The year 2016 was chosen as the simulation period because it recorded the highest number of billion-dollar flood disasters and the second-largest economic loss in the United States since 2000 according to the NOAA National Centers for Environmental Information (NCEI) (NCEI, 2025). These factors make 2016 an ideal test benchmark for assessing model performance under different precision reduction configurations, particularly with respect to the preservation of extreme precipitation events. Furthermore, the contiguous United States (CONUS) domain was chosen because it encompasses diverse climatological regions and benefits from dense observational networks, providing a robust basis for model assessment.

Simulations were conducted using the WRF model version 4.4.1 over the CONUS domain at a 12 km horizontal spatial resolution with 35 vertical layers. To prevent systematic model drift during the long-term integration, the four-dimensional data assimilation (FDDA) via grid-nudging was employed within the WRF framework, utilizing the North American Mesoscale (NAM) analysis, produced operationally by the National Centers for Environmental Prediction (NCEP). In model settings, weak nudging coefficients (1.0×10-4 s⁻¹ for wind and temperature, and 1.0×10-5 s⁻¹ for moisture) were deliberately selected for the free troposphere. This configuration acts as a large-scale constraint to anchor the synoptic circulation while granting the model sufficient degrees of freedom to generate free-evolving, high-resolution mesoscale features. Furthermore, atmospheric nudging was explicitly disabled within the planetary boundary layer and at the surface to avoid suppressing near-surface thermodynamic variability. Because the boundary-layer and surface atmospheric fields evolved entirely according to model physics, subsequent evaluations of the WRF outputs against independent observational station data remain scientifically valid and uncontaminated by the direct assimilation process.

To mitigate long-term model drift in deep soil temperature and moisture, we employed the Pleim-Xiu land surface model combined with indirect soil nudging, which specifically requires the continuous ingestion of two-dimensional surface analysis fields (wrfsfdda). Coupled with the three-dimensional atmospheric fields (wrffdda) utilized for upper-air nudging, the model is forced to ingest massive datasets every 3 h. The sheer volume of these high-resolution input arrays significantly exacerbates the overall storage and data management burden. Consequently, these massive time-varying input files represent a critical target for our proposed precision reduction. Table 1 summarizes the physical parameterization schemes used in the WRF simulations.

The WRF modeling system operates through a structured input–integration–output workflow. To establish dynamical consistency prior to the evaluation period, the annual simulation for 2016 was preceded by a 2 d spin-up initialized on 30 December 2015. The annual integration was conducted in consecutive daily segments, with each day initialized from a model restart file (wrfrst) generated at the conclusion of the previous day. These restart files provide the three-dimensional atmospheric and land-surface state required for seamless temporal continuity. In addition to daily initialization, the model evolution was continuously constrained by prescribed time-varying external forcing fields, including atmospheric and surface analysis nudging (wrffdda, wrfsfdda), lateral boundary condition tendencies (wrfbdy), and lower-boundary updates such as sea surface temperature (wrflowinp).

Because these time-varying inputs function as continuous external constraints, precision reduction introduced at this stage may propagate through the model integration and interact with nonlinear physical processes. In contrast, model outputs (wrfout) contain near-surface variables, three-dimensional atmospheric states, cloud microphysical quantities and energy fluxes, representing the prognostic results of the completed simulation. Post-processing modifications to these output files do not influence the meteorological evolution within the simulation itself. Recognizing this distinction is important for interpreting the impacts of precision reduction applied at different stages.

The input and output data of the WRF model are stored in single-precision (float32) format, which supports a numerical precision of approximately 7 significant digits. To control the precision of such single-precision netCDF datasets, this study implements a decimal significant-digit rounding method following Walters and Wong (2023). This scheme regulates numerical precision by retaining a user-specified number of significant digits. The rounding procedure was carried out using a dedicated Fortran routine based on internal character formatting: each floating-point value is first converted into a string in scientific notation using a dynamically specified Fortran format descriptor (i.e., Ew.d, where E denotes the exponential scientific notation, the total width w=n+7, and the number of decimal places d=n; here, n denotes the targeted number of significant digits to retain), and the formatted string is subsequently read back into floating-point representation. The precision-reduction method implemented in this study operates directly on the floating-point variables, except latitude and longitude, in the netCDF data part, which are the standard format used by WRF for both input forcing and model outputs. The rounding procedure modifies only the numerical values stored in the variable arrays and does not affect the netCDF header, metadata, or structural attributes. The deliberate adoption of this decimal-based approach, instead of direct binary mantissa manipulation, is motivated by the following considerations: decimal significant-digit rounding enables users to intuitively understand and verify the exact numerical modifications applied to the data, thereby lowering the adoption barrier for practical modeling workflows. Nevertheless, we acknowledge the inherent compression advantages of bit-level operations. As demonstrated by Delaunay et al. (2019), algorithms that map decimal precision requirements to the binary mantissa can maximize sequences of consecutive zero bits, thus generating data patterns with higher compressibility.

Furthermore, traditional decimal rounding (rounding half away from zero), which is natively handled by Fortran, may theoretically introduce systematic biases compared to IEEE 754 round-to-nearest, ties-to-even rules (IEEE, 1985). We conducted a statistical evaluation and found that exact tie cases are rare when we practically apply the method of rounding to significant digits. Across all examined core variables (e.g. surface meteorological field and precipitation, each comprising over 1.4 billion data points), exact tie situations occurred at low frequencies: approximately 0.003 %–0.005 % for retaining 3 significant digits, 0.03 %–0.04 % for 4 significant digits, and 0.2 %–0.4 % for 5 significant digits. Because over 99.6 % of values are rounded identically under both approaches, the practical impact of rounding-mode selection on the datasets analyzed herein is negligible.

Given that single-precision format inherently provides approximately at most 7 significant digits, reducing precision to 6 digits yields only marginal compression gains. Conversely, retaining only 1 or 2 significant digits would severely degrade key variables such as temperature and pressure, rendering such configurations physically unrealistic. As a result, this study conservatively focuses on retaining 3–5 significant digits. The range of 3–5 retained significant digits is not intended to represent a universal optimal precision level for each variable but rather to provide a practical evaluation window for single-precision WRF data. Establishing strict, variable-specific theoretical precision limits would require information-theoretic evaluations (Klöwer et al., 2021).

