| 06 Oct 2026
Spatial Distribution and Long-Term Changes in Surface Air and Wet-Bulb Temperature Thresholds for Classifying Cold-Season Precipitation Phase across Japan
Abstract. The precipitation phase (rain or snow) strongly influences land-surface water and energy budgets, yet the thresholds used to distinguish rain from snow vary widely across regions and are not determined by air temperature alone. Because atmospheric humidity affects phase transitions through the cooling of falling particles, wet-bulb temperature has been proposed as an alternative to air temperature. However, spatial differences and long-term changes in wet-bulb thresholds across Japan remain insufficiently characterized. Using hourly surface meteorological observations from 158 stations across Japan (1989–2024), we analyzed the surface air temperature (Ts,50) and wet-bulb temperature (Tw,50) at which the probability of snowfall was 50 %, along with their difference, ΔT50 (= Ts,50 − Tw,50). Rather than treating ΔT50 as a direct measure of cooling by evaporation and sublimation, we use it as a diagnostic index of humidity-related controls on the precipitation phase. This decomposition treats the conventional air-temperature threshold as the sum of a wet-bulb component and a humidity-related component (Ts,50 = Tw,50 + ΔT50). Across 115 stations, the mean Ts,50 was 2.63 °C and the mean Tw,50 was 1.31 °C. Inter-station variability in Tw,50 was less than half that in Ts,50, suggesting that a spatially uniform wet-bulb threshold is more broadly applicable. All three indices decreased with latitude and elevation, although these factors explained only a small fraction of the variability. ΔT50 was associated with relative humidity during precipitation, with larger values at drier sites. Stratifying snowfall frequency curves by relative humidity, station pressure, wind speed, and precipitation amount revealed systematic shifts in the rain–snow transition temperature. These shifts were generally larger for air temperature than for wet-bulb temperature, suggesting that the latter accounts for much of the variability associated with meteorological conditions. At 44 stations with continuous records, Ts,50, Tw,50, and ΔT50 decreased at more sites than they increased between 1990–2004 and 2005–2020. At more than half of the stations, wet-bulb and humidity-related components changed in opposite directions, indicating that at these sites the long-term changes in Ts,50 cannot be explained by a single factor. Because wet-bulb temperatures are widely available in reanalyses, climate simulations, and land-surface models, the proposed decomposition provides a practical basis for interpreting regional differences and future changes in the precipitation phase and associated hydrological responses.
Among the numerous factors influencing water balance and energy budgets, the form of precipitation plays a critical role. Historically, surface air temperature thresholds were used exclusively to determine whether precipitation fell as rain, snow, or a transitional phase. However, recent advancements have led to the adoption of wet-bulb temperature thresholds, as they implicitly account for atmospheric humidity. Despite this progression, the author notes that spatial and long-term variations in wet-bulb thresholds remain under-researched, leaving a significant gap in establishing concrete regional findings in Japan. To address this limitation, this study utilizes hourly meteorological observations—specifically surface air temperature measured at a height of 1.5 meters—from 158 stations across Japan, spanning a 35-year period from 1989 to 2024. By investigating these thresholds, the authors aim to provide insights into Japan's specific hydro-climatic dynamics. Based on the current version of the manuscript, the following points are brought forward for further discussion.
In Equation 3, the definition of the variable e is ambiguous. Assuming Equation 3 represents an optimization or minimization function, e likely denotes the observed (actual) vapor pressure. It appears the authors are determining the wet-bulb temperature by minimizing the absolute difference between the observed vapor pressure and the computed vapor pressure—derived by substituting Equation 2 into Equation 1—subject to a convergence threshold of 0.001 hPa. However, the current manuscript does not clearly articulate this methodology. The authors must explicitly state the underlying mechanism of this optimization step.
While modern computing power allows for mathematical precision to an arbitrary number of decimal places, numerical thresholds in modeling must align with the physical precision of instrumental measurements.
2.1 The authors set a strict minimization threshold of 0.001 hPa [line 119] for vapor pressure in Equation 3. However, this choice appears somewhat arbitrary and requires a robust physical justification. Is a precision of 0.001 hPa achievable or meaningful given the standard tolerance and precision of modern field instrumentation? The authors must address this limitation and justify the threshold from an instrumental and observational perspective.
2.2 Furthermore, the optimization or minimization algorithm (i.e., Equation 3) yields a wet-bulb temperature (Tw) that can extend to an arbitrary number of decimal places within the computational model. Such high mathematical precision may not be physically justified when compared to standard surface air temperature observations.
2.3 Of greater concern is that the authors subsequently round the optimized temperature to two decimal places. This truncation risks introducing a rounding error that could effectively override or reverse the strict threshold set during the minimization process, rendering the optimization mathematically inconsistent. For example, if the algorithm outputs a temperature of 10.1245°C and it is rounded to 10.12°C, reverse-engineering this rounded value back into the physical equations might reveal an effective threshold closer to 0.008 hPa rather than the stated 0.001 hPa. The authors need to clarify whether the mathematical formulation inherently constrains the wet-bulb temperature to a specific precision that prevents this decoupling. If it does not, they must reconcile the precision of the optimization threshold with the final rounding of the output variables to ensure physical and numerical consistency.
Hydrology and Earth System Sciences (HESS) caters to a broad audience across various sub-disciplines of water science. While Sprung’s and Tetens' formulae are foundational to specific subfields, they are not universally known (unlike fundamental physics equations such as Newton's second law). Therefore, the authors must provide citations for both Sprung’s and Tetens' formulae [line 105].
Because saturation vapor pressure is already defined in line 108, redefining it in line 112 is redundant. The authors should simply use the previously established symbol or refer to it textually as "saturation water-vapor pressure."
Given that HESS is a high-impact journal, the application of empirical equations requires rigorous scrutiny regarding regional validity. The parameters A, a, and b in Equations 1 and 2 are empirical. Consequently, using their default or literature values without assessing their applicability to the specific climatic conditions of Japan may introduce systemic biases. An analytical examination of Equation 2 reveals critical mathematical constraints governed by the exponent of 10:
When the exponent is less than 1, the wet-bulb temperature is bounded such that it is less than b / (a -1). Conversely, when the exponent exceeds 1, the wet-bulb temperature becomes greater than b / (a-1). The authors must evaluate these mathematical boundaries against observed air temperatures to validate whether the empirical parameters A, a, and b are physically sound and justified for this study's geographic scope.