Most services assessed each avalanche problem individually and assigned it a corresponding danger level. However, some issued a single overarching danger level despite assessing factors per problem (e.g., BAY in first year), grouped problems into broader categories (e.g., SWI separated dry-snow avalanche problems from wet- or gliding snow avalanche problems), or assessed the factors without assigning them to a specific problem (e.g., SCO). In certain services (e.g., SWE), no factor assessments were made when no avalanche problem was identified, a situation commonly observed for danger level 1 (low). Others documented such situations using the label no distinct avalanche problem (e.g., SVK, SWI).

Most services had integrated the EAWS-Matrix into their operational workflows, either using it to directly link factor assessments to a suggested danger level or as a reference framework. A notable exception was Switzerland (SWI), where forecasters assessed factors and danger levels independently, with the latter determined during group discussions rather than derived from the Matrix .

The majority of services used the EAWS-defined ordinal classes for estimating the three Matrix input factors (Table ), though some used North American terminology (as defined in the CMAH; ) for assessing stability and frequency (e.g., SCO, SWE). These were subsequently mapped to EAWS-classes based on . In Livigno (LIV), the Matrix was applied operationally, but the published forecasts followed North American terminology for describing the sensitivity to triggers. Additionally, some services implemented tools that allowed forecasters to express tendencies within a class. These included services using the ALBINA forecasting software platform , as used for instance in BOZ, TIR, and TRE, as well as the Swiss forecasting software . In ALBINA, tendencies within classes can be expressed via sliders allowing near-continuous values between 0 and 100 for snowpack stability, frequency of the lowest snowpack stability class, and avalanche size (Fig. a). Class boundaries and underlying numerical values allow unambiguous conversion into the EAWS classes, for example, poor corresponds to values from 50 to 74, and very poor to values from 75 to 100. In Switzerland, forecasters make distinctions within classes using modifiers such as minus (−), neutral (=), or plus (+) (e.g., poor−, poor=, poor+), or selected intermediate labels straddling two adjacent classes (e.g., fair/poor) (Fig. b). In SWI, factor assessments are used for internal purposes only, in ALBINA factors are published. For the purpose of this study, modifier-based entries (e.g., poor+) were aggregated into their primary class (poor), and intermediate labels (e.g., fair/poor) were randomly assigned to either the lower (fair) or higher (poor) class.

In most warning services, a single forecaster was responsible for the forecast for either the entire domain or a specific part of the domain containing one or several micro-regions (e.g., in NOR or SCO), sometimes supported by a second forecaster for review (e.g. TIR). In contrast, SWI followed a fundamentally different approach: the forecasting process always involved at least two (but up to four) forecasters who independently prepared full forecast drafts for the entire forecast domain (referred to as suggestions). These suggestions were then consolidated in a group discussion prior to publication. For this study, we derived the median factor assessment from the individual suggestions and linked these to the issued danger level resulting from the group consensus.

To harmonize data across services, we applied the following procedure: for each day and micro-region, we selected the decisive avalanche problem, typically the first listed in the bulletin or the one associated with the highest danger level. If neither criterion was available, the first entry was retained. This step was performed separately for dry-snow avalanche problems and for wet-snow or gliding-snow avalanche problems. After selecting the decisive problem, we retained unique entries defined by the combination of date, issuing warning service and/or forecaster, avalanche problem, danger level, and the associated Matrix factors. If the same combination appeared in multiple micro-regions on the same day within the domain of a service, only one instance was retained. This approach was feasible for all services except NOR and MMT, where the data structure did not permit such filtering.

Comparing the issued danger level with the Matrix-suggested danger level showed that nearly all warning services occasionally deviated from the Matrix (median Pdisagree = 4 %; Fig. a). The highest disagreement rates were observed in Andorra (AND), Scotland (SCO), and Switzerland (SWI), where deviations occurred in 36 %–39 % of cases. Piemonte (PIE), Livigno (LIV), and Sweden (SWE) also showed comparably frequent deviations (10 %–21 %), while in half of the warning services, deviations were relatively rare (Pdisagree < 4 %).

Figure  illustrates how the issued danger levels for dry-snow avalanche problems were assigned to combinations of stability, frequency, and avalanche size. Results are shown for the groups introduced in Fig. a and Sect. . As expected, warning services with high compliance with the Matrix (group compl-hi) generally assigned the Matrix-suggested danger level. In these services, alternations between the two danger levels shown in the Matrix were rare: the secondary danger level was only used in three factor combinations (fair-a few-size 1, poor-some-size 2, and very poor-some-size 3) in more than 1 % of cases. In contrast, forecasters in services with low Matrix compliance (group compl-lo, Pdisagree ≥ 7 %) and presumably greater heterogeneity in how the Matrix is integrated into the forecasting process, showed a much broader distribution of danger levels across Matrix cells and, consequently, greater overlap in the use of the same factor combinations for different danger levels.