To provide an intuitive visualization of the rounding results, Table 2 contrasts the original full-precision values against those retained at 5, 4, and 3 significant digits for key near-surface variables at a single grid point and time step: 2 m temperature (T2), 2 m specific humidity (Q2), and 10 m wind components (U10 and V10).

The systematic integration of this rounding framework into the overall experimental design is summarized in Fig. 1. The schematic depicts the three core workflow stages: preprocessing on input with the precision-reduction tool, model integration with full-precision input and precision-reduction input, and post-processing on model integration result, wrfout file, with the precision-reduction tool. Lossless compression will be applied to all input and output. For input precision reduction configurations, the rounding procedure was applied during the preprocessing stage, exclusively targeting the time-varying forcing files (wrffdda, wrfsfdda, wrfbdy, and wrflowinp). Because these files define the dynamic external constraints on the model, evaluating each input precision level necessitated a fully independent WRF simulation to capture the non-linear propagation of rounding errors. Conversely, for output precision reduction, rounding was applied to the final wrfout files after simulation completion. As a purely static post-processing operation, output precision can be flexibly adjusted without requiring computationally expensive model re-runs. In total, this systematic design yielded 15 distinct precision reduction configurations (Table 3).

It is important to note that the decimal significant-digit rounding procedure effectively reduces the information entropy of the datasets, but it does not alter the predefined 32-bit storage allocation of the floating-point arrays. To translate this enhanced compressibility into tangible storage savings, lossless compression was subsequently applied to all 15 precision reduction configurations. In this study, gzip and bzip2 were selected as the primary external compressors for evaluation, given their widespread availability in operational high-performance computing (HPC) environments and compatibility with existing modeling workflows. To account for format-integrated compression, we also evaluated the internal zlib compression of netCDF, which is commonly used within the netCDF/HDF5 framework and enables direct metadata access without full data decompression. In addition, to align with contemporary data storage practices, we included targeted evaluations using the newer-generation codec Zstandard (Zstd). A comparative assessment of compression performance across these compressors is presented in Sect. 3.1.

To quantitatively evaluate model performance, we employed observational datasets of surface meteorology and precipitation for the year 2016 within the CONUS domain. Hourly near-surface meteorological variables, including T2, relative humidity (RH), and wind speed (WS10), were obtained from the National Climatic Data Center (NCDC). To ensure data reliability and spatial representativeness, a two-step quality control procedure was applied. First, only stations with valid records for at least 330 d in 2016 and with less than 5 % missing data were retained. Second, to mitigate representativeness errors caused by complex terrain, we excluded stations with an elevation difference exceeding 100 m from their corresponding WRF grid cell. These criteria yielded a total of 1622 valid stations (Fig. 2a), providing dense spatial coverage across diverse climatic and physiographic regions. To spatially align the point-based measurements with the gridded model output, a nearest-neighbor interpolation scheme was applied, assigning each station to the WRF grid point with the smallest Euclidean distance in the latitude–longitude space. Despite the inherent representativeness limitations typical of point-to-grid regional climate validation, this extensive 1622-station network provides a robust benchmark for assessing the model's meteorological fidelity at both regional and CONUS-wide scales.

For precipitation validation, we used the Global Precipitation Measurement (GPM) Integrated Multi-satellite Retrievals for GPM (IMERG) Final Precipitation L3 product (Version 07) with a uniform spatial resolution of 0.1° × 0.1°. This dataset was processed across two distinct temporal scales to accommodate different evaluation objectives. First, to establish a climatological baseline, daily IMERG data for the period 2001–2015 (Huffman et al., 2023b) were used to compute the 95th and 99th percentile precipitation thresholds. These historical thresholds were subsequently applied to define and calculate extreme precipitation indices for the study period. Second, for the primary 2016 evaluation, IMERG half-hourly data (Huffman et al., 2023a) were temporally aggregated to an hourly resolution to align with the WRF model output frequency. These hourly records were further aggregated to daily intervals for the computation of the aforementioned extreme precipitation indices. Finally, all IMERG datasets were bilinear interpolated onto the WRF model grid prior to statistical evaluation to ensure spatial consistency between the satellite retrievals and the model domain.

To capture the spatial heterogeneity of errors induced by precision reduction, the CONUS domain was subdivided into nine climatologically coherent regions following Karl and Koss (1984): Northwest, West, Northern Rockies and Plains, Southwest, Upper Midwest, Ohio Valley, South, Northeast, and Southeast (Fig. 2b).

To systematically evaluate the impacts of precision reduction on model fidelity, we adopted a multi-level assessment framework designed to capture statistical consistency, maximum numerical deviations, spatial structure, and highly skewed precipitation characteristics.

First, overall statistical agreement between precision-reduced simulations and observational datasets was evaluated using two standard community metrics: the Root Mean Square Error (RMSE) and the Pearson correlation coefficient (R). These metrics quantify the overall magnitude of simulation errors and the strength of the linear association with the observations, respectively. These metrics are defined as follows: 1RMSE=1N∑i=1N(Mi-Oi)22R=∑i=1N(Mi-M‾)(Oi-O‾)∑i=1N(Mi-M‾)2∑i=1N(Oi-O‾)2 where Mi and Oi denote the evaluated values (precision-reduced configurations) and the observations, respectively, and overbars represent their corresponding means. For station-based validation against NCDC observations, N corresponds to the number of valid station–hour pairs across all stations. For comparisons against gridded satellite products, N corresponds to the total number of grid–time pairs within the evaluated domain.

