A multivariate analysis of summary-of-the-day snowfall statistics vs. same-day water precipitation and temperature recordings

Utilizing Minneapolis-St. Paul, MN (International Airport) Summary-of-the-Day October-April snowfall, precipitation, and temperature data for the period January 1965 through April 2007 (excluding the 2000-01 through 2003-4 seasons), the multivariate associations of daily reported snowfall (dependent variable) versus same day water precipitation and temperature recordings (independent variables) are explored.

In addition to shedding light on the nature and strength of the relationships, a capability is hopefully demonstrated that allows for reasonably accurate regression-based daily snowfall estimates for instances in which snowfall recordings do not accompany water precipitation and temperature ones (e.g., some of the pre-1890 Signal Corps-era years and earlier). A major assumption and requirement for the latter, however, is that the 1965-2007 procedures and instrumentation for measuring snowfall and water precipitation would be comparable versus earlier periods of records.

Preliminary trial and error regression exploration determined that due to the zero-bounded/positively-skewed nature of precipitation, and the critical 32 F phase-change temperature, the analysis was more tractable if the data were partitioned into five precipitation/daily mean temperature subclasses:

“light”/”cold”, “moderate”/”cold”, “heavy”/”cold”,

“light”/”mild”, and “non-light”/”mild”.

The “light” precipitation category extended from .01” to .06”, “moderate” from .07” to .42”, and “non-light” from .07” and above. The “cold” mean temperature category encompassed 27.5 F or lower statistics, the “mild” category 28 F or higher. A 33 F upper-limit constraint on daily minimum temperature was additionally imposed for inclusion in the empirical data base. Independent variable data transformation (square root, negative exponentiation, etc.) was done in some instances, and curvilinear (3D) model-fitting was attempted as well.

Multiple regression results showed statistically significant (beyond the .001 level) F-statistics and coefficient magnitudes. For the “cold” models (all precipitation classes), Precipitation, Mean Temperature, and Daily Temperature Range were key predictors; for the “mild” models (both precipitation classes), Precipitation and Daily Maximum Temperature were the key parameters. Negligible multicollinearities were noted in all cases.

The models are analyzed/interpreted, and tested on the nearby Chanhassen station's 2000-01 through 2003-04 and 2007-8 periods of record; also utilized is the Minneapolis-St. Paul station's 2007-8 record. In addition, they are applied to daily data for the extraordinarily snowy winter of 1880-81, a season for which no official daily snowfall amounts were recorded in St. Paul to go with the water precipitation, daily max, and daily min temperature observations. Anecdotal estimates of total snowfall for the season far exceed 100 inches.