persistence simulation, this time with a model only calibrated for the period 2000–2010, leaving 2010–2020 for validation. This is also the scenario that would occur when using persistence to forecast 2020–2030: the model is calibrated for the decade prior to the forecasted one. This leads to a markedly worse score for the persistence forecast, with a mean absolute error of 0.38 ± 0.36 m w.e. and a Pearson correlation coefficient of 0.26, indicating low correlation. For the sake of consistency, keeping calibration the same for all experiments, the persistence experiment results presented in Table  are from the simulation with the original calibration.

Finally, this study clearly benefits from the availability of two separate datasets of observed mass balance for the same 2000–2020 time period. This allows for more critical assessment not only of model results, but also of uncertainty within observations. The use of both datasets here warrants a comparison between overlapping observations. For the period 2000–2010, we calculate the mean mass balance for all glaciers where the WGMS dataset has full observations throughout the decade (N=90). For this subset of 90 glaciers, we find a mean bias/difference of -0.049 m w.e. and an absolute bias/difference of 0.23 m w.e. between the WGMS and geodetic mass balance data. For the period 2010–2020 we have 100 glaciers with uninterrupted mass balance coverage from the WGMS dataset. Comparing to the mean mass balances yields a mean bias/difference of -0.15 m w.e. and an absolute bias/difference of 0.32 m w.e. For the full time period of 2000–2020, a subset of 67 glaciers has observations throughout the full time period. The mean bias/difference here is -0.11 m w.e., and the absolute bias/difference is 0.23 m w.e. These results are of the same magnitude of error as that which we observe when comparing our decadal re-forecast simulation results to observations, as well as the uncertainties associated with the data (see Tables  and ). This not only reinforces the need for caution when interpreting observations but also confirms the satisfactory quality of the simulated results.

On the whole, the skill displayed in the decadal re-forecast experiment is comparable to or slightly better than in the other experiments. Regional differences in skill (“goodness of fit” in the global component) in the re-forecast experiment likely stem from differences in re-forecast quality. This means the degree of correspondence between observed and simulated temperature and precipitation. We refer to for a comprehensive analysis of the quality of the re-forecasts used here. Their results show generally high skill for DCPP forecasts of temperature, especially over land masses. For precipitation, however, skill is limited in several regions, including central Europe (region 11) and Western Canada/US (region 2), which also show the least mass balance skill out of all regions (see Tables  and ). Good precipitation skill is observed for northern Europe and Central Asia, in line with our yielded “good fit” results for Svalbard and Jan Mayen (region 7) and Central Asia (region 13) (Tables  and ). find the quality of decadal re-forecasts of temperature to be higher than that of historical temperature simulations for multiple regions, while added value is smaller when simulating temperature. With accurate representation of precipitation being essential for mass balance modeling, it is likely that precipitation forecasts are a limiting factor in seeing significant improvement when simulating near-term mass balance with decadal re-forecasts as forcing, over persistence or historical/projection data. Additionally, addressing precipitation in a more complex calibration and downscaling approach may decrease uncertainty in this area. This is to be kept in mind when designing future studies, especially if these include regions where predictive skill for precipitation is low.

The primary source of decadal (re-)forecast skill, beyond free-running simulations, is initialization. The main benefit of initialized decadal forecasts is that the initialization allows them to capture both the response to external forcing and the phase of the internal variability in the climate system. For example, initialized re-forecasts better capture Atlantic multi-decadal variability than GCM historical simulations in a study by . note that improvements from initialization generally take place in regions where the uninitialized simulations already have some skill. This can also be seen in the similar skill patterns between the GCM historical and decadal re-forecast experiments in Tables  and . Initialized forecasts better represent internal climate variability due to accurate initial conditions . This enhances their predictive skill for timescales of 1–10 years compared to uninitialized projections. Initialized decadal forecasts also provide a more constant uncertainty over time than uninitialized projects, whose uncertainty increases significantly with lead time . Future improvements in initialization, e.g., regarding the initialization of the North Atlantic Oscillation , may therefore still offer potential for reducing uncertainties in near-term glacier modeling, even if the current benefits are limited. In addition, decadal forecasts outperform uninitialized projections in representing regional climate variability, especially in temperature and precipitation, which are crucial for accurately modeling glacier mass balance. As studies such as describe, climate variability often exacerbates the impact of climate change on vulnerable communities. In a glacier context, this could mean, for example, above-average melt events impacting downstream communities, so accurate prediction is essential. Finally, note in their assessment of forcing with decadal re-forecasts vs. uninitialized projections that there is an established demand for communicating both the likely values and the uncertainty in a forecast made with an impact model . When the effort is made to minimize this uncertainty and make a forecast that is as precise as possible, forcing with initialized forecasts is likely preferable on the decadal scale. Despite these advantages, decadal forecasts are still in development, and the continuation of projects such as the DCPP contribution to CMIP6 is essential to ensure their operational use.

This study also reveals arguments for applying decadal (re-)forecasts over persistence or uninitialized projections in future near-term glacier modeling studies. Especially warming and glacier mass loss accelerating support an argument for forcing near-term simulations with initialized forecasts over persistence forecasts, which lack the warming trend over the simulation period. The choice of initialized forecast forcing over uninitialized projections stems mainly from the probabilistic context: projections, especially as pathway differences increase over time, are inherently more uncertain than a forecast initialized at the beginning of the forecast period. Statistically, we observe no significant difference between the decadal re-forecast and GCM historical experiment per individual glacier (Sect. ). Binomial tests however show a general improvement when forcing OGGM with decadal re-forecasts. Also, note that significance tests, such as those applied here, often underestimate the improvement from initialization because there is a significant overlap of skill in both experiments (e.g., simulating the global warming trend). state, “This common signal introduces a bias that is not taken into account in standard significance tests and diminishes their power .” Therefore, the small improvements in the skill statistics of the decadal re-forecast experiment over the other experiments may indicate a larger benefit of forcing glacier models with decadal re-forecasts than is evident in Student's t test. This indicates that even modest skill increases from initialization may be reliably attributed to improved forecast initialization rather than to random chance.