Second, to evaluate the impacts of precision reduction on both local numerical accuracy and spatial structures, we analyzed point-wise deviations together with spatial similarity metrics. At the grid scale, we computed the absolute grid-scale deviation (AD), defined as the absolute difference between the precision-reduced configurations and the full-precision baseline simulation WRF_bl at each grid point and hourly time step. Because point-wise metrics alone cannot capture changes in the spatial organization of meteorological fields, we additionally employed the Structural Similarity Index Measure (SSIM) (Wang et al., 2004; Baker et al., 2019; Klöwer et al., 2021). This metric is particularly important for evaluating simulations driven by precision-reduced inputs, where small numerical perturbations may propagate through nonlinear dynamics and alter evolving mesoscale structures. Unlike AD, which measures local differences, SSIM quantifies the preservation of large-scale spatial patterns and structural textures. For a full-precision reference spatial window x and the corresponding window y from precision-reduced configurations, the SSIM is calculated as: 3SSIM(x,y)=(2μxμy+C1)(2σxy+C2)(μx2+μy2+C1)(σx2+σy2+C2) where μx and μy are the local means, σx2 and σy2 are the local variances, and σxy is the local covariance between the two fields. The stabilization constants C1 and C2 are scaled by the dynamic range of the specific meteorological variable being evaluated to accommodate diverse atmospheric fields. SSIM values range from 0 to 1, with unity indicating perfect structural similarity. Structural similarity was computed using an 11×11 Gaussian weighting window sliding across the domain. Given the 12 km horizontal grid spacing, this corresponds to a spatial footprint of approximately 130 km, enabling assessment of mesoscale structural consistency. To avoid artificial inflation of scores caused by large, structurally uniform dry regions, a standard wet-day mask with a threshold of 0.1 mm h⁻¹ was applied prior to the calculation of precipitation SSIM.

Finally, the evaluation of precipitation for both the lower-tail thresholds that control the occurrence of light rainfall and the behavior of upper-tail extreme events is necessary given the highly skewed distribution of precipitation fields. Moreover, because total precipitation in WRF is represented as the cumulative sum of grid-resolved (RAINNC) and parameterized convective (RAINC) components, it exhibits a compounded sensitivity to numerical precision loss.

To assess structural fidelity at the lower bound of the precipitation spectrum, we first performed a categorical verification for hourly precipitation, using a wet–dry threshold of 0.1 mm h⁻¹. For each precision-reduced configuration, grid cells were classified relative to WRF_bl. Based on this comparison, several categorical verification metrics were calculated (Roebber, 2009), including the Probability of Detection (POD), False Alarm Ratio (FAR), Critical Success Index (CSI), and Frequency Bias (Bias). In addition, a Zero Preservation Ratio (ZPR) was introduced to quantify the fraction of dry grid cells that remain correctly classified after precision reduction. We further evaluated daily precipitation diagnostics, including eight indices recommended by the Expert Team on Climate Change Detection and Indices (ETCCDI) (Frich et al., 2002; Nastos et al., 2013; Ozer and Mahamoud, 2013). These indices collectively characterize precipitation intensity, frequency, and persistence. Additionally, to explicitly quantify any systematic overestimation or underestimation of these extreme precipitation magnitudes resulting after precision reduction, we computed the Normalized Mean Bias (NMB). To ensure climatological representativeness, percentile-based thresholds used by indices such as R95p_days and R99p_days were derived from the 2001–2015 daily GPM IMERG baseline dataset. The definitions and units of all precipitation diagnostics used in this study, including both the categorical verification metrics and the extreme precipitation indices described above, are summarized in Table 4. Note that unlike the standard ETCCDI definitions which calculate R95p and R99p as accumulated precipitation amounts, this study utilizes R95p_days and R99p_days to represent the frequency of extreme events.

To quantify the impact of decimal significant-digit rounding on data compressibility, we analyze compression performance using two complementary metrics. First, we evaluate the additional compression gain relative to lossless compression alone, which isolates the contribution of rounding. Second, we assess the overall storage reduction relative to the original uncompressed datasets to provide an intuitive measure of practical data savings. All calculations are benchmarked against a full-precision baseline (stored in the standard 32-bit single-precision floating-point format) comprising 837.0 GB of uncompressed input forcings and 7395.8 GB of uncompressed output data.

As summarized in Table 5 and illustrated in Fig. 3, data compressibility improves progressively with more aggressive precision reduction. Here, the relative compression ratio is defined as the compressed size of the precision-reduced configurations divided by the compressed size of the full-precision baseline. This metric isolates the additional space savings attributable specifically to decimal significant-digit rounding. For input datasets (Fig. 3a), the relative compression ratio under gzip decreases from 91.9 % (retaining 5 significant digits) to 46.4 % (retaining 3 significant digits), while bzip2 achieves a reduction from 70.6 % to 25.0 %. For output datasets (Fig. 3b), the ratio decreases from 84 % to 44 % under gzip, and from 64 % to 25 % under bzip2. As physically expected, the final compressed volume of the output is dictated by the precision applied during the output post-processing stage; varying the input precision exerts no immediate influence on the final compressed wrfout file size. On average, bzip2 outperforms gzip by 15–30 percentage points across all precision-reduced configurations (Table 5). From a practical storage perspective, when retaining 3 significant digits and using bzip2, the size of the compressed input and output datasets is approximately one-quarter of that achieved with lossless compression alone. Specifically, the compressed datasets account for 18.5 % and 7.5 % of the original uncompressed data volume, respectively.

We additionally evaluated format-native netCDF internal compression (utilizing zlib deflation) alongside external compressors, including gzip, bzip2, and the newer-generation, multi-threaded Zstd codec. Because our precision-reduction procedure strictly modifies only the floating-point data arrays while preserving the original file structure, the resulting datasets remain fully compatible with the internal compression functionality of netCDF. This native integration provides an important operational advantage: because netCDF internal compression applies strictly to data variables, the metadata headers remain uncompressed and directly accessible. This enables rapid metadata inspection and lazy loading without triggering decompression of the underlying data variables, resulting in effectively zero decompression time in our benchmarks (reported as 0.00 s). Benchmark experiments were conducted for both input and output datasets across different precision-reduction configurations, and the compression performance for a representative 5 d WRF input dataset and a 1 d WRF output dataset is summarized in Tables 6 and 7, respectively. Throughout the following discussion, specific compressor configurations are denoted by parentheses indicating their settings; for instance, Zstd (19,8) denotes Zstandard applied at compression level 19 using 8 threads, and zlib (9) refers to zlib deflation at compression level 9.