Two factor combinations, highlighted in Figure , stood out for both groups: poor-some-size 2 and very poor-some-size 3. These combinations were among those where deviations from the Matrix-suggested danger level were more frequent, even among forecasters with high Matrix compliance. According to the Matrix (Fig. ), the suggested danger level for poor-some-size 2 is 2 (moderate), with 3 (considerable) as the second option. Warning services with low Matrix compliance used this factor combination equally often to describe danger levels 3 (considerable) (26 % of level 3 cases) as 2 (moderate) (27 %) (Fig. b). In contrast, warning services with high Matrix compliance rarely used the poor-some-size 2 cell when choosing 3 (considerable). Instead, they typically selected neighbouring Matrix cells that differed in one factor, either very poor stability rather than poor, many rather than some, or size 3 rather than size 2, when choosing 3 (considerable). Nonetheless, even in this high compliance group, 7 % of all 3 (considerable) assessments fell into the poor-some-size 2 combination. A second notable difference involved the factor combination very poor-some-size 3, where the Matrix suggests 3 (considerable) and 4 (high) as the secondary level. Services with low Matrix compliance used this combination for 4 (high) in 25 % of cases, while it was less frequently used for 3 (considerable) (10 %). In contrast, warning services with high Matrix compliance used this combination in 11 % of cases for 3 (considerable), and only 3 % of cases for 4 (high). These two factor combinations appear to represent key transition zones between these danger levels, where danger level assignment differs depending on the degree of Matrix compliance.

Despite these differences, both groups shared several patterns. For 1 (low), the most frequently used combinations were fair-a few-size 1 or poor-a few-size 1, for 2 (moderate), the typical combinations were poor-some-size 2 and poor-a few-size 2. And when issuing 4 (high), both groups predominantly used the factor combination very poor-many-size 3.

Although the Matrix required forecasters to classify conditions into a small number of discrete categories, the underlying processes are inherently continuous. In BOZ, TIR, and TRE (using the ALBINA software), as well as in SWI, forecasters were able to assess the Matrix factors with finer granularity (Fig. ). This allowed a closer examination of how subtle differences in factor assessments translated into differences in the issued danger level. We focused on the combination poor-some-size 2, the most frequently used Matrix cell (Fig. ), which also showed considerable variation in the issued danger level (Fig. ), either 2 (moderate), as suggested by the Matrix, or 3 (considerable).

For the three warning services BOZ, TIR, TRE (using ALBINA) and for SWI separately, Fig.  shows how the issued danger levels varied within this cell. Panels (a) and (b) display the distribution of danger levels as a function of snowpack stability and frequency, while avalanche size was fixed to size 2. Panels (c) and (d) focus on cases where stability was classified as poor, showing how danger levels varied as a function of frequency and size, corresponding directly to the Matrix cell shown in Fig. .

In SWI, the issued danger levels were either 2 (moderate) (42 %) or 3 (considerable) (57 %); 1 % (12) of the 964 cases were assigned to level 1 (low). In contrast, the ALBINA services issued level 2 in 75 % and level 3 in 25 % of 282 cases. Despite this difference in the relative preference for level 2 versus level 3, similar tendencies emerged across groups. Slider positions leaning toward very poor stability and many locations were more often associated with level 3 (considerable) (Fig. a, b), whereas shifts toward fair stability and a few locations tended to result in level 2 (moderate). The services BOZ, TIR, TRE showed a pronounced diagonal pattern in slider use, highlighting the interplay between stability and frequency (Fig. a). In SWI, the proportion of level 2 (moderate) assignments decreased systematically with decreasing stability and increasing frequency (Fig. b). A similar trend was observed for the combination of frequency and size (Fig. c, d): danger level 3 (considerable) was more often given when both factors tended towards higher categories. The CART predictions shown in the figure backgrounds closely mirrored these tendencies. While the prediction surfaces were generally well defined, some scatter was present (notably in Fig. a).

Figure b illustrates the use of very poor stability to describe wet-snow or gliding snow avalanche problems and the proportion of disagreements between the issued danger level and the Matrix-suggested danger level. While forecasters in several services (notably SWI, TIR, and BAY) predominantly assessed wet-snow and gliding snow avalanche problems using very poor stability, a few services never used this stability class. This was striking, given that wet-snow and gliding snow avalanches are typically associated with natural avalanche release , and are thus conceptually linked to very poor stability (Table , see also Tables A2 and A3 in ). This divergence in the use of the stability classes was also reflected in the degree of disagreement with the Matrix-suggested danger level. Services that used very poor stability more frequently also tended to show greater disagreement, and vice versa (Spearman ρ = 0.38, p < 0.1). Notable exceptions included BAY, where stability was described as very poor in most situations (92 %) while high agreement with the Matrix was maintained (99 %), and Piemonte (PIE), where Pdisagree was high (25 %) even though stability was essentially never assessed as very poor (1 %). In the case of BAY, forecasters typically assigned smaller avalanche sizes to the same danger levels compared to, for instance, SWI and TIR, who showed much lower agreement with the Matrix-suggested danger levels. For example, at 1 (low), 93 % of BAY cases were size 1, compared to 37 % in SWI and 13 % in TIR. Overall, for wet-snow and gliding snow problems, the median disagreement rate Pdisagree was 7 %, slightly higher than the 4 % observed for dry-snow avalanche problems.

