Snow Maps, Algorithms, and Winter Precipitation

Last updated 3 April 2024

Snow maps — love them or hate them, they're everywhere in the wintertime! When it comes to different snow map algorithms, confusion reigns. Although this is a messy topic with few simple answers, our aim is to clear up some of the confusion in a central location.

What is snowfall?

On Pivotal Weather, "snowfall" refers to snow that reaches Earth's surface over the specified time period. If a particular ground surface is warm enough for melting to occur, then the accumulated pile of snow you see on that surface at the end of a storm may be noticeably less than what we call snowfall. Suppose you had a snow board whose temperature you maintained at well below freezing, and you diligently went outside every hour to measure and clear new snow. Not much melting, sublimation, or compacting would occur during those hourly intervals, regardless of the weather conditions. The sum of all snow you cleared off the chilled snow board over the course of the storm would represent the observed "snowfall" that our 10:1 and Kuchera* snowfall maps attempt to forecast.

To forecast the final accumulation on a ground surface at the end of a long-duration snowstorm is more complex. It will depend on the surface type, in addition to weather conditions at ground level and their evolution throughout the storm. Even solar radiation passing through clouds, and therefore time of day, can have an impact on melting. We do not attempt to forecast any of this explicitly, but our snowfall products are still often a useful proxy for the final accumulation on untouched natural surfaces. However, this may not be true when ground temperatures are warm, air temperatures are above freezing, or when a storm is particularly long in duration and compacting plays a large role.

*The Kuchera method was originally formulated to fit a sample of observed snow depth measurements (e.g., a ruler measurement after a storm), so even our attempt to define “snowfall” has caveats — more below.

Assessing model precipitation type

Our primary snowfall product types, 10:1 and Kuchera, apply certain snow-to-liquid ratios (SLRs) to precipitation in the model we deem to have fallen as snow between data output times. But, hold on… do we really know how much fell as snow?

  • ECMWF, UKMET, and Environment Canada models keep track of precipitation type in a precise way as the model integrates, so we know how exactly much precipitation falls in the form of snow (at least, based on the model’s internal diagnostics). This eliminates any concern about including sleet, graupel, or rain when we compute snowfall for those models.

  • For NCEP models, the bookkeeping for precipitation types is less precise, so mis-categorizing some of the precipitation that fell between data output times is always a risk during mixed precipitation or precipitation that is rapidly changing type. We have adopted an approach that usually avoids erroneously treating sleet as snow for NCEP models, so you should not see a shield of "fake snow" extending well equatorward of the actual snow-sleet line in a large mid-latitude cyclone, for example. Still, it is inevitable that we will sometimes overestimate the fraction of mixed precipitation falling as snow in borderline and transitional environments (usually small in area).

Snow-to-liquid ratio (SLR)

Now, to the topic of the SLR (often informally called “snow ratio” or just “ratio”). After snow falls, we can melt it and measure the liquid equivalent precipitation it comprises. Dividing the snowfall by this liquid equivalent amount gives the SLR. Because current numerical weather prediction (NWP) models predict liquid equivalent precipitation directly, some SLR must be applied to the predicted liquid amount to get a meaningful snow forecast.

For over a century in weather forecasting, a 10:1 SLR (1 inch of liquid = 10 inches of snow) has commonly been used as a default value. A large climatology of SLRs in the United States by Baxter et al. 2005 found a distribution of values centered near 12:1, with values between 10:1-12:1 being more common than any other bin (see their Fig. 9). Values ranging all the way from 6:1 to 18:1 are relatively common in the US, and can occasionally approach 2:1 on the low end and 44:1 on the high end. It is apparent that while 10:1 is a reasonable “default” value if you had to pick one, SLR errors >50% will be seen on a regular basis using that approach!

From a physics perspective, SLR comes down to the structure and density of the snow crystals, the formation mechanisms of which are quite complex (see Takahashi et al. 1991). Like any such pinpoint-small detail, though, current NWP models can only parameterize (estimate) this based on larger-scale variables like the predicted air temperature, moisture, and wind. Within the model, these variables could theoretically be used in a nuanced way to estimate SLR with considerable accuracy, but this is rarely done in current operational NWP. Instead, external users like Pivotal Weather must estimate SLR themselves based on the more limited data provided publicly.