The benchmark results reveal a clear trade-off between storage efficiency and computational cost, and this trade-off differs between full-precision and precision-reduced datasets. For the raw full-precision data, the best storage reduction is achieved by high-level Zstd, which slightly outperforms both bzip2 and zlib. For example, for the WRF output file (Table 7), Zstd at level 19 reduces the file to 29.78 % of its original size, compared with 30.34 % for zlib (9), 30.46 % for bzip2, and 30.66 % for gzip. A similar but smaller advantage is found for the full-precision input file (Table 6), where Zstd (19,8) reduces the file to 74.14 % of its original size, compared with 74.80 % for zlib (9) and 75.11 % for bzip2. In addition, low-level Zstd provides markedly faster compression than bzip2 and gzip, while multi-threaded Zstd (19,8) recovers much of the runtime cost associated with high compression levels.

Once significant-digit rounding is applied, however, the relative ranking changes substantially. Across all tested precision-reduced configurations, bzip2 consistently achieves the smallest final file sizes, while Zstd remains the strongest practical alternative, and zlib and gzip occupy an intermediate position. For example, for the WRF input file with 3 significant digits retained (Table 6), bzip2 reduces the dataset to 18.56 % of its original size, compared with 25.47 % for Zstd (19,8), 33.63 % for zlib (9), and 34.95 % for gzip. For the WRF output file with 3 significant digits retained (Table 7), the corresponding values are 7.65 % for bzip2, 10.16 % for Zstd (19,8), 12.96 % for zlib (9), and 13.58 % for gzip. Thus, after precision reduction, the practical ordering is generally bzip2 > Zstd > zlib ≈ gzip in terms of compression ratio. Notably, zlib level 1 provides a balanced native option, but maximum native compression at zlib level 9 becomes increasingly expensive as precision is reduced, with compression times rising sharply for heavily rounded datasets (e.g., 1289 s for the input with 3 significant digits retained and 1125 s for the output with 3 significant digits retained) without proportional storage benefits.

These differences reflect both the underlying compression mechanisms and their algorithmic implementations. Within the LZ77-based family (Zstd, gzip, zlib), Zstd employs more efficient entropy coding (Finite State Entropy, FSE), which explains its superior performance on raw full-precision data (Collet and Kucherawy, 2021). However, decimal rounding transforms long repeated byte sequences into quasi-repetitive, imperfect patterns primarily reflected in the lower-order mantissa bits, reducing the effectiveness of dictionary-based matching. For zlib, this limitation is further amplified by its operation within HDF5 chunk boundaries, which limits the exploitation of redundancy beyond local chunks, and by deeper dictionary hash-chain traversals at high compression levels. As a result, the algorithm incurs substantial computational overhead while searching for longer matching sequences among near-matches, without proportional gains in compression efficiency. In contrast, compressors such as bzip2 process data in larger blocks and employ the Burrows–Wheeler Transform (Burrows and Wheeler, 1994). By globally reordering data prior to entropy encoding, BWT effectively clusters scattered, non-contiguous bit patterns introduced by precision reduction, enabling more efficient exploitation of redundancy than LZ77-based methods. Consequently, bzip2 consistently achieves the highest compression ratios for these rounded datasets.

In conclusion, consistent with previous studies (Zender, 2016; Silver and Zender, 2017), precision reduction substantially improves subsequent standard lossless compression, which is also reflected in our results obtained with the decimal significant-digit rounding method. The substantial reduction in storage footprint achieved by reducing input and output precision underscores the potential of this coupled precision reduction and lossless compression strategy within the WRF workflow. However, while these physical storage benefits are substantial, the scientific consequences of precision reduction remain a critical concern.

While improvements in data compressibility are important, they must be weighed against potential degradation in scientific fidelity. To ascertain whether precision reduction undermines the model's capacity to simulate real-world processes, we first validated the simulations against observational datasets. Figure 4 presents the relative changes in RMSE and correlation coefficient R for WS10, T2, RH, and precipitation, evaluated against observational references. The relative change is defined as the percentage difference in these metrics between each precision-reduced configuration and the WRF_bl, with both configurations independently evaluated against the same observational datasets. For precipitation, RMSE and R were calculated using the spatially averaged regional time series. For all other variables, these statistics were first computed at individual stations and subsequently averaged across all sites.

For WS10, the error growth is predominantly driven by input precision reduction, exhibiting a larger and nonlinear response compared to output-only precision reduction. This suggests that wind dynamics are more sensitive to perturbations in input forcings. However, this variable exhibits the smallest relative error variation among all variables evaluated. This indicates that despite its high sensitivity to input perturbations, the overall magnitude of the induced bias remains strictly bounded. In contrast, thermodynamical fields such as T2 and RH exhibit different behavior. Reducing the output of T2 to 3 significant digits produces larger changes relative to other configurations, with RMSE increasing by about 1.1 % and R decreasing by about 0.05 %. This behavior is largely a numerical artifact stemming from the Kelvin scale used in WRF outputs, where retaining 3 significant digits effectively removes all sub-degree decimal precision. Importantly, the pronounced sensitivity of RH, when output precision is reduced to 3 significant digits, is intrinsically tied to these temperature deviations. Governed by the non-linear Clausius–Clapeyron relationship, numerical artifacts from temperature directly propagate into saturation vapor pressure calculations, rendering the observed RH deviations largely secondary thermodynamic artifacts. Additionally, direct observational validation of absolute moisture was precluded: deriving specific humidity or mixing ratio from dew point temperature requires concurrent pressure data, yet rigorous quality control of these pressure records limited the available data to merely a few hundred valid stations domain-wide, rendering the network statistically insufficient for robust spatial verification. For precipitation, while reducing the input precision to 3 significant digits leads to larger deviations relative to other configurations, the absolute degradation remains minimal. This demonstrates that although precipitation is strongly modulated by upstream dynamical fields, its bulk macroscopic fidelity is still resilient.