These differences in stability assessments and levels of compliance with the Matrix-suggested danger level carried over into the final danger level assignments, leading to a broad range of factor combinations and considerable variation in how the same danger level was described. Splitting the warning services into three groups (Sect. , Fig. b) based on their use of very poor stability, and focusing on the two groups that either used this class infrequently (group wet-P, Pstab:verypoor < 0.25) or often (group wet-VP, Pstab:verypoor ≥ 0.56), revealed substantial differences in Matrix cell usage (Fig. ). Group wet-P forecasters most often used poor and fair stability across danger levels 1 (low) to 3 (considerable). Even for 3 (considerable), 62 % of cases involved poor stability. In contrast, group wet-VP forecasters predominantly used the very poor stability panel, even when describing 1 (low) (66 % of cases). Furthermore, group wet-P forecasters did not use danger level 4 (high) at all when assessing wet- or gliding snow problems. As a result, similarities between these groups related primarily to avalanche size, which increased with rising danger level in both groups, from size 1 at 1 (low), to size 2 at 2 (moderate), and size 3 at 3 (considerable) in group wet-P and size 2 to size 3 in group wet-VP.

Our analyses showed that most combinations of snowpack stability, frequency, and avalanche size were consistently linked to a single danger level. This was particularly pronounced for danger levels 1 (low), 2 (moderate), and 4 (high), indicating that the Matrix provides a robust and interpretable structure for operational use. Notably, even though about half the Matrix cells show a secondary danger level (D2, see Fig. ), most factor combinations were almost always used for a single consistent danger level in practice, even by services with comparatively low Matrix compliance. This suggests a broad consensus on the danger level for these factor combinations and indicates that such cells could potentially be simplified.

In contrast, a small number of cells, most notably poor-some-size 2 and very poor-some-size 3, functioned as transition zones between adjacent danger levels. These cells showed frequent overlap in danger level assignment and played different roles across forecaster groups. For danger levels 3 (considerable) and 4 (high), respectively, they were among the most frequently used cells by services with low Matrix compliance (Fig. b), even though the Matrix indicates these danger levels only as second options. The reasons for this discrepancy remain speculative. This may be due to differences in how factor classes are interpreted, particularly the frequency categories . Alternatively, it may reflect a tendency among more Matrix-compliant services to avoid cells that do not yield the desired Matrix-suggested danger level. Notably, even services with high Matrix-compliance occasionally selected these cells issuing the second danger level suggested in the Matrix, underscoring their role as boundary regions between adjacent danger levels.

Beyond the dominant and transitional cells, some Matrix cells remained rarely used across all services (Figs.  and ). This lack of empirical support reduces confidence in the danger levels suggested for these cells and highlights that these assignments still rely solely on expert elicitation during Matrix development .

Several warning services applied a finer-granularity when assessing the Matrix input factors, reflecting a fundamental tension between simplicity – few, well-defined classes – and nuance – expressed through finer-grained, ordinal rankings within otherwise discrete classes. On the one hand, the Matrix relies on a limited number of discrete classes, a design choice that aligns with evidence that humans can reliably assess only a small number of categories (e.g., ). On the other hand, requiring forecasters to commit early to a single class is analogous to rounding intermediate results, which can discard relevant information and introduce discontinuities in subsequent decision steps. Such rounding effects are particularly relevant when assessments lie near the boundary between two neighbouring classes; expressing these tendencies through sub-classes would preserve this information for the final danger level decision.

At the same time, humans are comparatively good at making relative judgments, such as ranking conditions within an absolute class (e.g., ). Combining absolute classifications with relative assessments by first selecting a discrete class and then indicating tendencies within that class therefore represents a promising way to preserve nuance while remaining within the overall structure of the Matrix. This is illustrated by the analysis of finer-granularity factor assessments for the frequently used factor combination poor-some-size 2 (Sect. ). While this cell was predominantly associated with danger level 3 (considerable) in SWI and with level 2 (moderate) in BOZ, TIR, and TRE (Fig. ), tendencies within the cell toward either danger level were broadly comparable across services. This convergence occurred despite differences in how relative positioning within the cell was implemented (Fig. ) and regardless of whether the Matrix was used for danger level determination.