In late 2004, then-graduate student Evan Kuchera of the Air Force Weather Agency developed what has since become widely known as the Kuchera SLR method. It is one attempt to link model-predicted variables with SLR, and is a linear function of just one value at each horizontal grid point: the warmest temperature in the air column from the surface to 500 mb. Describing to us the origins of his approach, Evan said:

“I basically manually curve-fit data from various snow events I was aware of around that time [2004] until I was happy with it. Of note, the bifurcation at 271.16 K was to try to account for melting effects after the snow was on the ground for warmer events. So I really was trying to aim at the storm total snowfall that a COOP observer or member of the public would measure, not a pure, by-the-book snowfall properly measured and cleared from a snow board.” — Evan Kuchera

Shortly after the method was developed, Evan’s colleague Earl Barker (www.wxcaster.com) implemented it for his online NWP graphics, and the rest is history — “Kuchera snowfall” is now part of almost every winter weather enthusiast’s vocabulary and computed by numerous NWP graphics providers! Although this method has not been published in a peer-reviewed scientific journal, it has grown in popularity due to its straightforward formulation and subjective usefulness, and verification work presented at academic conferences has also supported its utility. Air temperature does not exclusively determine SLR in the real world, but several published studies have demonstrated a fairly strong relationship between low-to-mid level temperatures and observed SLRs (e.g., Roebber et al. 2003; Alcott and Steenburgh 2010). If NWP users are looking to implement a simple approximation of SLR that will not grind their data processing to a halt or demand obscure model diagnostics they lack access to, they’re unlikely to do much better than Kuchera.

Although Kuchera may depart from observed SLR significantly in some cases, it should still provide a first-order improvement over assuming a blanket 10:1 ratio. Its benefit may actually be most apparent when temperatures are borderline, a situation where it will correctly reduce snowfall below a 10:1 estimate, as Evan intended. Still, we emphasize that Kuchera is highly imperfect, as true SLRs depend on cloud and precipitation physics far more complex than a single statistic of the column temperature distribution. In the future, we are hopeful that NWP models may begin tracking snowfall internally using more physically sound diagnostics to estimate SLR at subhourly intervals, which could markedly improve snowfall forecasts over those derived from 10:1 and Kuchera SLRs.

Model snow depth

Finally, we would like to address the use of model snow depth. We plot snow depth for many models; additionally, for some, we plot an estimate for snowfall that leverages "accumulated positive snow depth change." The name “snow depth” may seem to suggest that it represents a highly accurate account of snow that accumulated on the ground during the model run, with non-snow precipitation removed and highly accurate SLRs applied. Unfortunately, this usually is not the case, leading to misconceptions in the weather community. The details of how snow depth is computed vary from model to model, even within the NCEP suite. Below are links to technical descriptions of snow cover, density, and depth for three different classes of NCEP models:

Of note: modeled precipitation is typically counted as all snow on the condition that more than half of what is falling is frozen, even if some or all is actually sleet. Furthermore, the SLR applied to this frozen precipitation is based solely on the near-ground air temperature for the NAM and RAP/HRRR; the situation is similar for the GDPS/RDPS, except that near-ground wind speed is also considered. In essence, these SLRs are just simpler and less accurate versions of what Kuchera does, considering only one temperature level instead of many. Thus, we cannot assume that snow depth has accrued in the model using an accurate SLR, nor that it only includes snow. [Note that an especially common error when using near-ground temperature to infer SLR is when a “warm nose” is present above very cold air at the surface, in which case SLR can be greatly overestimated; Kuchera addresses this scenario more realistically].

On the other hand, the snow depth variable does attempt to account for melting, compacting, and sublimation on a representative ground surface, and is even able to take advantage of minute-to-minute changes in the soil model state while doing so. So, in that regard, it can be more useful for estimating the ground accumulation at the end of a snowstorm than our 10:1 and Kuchera snowfall products. Still, this benefit is offset by the substantial pitfalls of using very imprecise SLRs and typically treating sleet as snow.