Further decomposition of these errors highlights substantial regional and seasonal heterogeneity, as shown in Fig. 5. Figure 5 illustrates the absolute relative change in RMSE for other configurations relative to WRF_bl across nine climate regions and four seasons. When output-only precision is reduced to 5 or 4 significant digits, the resulting error increments are negligible for all variables across regions and seasons. By contrast, reducing the output to 3 digits exerts a discernible influence: while WS10 remains largely stable, T2 and RH show consistent relative RMSE increases across all regions and seasons, and precipitation displays noticeable degradations.

Regarding WS10, it remains the most robust variable, with relative RMSE increments remaining below 0.1 % across nearly all regions and seasons. The small error peaks observed are primarily associated with input precision reduction and exhibit modest regional and seasonal signatures, such as slight increases over the Southwest and Ohio Valley during summer. This behavior suggests that wind fields are comparatively tolerant to precision reduction and can accommodate more aggressive output precision reduction. Across configurations with 3-digit output precision, the relative RMSE increment of T2 is approximately 1.2 % with spatial coherence. A similar pattern is also observed for RH, although with minor regional variability, likely attributed to its nonlinear dependence on temperature via the Clausius–Clapeyron relationship. Precipitation emerges as the most heterogeneous field: relative RMSE increases are largest in fall, followed by summer, and smaller in winter and spring, with regional contributions shifting seasonally from the Upper Midwest, West, Southwest, and Northern Rockies and Plains in summer to the West, Southeast, Upper Midwest, and South in fall. Compared with these predictable output responses, precision-reduced input exerts a less systematic influence, producing non-monotonic and regionally heterogeneous biases, particularly evident in wind speed and precipitation. Together, these results highlight a fundamental distinction in how precision loss influences model fidelity: retaining 4–5 significant digits in model outputs generally preserves meteorological consistency, whereas more aggressive precision reduction introduces variable-dependent sensitivities. Thermodynamic variables such as T2 and RH exhibit increased susceptibility when retaining 3 significant digits, while WS10 remains comparatively insensitive. In contrast, input perturbations interact with the model's nonlinear dynamics, leading to spatially heterogeneous and temporally evolving deviations in dynamical and diagnostic fields.

While domain-averaged metrics provide a robust macroscopic assessment of simulation fidelity, they may obscure localized extremes and spatial distortions. To more comprehensively evaluate model reliability under different precision-reduced configurations, we therefore examined grid-scale maximum AD and the domain-wide SSIM.

As summarized in Table 8, precision reduction applied to model inputs generally produces substantially larger maximum AD than that of output. In some cases, these deviations appear extreme. For example, under the WRF_4 configuration, T2 exhibits grid-point maximum AD approaching ∼ 21.45 K. Similarly, under WRF_3, hourly precipitation reaches a maximum AD of ∼ 145.45 mm h⁻¹. Despite these seemingly severe local deviations, the annual minimum SSIM for T2 remains above 0.97 under WRF_4. The annual minimum SSIM for precipitation is approximately 0.86 under WRF_3, but at the exact moment when precipitation deviation reaches its peak, the SSIM approaches 0.99. This indicates that the occurrence of large point-wise deviations is not necessarily accompanied by structural breakdown of the simulated fields. The corresponding results for the remaining configurations in Table 8 are provided in Table S1 in the Supplement.

To further clarify this behavior, we examined the relationship between the maximum AD at each grid point and the SSIM computed at the corresponding time when that maximum deviation occurs (Fig. 6). The results reveal a clear decoupling between grid-point maximum deviation and structural fidelity under input precision-reduced configurations. This suggests that large point-wise deviations can arise from spatial or temporal phase shifts of otherwise coherent meteorological features, rather than indicating a fundamental degradation of the simulated atmospheric structure. In other words, under input perturbations, the simulated system maintains morphological integrity yet may have undergone spatial or temporal displacement. Snapshot comparisons at the time of maximum AD for T2 and precipitation (see Figs. S1 and S2 in the Supplement) provide further visual evidence supporting this interpretation. Structural sensitivity also exhibits strong variable dependence. Large-scale continuous fields such as PSFC remain highly robust: even under WRF_3, the 1st percentile SSIM exceeds 0.9997. In contrast, precipitation as an intermittent diagnostic variable shows more pronounced degradation.

The temporal evolution of SSIM (Fig. 7) further highlights two fundamentally distinct error modes associated with precision reduction. As illustrated in the left column of Fig. 7, input precision reduction exhibits a consistent seasonal variability characterized by a “U-shaped” depression in SSIM from May to September. During dynamically active periods, nonlinear atmospheric processes amplify small perturbations introduced through time-varying forcing fields. In contrast, output-only precision-reduced configurations (right column of Fig. 7) produce a markedly different temporal signature. The degradation in SSIM appears as a steady, step-like decline with minimal seasonal influence, consistent with static mathematical rounding artifacts rather than dynamically evolving divergence. This is particularly evident in Table 8, as exemplified by PSFC, where the maximum AD under WRF_fx5, WRF_fx4, and WRF_fx3 is strictly bounded at 5, 50, and 500 Pa, respectively.

Output-only precision reduction exposes an inherent sensitivity in cumulative variables when hourly precipitation is derived through temporal differencing. Under WRF_fx3, this sensitivity manifests as a time-dependent degradation of structural fidelity in hourly precipitation fields. From late January to April, the rolling median SSIM decreased to approximately 0.95, as 72 % of grid cells exceeded ∼ 100 mm for RAINNC and 34 % for RAINC (Fig. S3a, b). At this magnitude, retaining 3 significant digits for both RAINC and RAINNC variables introduces a rounding error of approximately 2 mm h⁻¹, which readily overwhelms weak stratiform precipitation signals.