Despite these procedural differences, the observed agreement provides evidence of convergent validity : independent approaches aimed at assessing the same underlying concept yielded broadly similar outcomes. Even in the absence of external reference data, this supports the feasibility of a harmonized interpretation across warning services. While finer granularity helps preserve variation within coarse classes, the appropriate level of resolution remains a subject for discussion. Evidence from parallel forecasting in SWI indicates that reasonably reliable estimates are achievable even with higher-resolved absolute–relative scales . Together, this suggests that combining absolute and relative assessments can capture meaningful tendencies while remaining cognitively manageable and compatible with the Matrix framework.

We distinguish between Matrix compliance (agreement with the danger level suggested by the Matrix), consistency (the degree to which the same factor combination leads to the same danger level), and accuracy, the latter of which cannot be evaluated in the absence of external reference data. When viewed through the lens of Matrix compliance, differences in how warning services applied the Matrix provide insight into both the consistency of danger level assignment and its potential limitations.

The stratified analyses (Sect. ) confirmed that Matrix compliance influenced Matrix usage. Services, which disagreed more frequently with the Matrix-suggested danger level (D1), exhibited broader distributions and more frequent use of alternative danger levels (D2) than services with more standardized use. Notably, however, even the services generally in strong alignment with the Matrix for dry-snow avalanche problems, showed comparably large deviations when assessing wet- and gliding-snow avalanche problems.

A primary objective of integrating the Matrix into the forecasting process is to improve consistency. Our findings indicate that services with high Matrix compliance indeed used a narrower set of Matrix cells for each danger level, suggesting greater consistency in how factor combinations were linked to danger levels. However, consistency in output does not necessarily imply consistency in the assessment of the input factors. It is possible though speculative that forecasters occasionally adjusted input factor estimates to achieve a desired Matrix outcome rather than allowing factor assessments alone to determine the danger level.

While differences in danger levels assigned to factor input combinations clearly highlight inconsistency, they do not necessarily imply that one outcome is “wrong”. Rather, they may reflect shifts in how specific danger levels are interpreted relative to earlier practice of assessing the input factors, whether intentionally or not. Prior to the introduction of the revised Matrix in 2022, warning services did not explicitly assess the Matrix input factors or combine them systematically to derive danger levels. Since then, many services have learned to apply factor classifications within the Matrix framework, potentially anchoring factor assessments to a desired danger level. Possibly, services with low Matrix compliance applied a more independent approach when estimating factor classes and relating them to danger levels. From an operational perspective, however, a broad overlap of factor combinations across multiple danger levels, as observed for these services, remains problematic because it reduces consistency in communication and makes it more difficult for users to associate a given danger level with a set of avalanche conditions.

In addition, each factor estimate carries uncertainty, depending on data availability and the forecasters' ability to retrieve and correctly interpret information . Even small inconsistencies in factor assessment can propagate through the Matrix and lead to different danger levels. For example, if two forecasters assessing identical conditions differ by only one neighbouring class for a single factor in half of all cases, while fully agreeing otherwise, the danger level suggested in the Matrix would differ in approximately 21 % of cases on average . Without access to external validation data or forecaster rationale, it remains impossible to determine whether the Matrix promotes genuinely consistent interpretation or merely uniform outputs.

Even though the assessment of the input factors is subject to considerable uncertainty and subjectivity, and thus to variation in outcome, it is important to recognize that danger levels are increasingly defined by the Matrix logic and by the frequency with which the Matrix-suggested danger level is selected for specific factor combinations. Consequently, consistency in input factor estimation, within and across warning services, becomes even more important. Achieving this may require clearer factor definitions (e.g., for frequency categories) as well as improved availability of relevant data, such as snow-cover simulations, to support robust and harmonized factor assessment.

Inconsistencies became particularly evident when considering different avalanche problems. While Matrix use was relatively consistent for dry-snow avalanche problems, forecasts for wet-snow and gliding snow problems showed considerably more variation between services. Similar discrepancies have been documented in Canada , where identical combinations of likelihood of avalanches (the North American counterpart to stability and frequency in the Matrix) and avalanche size resulted in different danger levels depending on avalanche problem type and, at times, the forecasting agency. In our analysis, the most notable differences related to the classification of snowpack stability for wet-snow and gliding snow avalanche problems. Although wet-snow and gliding snow avalanches are generally associated with natural avalanche occurrence , and thus conceptually with very poor stability (Table ), services showed considerable divergence in their stability ratings (Figs. b, ). Again, we can only speculate whether this reflects different conceptual models or deliberate adjustments of factor inputs to achieve expected Matrix outcomes. To promote harmonized application of the Matrix, a clearer, shared framework for assessing stability in wet- and gliding snow contexts appears necessary.