Conceptually, users should realize the snow depth variable is just a byproduct of internal model considerations around surface fluxes; this is a domain of physics where the precise snow depth may not be quite as crucial as the total mass of frozen precipitation covering the ground. As such, using model snow depth to forecast snowfall is subject to caveats and errors that are of similar magnitude to 10:1 or Kuchera, and it may perform even worse in some situations!

Explicit model snowfall

The HRRRv4 and RAPv5 (implemented at NCEP in December 2020) began providing explicit forecasts of snowfall; to our knowledge, this is a first in mainstream operational NWP. These forecasts can be found on Pivotal Weather as the “Total Accumulated Snowfall” parameter. Although the HRRR/RAP use a very simplistic SLR that is a strict function of 2-m AGL temperature, they are able to assess SLR and melting at every model time step, which affords far greater temporal precision than our post-processed products (e.g., Kuchera).

In addition, the NWS National Blend of Models applies relatively sophisticated SLRs to each input model’s QPF. Although NWS NBM precipitation forecasts are essentially post-processed ensemble means, and therefore may tend toward smoothing out maxima in forecasts beyond the first 12-24 hours, the NBM’s SLR approach is more advanced than any individual NWP model on Pivotal Weather.

Summary and practical recommendations

  1. Our snowfall products generally attempt to forecast the snow that falls to the surface; not necessarily the snow pile you see on the grass, interstate, your rooftop, or anywhere else after a long storm. There are some caveats with Kuchera (penalizes warm temperatures in part to account for on-ground melting) and accumulated positive depth change (explicitly accounts for melting, albeit with model data file frequency as a confounding factor) — but none of these products will consistently provide an accurate forecast of final ruler-measured snow depth, even if the model’s QPF and vertical profile are spot on!

  2. We recommend using the Kuchera snowfall products in most situations. Kuchera snowfall is certainly imperfect, but from our perspective, it is the least flawed practical option on the table right now for most models.

  3. Model snow depth can also be quite useful if your main forecast problem is the final ruler measurement on a natural surface, especially for events where melting is a major concern. This product sometimes includes sleet, however, and the SLRs it uses implicitly are probably less accurate than Kuchera much of the time.

  4. The 10:1 ratio snowfall products exist primarily as a very conservative estimate for legacy purposes, and because they are painless to compute. For certain datasets, we may not be able to compute Kuchera, leaving 10:1 as the only practical option. In the future, we may consider removing some or all 10:1 products, but they still may have value to some users as a baseline approach that is easy to compare between all datasets.

  5. In our view, the best path forward toward more accurate and less confusing NWP snow forecasts is for modeling centers to track snowfall internally during integration, rather than just liquid equivalent frozen hydrometeors. The current situation leaves it to end users like us to apply SLRs (and, in some cases, infer precipitation type) based on limited and temporally sparse data. Even a simplistic in-model SLR algorithm estimating the expected crystal type and riming (with the benefit of full-grid data and microphysics parameters), applied much more frequently during integration than publicly available data files, may yield drastically better snow forecasts than today’s. ADDENDUM: the RAP and HRRR have started providing explicit snowfall forecasts as of December 2020, so hopefully more models will follow suit in the near future!

Freezing rain

The situation with freezing rain in many ways mirrors snow: we know a certain amount of liquid precipitation is forecast to fall as rain into subfreezing near-ground air, but that does not mean the accretion on a given surface will match the liquid equivalent. In fact, ice accretion is almost always less than the liquid equivalent precipitation (Freezing Rain QPF) in significant ice storms — sometimes less than half, if the precipitation falls in heavy bursts or temperatures are close to freezing. Our Freezing Rain QPF maps should never be used verbatim as forecasts of accretion; they are simply a starting point in making such a forecast.

For Plus subscribers and for some models, we have recently implemented the Freezing Rain Accumulation Model (FRAM; Sanders and Barjenbruch 2016) as a rough estimate of accretion thickness on elevated horizontal surfaces. This product predicts the ice-to-liquid ratio (ILR) empirically from a large climatology and is rather analogous to Kuchera for snowfall, except that wind speed and precipitation rate are also considered in addition to (wet bulb) temperature. Bear in mind ice accretion is even trickier than snowfall accumulation and varies widely by surface type, shape, exposure, and orientation, so we urge responsibility and context in using even FRAM for public-facing forecasts.