Interestingly, although individual grid cells cross the 1000 mm accumulation threshold much earlier in the simulation, by March for RAINNC and June for RAINC, the SSIM collapse occurs much later. This apparent temporal inconsistency can be explained by the combined effects of spatial coverage and precipitation regime. In the early months of the simulation, only a small fraction of grid cells exceeds this threshold (∼ 1.3 % for RAINNC in May, with RAINC being negligible), limiting its impact. From June to October, although the affected fraction increases (RAINNC ∼ 6.8 %, RAINC ∼ 16.9 %), intense convective rainfall produces large hourly increments to partially mask the quantization noise. This effectively restores the signal-to-noise ratio and partially masks the numerical artifacts. However, a sharp SSIM decline occurs post-November (SSIM rolling median ∼ 0.88). By this time, the fraction of grid cells exceeding 1000 mm further increases (RAINNC ∼ 10 %, RAINC ∼ 18 %) (Fig. S3c, d). At this > 1000 mm baseline, the 3-significant-digit constraint significantly expands the quantization interval, potentially generating artificial jumps approaching ∼ 20 mm h⁻¹. Meanwhile, the precipitation regime reverts to being dominated by weaker stratiform precipitation. Under these conditions, the massive quantization noise entirely dominates the physical signal, rendering the true precipitation gradients largely unresolvable. A similar, though weaker, behavior is observed under WRF_fx4. While retaining 4 significant digits preserves near-perfect structural similarity (SSIM approaches 1) through most of the simulation period, a similar structural degradation paradigm emerges post-November.

These findings provide important methodological implications for balancing storage efficiency and scientific validity. In the context of this study, one practical strategy is to retain 4 significant digits prior to November and increase the precision to 5 significant digits thereafter, thereby protecting the weak stratiform precipitation signals that dominate during the later stages of the simulation. More generally, if scientific accuracy is prioritized, a dynamic precision reduction configuration can be adopted for cumulative precipitation variables. In such a scheme, the compression algorithm monitors accumulated precipitation and initially retains 4 significant digits, automatically upgrading to 5 significant digits once cumulative precipitation exceeds 1000 mm at the regional average or even grid scale.

Finally, the appropriate threshold for SSIM warrants further investigation, particularly when accounting for model resolution and the sources of precision reduction. Baker et al. (2019) adopted SSIM thresholds exceeding 0.99995 for coarser-resolution datasets (∼ 100 km). At the 12 km resolution considered here, SSIM becomes more sensitive to the spatial displacement of fine mesoscale structures. Importantly, tolerance for SSIM degradation should be interpreted differently for input and output precision reduction. When precision reduction is applied to time-varying input forcings, the moderate reductions in SSIM may reflect physically interpretable displacement rather than structural collapse. In contrast, output-only precision reduction introduces purely static numerical artifacts without interacting with model dynamics. Consequently, SSIM degradation in this pathway reflects artificial structural distortion rather than physical displacement. For this reason, the tolerance for SSIM should remain substantially stricter, typically requiring values exceeding 0.999 to ensure that numerical artifacts do not corrupt spatial structures.

While the SSIM analysis reveals how these numerical artifacts alter the spatial structure of precipitation fields, an equally important question is how distortions introduced by precision reduction in cumulative precipitation fields propagate into downstream scientific diagnostics. Precipitation exhibits a highly skewed spatial and temporal distribution, characterized by two distinct and sensitive regimes: a widespread lower tail dominated by zero or near-zero values, and a rare but high-impact upper tail driven by extreme rainfall events. Both regimes are particularly vulnerable to numerical artifacts introduced by precision reduction. To quantify these impacts, the following section evaluates how precision-reduced configurations affect precipitation diagnostics, including zero-value preservation and extreme precipitation indices.

We first evaluate the preservation of the precipitation occurrence spectrum, specifically focusing on the zero-value boundary (using the 0.1 mm h⁻¹ wet-day threshold). Standard contingency metrics, including ZPR, POD, FAR, CSI, and Bias, are employed to diagnose how different compression configurations alter the fundamental wet/dry morphology (Table 9).

For input-only precision reduction configurations, the metrics indicate that the overall precipitation spectrum is largely preserved. The Frequency Bias remains close to unity (e.g., 0.99942 for WRF_3), confirming that the total precipitation area is conserved. Furthermore, the nearly symmetric error rates, where the moderate FAR (7.84 %–8.72 %) closely balances the corresponding miss rates (1 – POD), together with a stable CSI (∼ 0.84) indicate that input precision reduction induces spatial phase shifts in precipitation systems rather than systematically disrupting their structure. In contrast, aggressive output precision reduction introduces substantial numerical distortions that directly erode the bottom end of the precipitation spectrum, most prominently in the WRF_fx3 configuration. Under this configuration, the POD drops sharply to 71.94 %, indicating that approximately 28 % of valid light precipitation events are artificially truncated to zero due to the loss of significance in the arithmetic of cumulative precipitation variables. As a result, a pronounced systematic dry bias emerges (Bias ≈ 0.77).

Interestingly, WRF_fx3 exhibits an apparently higher ZPR (99.12 %) and a lower FAR (6.90 %) compared with WRF_fx4 (98.5 % and 8.98 %, respectively). However, this does not indicate improved structural fidelity. Instead, it reveals that WRF_fx3 suppresses both numerical noise (reducing FAR) and genuine light stratiform precipitation (reducing POD), effectively converting them into widespread non-physical dry regions.

The structural degradation previously indicated by the late-stage decline in SSIM is further corroborated by the temporal evolution of precipitation occurrence metrics under the WRF_fx4 configuration (Fig. S4). At the domain scale, the ZPR remains high (> 97 % throughout the year), largely reflecting the overwhelming dominance of climatologically dry background grids. However, metrics that evaluate performance specifically within precipitation events (CSI, POD, and FAR) reveal a pronounced late-stage deterioration. Consistent with the SSIM decline observed in November, the CSI decreases from its summer peak (∼ 0.89) to 0.769 by December. This degradation reflects a dual numerical distortion associated with the expanding accumulation baseline. As the quantization step increases during November and December, the FAR rises substantially (reaching 11.4 %), indicating the growing occurrence of spurious drizzle signals introduced by rounding artifacts. At the same time, the POD declines to 85.4 %, implying that approximately 15 % of genuine winter stratiform precipitation events are artificially truncated to zero. The Frequency Bias further highlights this shift in behavior. While the system exhibits a slight wet bias in spring, it gradually transitions to a systematic dry bias by December (Bias = 0.964). The simultaneous increase in false alarms and the loss of weak precipitation events progressively disrupt the spatial consistency of precipitation structures, definitively explaining the late-stage SSIM collapse.

The analyses above focus on the lower boundary of the precipitation spectrum, where precision reduction primarily affects the occurrence of light rainfall and the preservation of dry conditions. However, precipitation diagnostics are also strongly influenced by the opposite end of the distribution. To assess these upper-tail characteristics of precipitation, we next evaluate a suite of extreme precipitation indices. For clarity, the indices are grouped into two categories. The first category consists of percentile-based and maximum-based extreme precipitation indices (R95p_days, R99p_days, Rx1_day, Rx5_day), which emphasize the upper tail of the daily precipitation distribution and the magnitude of rare extreme events. The second category includes precipitation frequency and accumulation indices (R10mm_days, PRCPTOT, wet_days, SDII), which describe total precipitation amounts, mean intensity, and the occurrence of moderate wet events.

Figure 8 focuses on two representative diagnostics, R99p_ days and SDII, while results for the remaining six indices are provided in Figs. S5–S10. These extreme precipitation metrics further corroborate that distinct precision reduction pathways (input vs. output pathways) exert impacts on different components of the precipitation spectrum. For the percentile-based index R99p_days, NMB fluctuates within ±3 % during winter, spring, and fall, while it amplifies in summer to a maximum bias of 8.33 % (Fig. 8a–d). This pronounced summer overestimation is highly localized, particularly in the Northwest and Northeast, and is fundamentally driven by input precision reduction (retaining 3 significant digits). In the conditionally unstable summer atmosphere, input perturbations can artificially induce and expand spurious convective initiation, thereby systematically inflating the R99p_days count. In contrast, output-only precision reduction produces comparatively small (<1.5 %) and near-linear response from WRF_fx5 to WRF_fx3. Once combined with the precision-reduced input, however, the response becomes distinctly nonlinear. Consequently, percentile-based extreme precipitation metrics are particularly sensitive to the spatial perturbations associated with input precision reduction. In contrast, SDII exhibits a different behavior. Negative biases dominate across most regions and seasons, and these biases are primarily governed by output precision configuration (Fig. 8e–h). The WRF_fx4 configuration yields consistent reductions of approximately -1 % to -3 %, while the more aggressive WRF_fx3 configuration produces substantially larger decreases ranging from -3 % to -13 %.

The distinct mechanism underlying these responses becomes clearer when examining the full set of eight indices using box plots (Fig. 9). For the extreme-intensity group (R95p_days, R99p_days, Rx1_day, Rx5_day), output-only precision reduction configurations keep tight interquartile ranges, whereas input precision reduction configurations generate broader spreads and numerous outliers due to spatial phase displacement. In contrast, the frequency and accumulation group (R10mm_days, PRCPTOT, wet_days, SDII) is primarily governed by quantization artifacts associated with output precision reduction. When outputs are retained to 3 significant digits under large accumulation baselines, coarse quantization steps (e.g., artificial increments approaching ∼ 20 mm) can spuriously push daily totals across fixed thresholds such as 1 or 10 mm. This effect artificially increases the occurrence of wet days, producing positive biases in both R10mm_days and wet_days. Because SDII is defined as PRCPTOT divided by wet_days, the artificial expansion of the denominator directly induces the systematic negative bias observed in SDII. To isolate the systematic error trajectories from the regional spatial noise observed in the box plots, Fig. 10 synthesizes the absolute values of the median NMB across all 15 configurations, reinforcing these conclusions.

Figures 8–10 collectively demonstrate that downstream diagnostic outcomes at the extreme tail of the precipitation spectrum are inherently more sensitive to input precision reduction, with their biases exhibiting highly nonlinear characteristics and marked regional and seasonal divergence. While aggressive output precision reduction (retaining 3 significant digits) can induce error magnitudes comparable to those from input precision reduction, the resulting biases remain more concentrated statistically. In contrast, precipitation frequency and accumulation indices follow fundamentally distinct degradation pathways: as output precision decreases, they are strictly dominated by systematic biases, a structural distortion that is severely amplified when retaining 3 significant digits. Finally, it is critical to recognize the inherent limitations in interpreting the seasonal divergences of precipitation. Given that output precision reduction acts on a continuously accumulating precipitation field, this temporal classification can occasionally conflate true atmospheric seasonality with the mathematical artifacts of cumulative growth. For example, as illustrated in Fig. 9, retaining only 3 significant digits for precipitation output generates anomalously high R10mm_days frequencies heavily concentrated in autumn (September–November). This apparent 'seasonal' peak is, in reality, a numerical illusion: by autumn, the annual accumulated precipitation has grown to a massive background magnitude where 3-digit retention enforces excessively coarse quantization steps. Consequently, temporal differencing at this late stage of integration artificially and frequently triggers the 10 mm daily exceedance threshold. However, it is worth noting that for precipitation intensity indices (e.g., the left column in Fig. 9), the pronounced summer anomalies are indeed physically meaningful. This limitation profoundly underscores the inherent challenges of conducting traditional seasonal analyses on cumulative variables under precision-reduced configurations.

Precision reduction applied to time-varying model inputs introduces perturbations that interact with nonlinear atmospheric dynamics during model integration. These perturbations propagate through the simulation and may alter the precise spatial and temporal positioning of weather systems. As demonstrated in Sect. 3.3, such perturbations can generate large grid-scale maximum AD. However, the simultaneously high SSIM values indicate that the overall morphology of the simulated atmospheric systems remains largely preserved. Consequently, the resulting errors primarily manifest as pronounced maximum AD driven by local spatial or temporal phase shifts, accompanied by a background of widespread, disordered weak perturbations, rather than a fundamental structural collapse of the simulated fields. Therefore, input precision reduction may be acceptable for applications that prioritize large-scale statistics or aggregated diagnostics, where exact grid-scale correspondence is not required. However, this pathway introduces intrinsic nondeterministic perturbations into the simulation, meaning that the exact location and timing of individual weather systems may shift. For impact-oriented applications requiring strict spatiotemporal consistency, such as event attribution or local hydrological analyses, this loss of deterministic correspondence may be undesirable.

In addition, the chaotic amplification of these input perturbations exhibits strong seasonal dependence. Error propagation peaks during the summer when local land-atmosphere feedback and convective processes dominate. Hypothetically, aggressive precision reduction could be applied to input forcings during less sensitive, non-summer months, while retaining full precision during the dynamically volatile summer to help constrain the cascading growth of nonlinear errors. However, the extent to which this adaptive approach would restore summer fidelity remains an open question warranting further investigation.

In contrast to the input precision reduction, output precision reduction acts as a post-processing filter. It provides a more controllable approach for impact-oriented studies requiring strict deterministic fidelity, as it ensures weather systems occur at the exact time and location simulated by the baseline physics. However, the optimal precision level is highly contingent on the intrinsic mathematical properties and computational derivations of the target variable. Based on our evaluation, several prominent typologies emerge that dictate distinct compression behaviors and require tailored precision strategies.

For fundamental state variables, compressibility is primarily governed by their numerical distributions and physical measurement limits. Atmospheric state variables exhibit markedly different compressibility characteristics determined by their numerical distributions. Dynamic variables such as WS10 are typically concentrated within a narrow numerical range, retaining 3 significant digits completely guarantees the preservation of at least one decimal place (e.g., a resolution of 0.1 m s⁻¹). Therefore, applying a universal 3-digit retention for wind fields represents the most conservative compromise between storage reduction and precision, introducing negligible numerical distortion in our evaluation. Theoretically, retaining 2 significant digits could also be a viable configuration. Because 2 digits mathematically preserve single-decimal resolution for values below 10 m s⁻¹, perceptible quantization errors would primarily be expected to emerge only when wind speeds exceed this threshold. Consequently, to maximize storage benefits without compromising physical fidelity, future applications could implement a magnitude-aware adaptive strategy for wind fields: dynamically toggling between 2 and 3 retained significant digits based on a 10 m s⁻¹ threshold. In contrast, thermodynamic variables like T2 exhibit greater sensitivity and generally require at least 4 significant digits to prevent systematic, sub-degree information loss associated with rounding in Kelvin units. Unlike wind speed, which is subject to distinct magnitude threshold jumps (e.g., crossing the 10 m s⁻¹ boundary), temperatures measured in Kelvin consistently occupy a stable, high-magnitude numerical range. Because of this stable magnitude, applying a uniform retention of 4 significant digits across the entire temperature field is entirely sufficient and structurally robust, precluding the need for dynamic precision switching. This pronounced heterogeneity in compressibility aligns profoundly with Klöwer et al. (2021), which demonstrates that a variable-specific precision reduction strategy emerges as a key paradigm for optimizing output data compression.

In stark contrast to instantaneous state variables, the WRF precipitation variable, a cumulative quantity with a highly skewed distribution, can reach thousands of millimeters annually. This continuously growing accumulation introduces fundamentally different numerical vulnerabilities, making it the primary bottleneck for precision reduction design. Specifically, retaining a fixed 3 significant digits critically widens the effective quantization interval over time (e.g., approaching ∼ 20 mm h⁻¹). When hourly or daily precipitation is derived through temporal differencing, this coarse quantization introduces contradictory artifacts: it suppresses very light (0.1 mm h⁻¹) rainfall increments (producing a systematic dry frequency bias) while intermittently generating large, discrete step-increments, which artificially elevates the frequency of false wet_days and R10mm_days threshold exceedances. To maintain realistic precipitation statistics without indiscriminately inflating file sizes, a magnitude-aware dynamic precision strategy, scaling the retained digits according to the evolving cumulative total, emerges as a highly practical solution. Specifically, for grid cells where the accumulated precipitation remains below 1000 mm, retaining 4 significant digits is generally sufficient to preserve a scientifically viable sub-millimeter resolution. Once the accumulation surpasses the 1000 mm threshold, the precision should be dynamically increased to 5 significant digits to explicitly prevent the decimal resolution from degrading. For multi-year simulations, where total accumulations routinely exceed 10 000 mm, retaining 6 significant digits becomes strictly necessary. It is worth noting that designing a lower-tier threshold (e.g., at 100 mm) is operationally unnecessary; most simulated regions rapidly exceed this baseline shortly after initialization, rendering any lower-precision tier computationally transient and practically redundant.

Considering the specific application context, precision required for post-processed diagnostics is not universally applicable. The acceptable extent of precision reduction is ultimately determined by the relative magnitude between the physical signals that downstream analyses intend to resolve and the background state of the variable. The retained precision must be sufficient to resolve the order-of-magnitude contrast between the background state and the targeted physical perturbation, but only when resolving that perturbation is scientifically necessary. For example, atmospheric pressure typically has a background magnitude of ∼ 10⁵ Pa. If a study seeks to diagnose mesoscale pressure gradients on the order of ∼ 10¹ Pa, retaining at least five significant digits becomes necessary to avoid numerical loss of information. Conversely, if the scientific objective focuses only on large-scale synoptic patterns, where variations of ∼ 10² Pa are sufficient to characterize the system, retaining four significant digits may already provide adequate fidelity while significantly improving storage efficiency. Following analogous reasoning, water vapor mixing ratio typically exhibits background magnitudes of ∼ 10⁻²–10⁻⁴ kg kg⁻¹, while dynamically relevant perturbations associated with moisture advection may occur at ∼ 10⁻⁵ kg kg⁻¹. Resolving such subtle signals requires at least four significant digits. However, studies concerned primarily with bulk moisture transport or large-scale moisture budgets may tolerate lower precision because these micro-scale perturbations contribute negligibly to the targeted diagnostics. Therefore, the level of precision reduction should ideally be chosen based on the requirements of the intended downstream scientific analysis, ensuring that numerical compression does not obscure the physical signals that the research aims to diagnose. When downstream applications are broad and unpredictable, as is typically the case for static reanalysis datasets distributed by institutional centers, providers are typically required to maintain conservative, high-precision baselines. Conversely, in the context of active model post-processing (e.g., targeted WRF simulations), researchers often have well-defined scientific objectives. This allows them to precisely tailor the extent of precision reduction to their specific needs, maximizing storage efficiency without compromising the physical signals of interest.