Realtime forecasting of snowfall using a
neural network
Paul J. Roebber, Melissa R. Butt and Sarah J. Reinke
Atmospheric Science Group, Department of Mathematical Sciences,
University of Wisconsin at Milwaukee, Milwaukee, Wisconsin
Thomas J. Grafenauer
National Oceanic and Atmospheric Administration/National Weather Service Grand
Forks, North Dakota
Weather and Forecasting
Submitted as a Note: April 11, 2006
___________________________________________________________
Corresponding author address: Paul J. Roebber, Department of Mathematical Sciences,
University of Wisconsin at Milwaukee, 3200 N. Cramer Ave., Milwaukee, WI 53211. E-
mail: roebber@uwm.edu
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Abstract
A set of 53 snowfall reports were collected in realtime from the 2004-05 and 2005-06
cold seasons. Three snowfall amount forecast methods were tested: neural network,
surface temperature based lookup table, and climatological snow ratio. Standard
verification methods (mean, median, bias, root mean square error) and a new method that
places the forecasts in the context of municipal snow removal situation and assesses
forecast credibility are used. Results suggest that the neural network method performs
best, owing to the inverse relationship in the network (and actuality) between melted
liquid equivalent and snow ratio; hence, the QPF problem is compensated rather than
amplified when converting to snowfall amounts. This analysis should be extended to a
larger selection of reports, which it is anticipated will be accomplished in conjunction
with efforts currently ongoing at the NOAA Hydrometeorological Prediction Center
(HPC).
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1. Introduction
Recently, there have been attempts to provide improved guidance to forecasters
concerning forecasts of snowfall (Roebber et al. 2003; Dube 2003; Cobb and
Waldstreicher 2005; Baxter et al. 2005; Ware et al. 2006). Roebber et al. (2003), in a
carefully validated study, conducted a principal component analysis of radiosonde and
surface data and identified seven factors that influence the diagnosis of snow ratio: solar
radiation/month, low- to mid level temperature, mid- to upper-level temperature, low- to
mid-level relative humidity, mid-level relative humidity, upper-level relative humidity,
and external compaction, as measured by surface wind speed and liquid equivalent
precipitation amount. They then constructed ten-member ensembles of artificial neural
networks which substantially improved the diagnosis of snow-ratio class compared to
then existing techniques (ten-to-one ratio, sample climatology, NWS new snowfall to
estimated meltwater conversion table). In Fall 2004, this ensemble system was made
available on the web (http://sanders.math.uwm.edu/cgi-bin-snowratio/sr_intro.pl), using
soundings derived from the NCEP operational forecast models (BUFKIT).
In this note, we report on tests of this system performed in the cold seasons of
2004-05 and 2005-06 in a forecast rather than diagnostic context. Specifically, QPF from
the output of a realtime numerical model (ETA or GFS) is used to determine the amount
of liquid equivalent precipitation; then, forecast soundings obtained from the ETA model
are used within the neural network framework described in Roebber et al. (2003) and
made available on the web site to diagnose the snow-ratio class; finally, the snowfall
amount is derived from the previous two steps by converting the snow ratio class to a
number using a simple procedure. Details of the datasets and procedure are described in
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section 2, while the results of the realtime forecast application of this technique are
reported in section 3. Concluding remarks are provided in section 4.
2. Data and methods
The dataset is comprised of a collection of 53 reports from the 2004-05 and 2005-
06 cold seasons across the CONUS east of the Rocky Mountains (Fig. 1). Although many
of the sites are collocated with a radiosonde launch, the only criterion for these events
was that the observed new snow be at least 2.5 cm (1 inch; hereafter, English units will
be used to reflect the operational orientation of this work). The mean and median
snowfall (liquid equivalent) was 5.4 (0.35) and 3.1 (0.18) inches, respectively (Table 1),
while the maximum observed event featured a snowfall of 24 inches. The mean and
median snow ratio for the dataset was 19.9:1 and 18.2:1, respectively.
The procedure used to make a snowfall amount forecast is as follows. First, 12-36
hour ETA or GFS forecasts of surface wind speed, liquid equivalent precipitation and the
vertical profiles of temperature and humidity were used as inputs to the ensemble of
neural networks of Roebber et al. (2003) to obtain a forecast snow-ratio class. The class
was then assigned according to the highest individual snow-ratio class probability (e.g.,
with probabilities of 0.10, 0.30 and 0.60 for heavy, average and light, respectively, the
assigned class would be light). Second, a numerical snow ratio was assigned based on a
representative value for that class. Specifically, for "heavy", a snow-ratio of 8:1 was
assumed; for "average", a snow-ratio of 13:1 was assumed; for "light", if the probability
in that class was less than 0.67, 18:1 was assumed, otherwise 25:1 was assumed. This
differentiation for the light class is based on the observation, documented in the dataset
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collected by Roebber et al. (2003), that higher snow ratios are correlated with higher
network probabilities for the light class. Third, the snow-depth for each 6-hour period of
the event was then computed based on the product of the snow-ratio obtained for that
period in the second step and the model QPF. Hence, for a snow-ratio of "average" with
0.40 inches QPF, the forecast snow amount in that 6-hour period would be 13 times 0.40
or 5.2 inches. Analysis of the results from the two datasets relative to the NWS new
snowfall to estimated meltwater conversion table (a baseline standard as shown in
Roebber et al. 2003; hereafter denoted as “Lookup”) is reported in section 3.
3. Results
Table 1 shows that both QPF and snow ratio errors contribute to the overall
snowfall depth errors. For this sample of 53 reports, the model QPF reveals an
overforecast bias. For the Lookup, this combines with disastrous consequences with a
high bias in snow ratio (the result of a number of reports with cold surface temperatures
but warm air aloft) to produce a substantial overforecast bias of snowfall amount. In
contrast, a distinct feature of the network methodology is that there are compensating
errors that result from the physical process of compaction. Specifically, when the QPF is
too high, the forecast snow-ratio will be too low, and their product will remain relatively
bounded compared to the unconstrained Lookup. The reverse is also true: underforecasts
of liquid equivalent will lead to an overestimation of snow ratio, and their product will
remain bounded. Overall, the network shows only a slight overforecast bias in snow
amount and the lowest overall root mean square error (RMSE). This strongly suggests
that the network approach can add significant utility to snowfall forecasts, relative to the
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Lookup baseline. It should be noted that the NOAA Hydrometeorological Prediction
Center has begun evaluation of a variety of snowfall forecast techniques (Keith Brill
2005, personal communication). Although data are unavailable at this time to evaluate the
network approach, these data indicate that the climatological snow ratio approach [the
product of the climatological snow ratio of a particular site as obtained from Baxter et al.
(2005) times the QPF] provides useful guidance. Consistent with this, for the 2004-05
and 2005-06 dataset reported herein, the climatological approach provides the smallest
mean and median snowfall errors. Also notable, however, is the considerably larger
RMSE, suggesting that for key events, the effectiveness of this approach may be reduced
by large forecast errors.
To examine these impacts in an operational context, we place the dataset results in
the evaluative framework of the municipal snow removal problem. Although this is only
one aspect of the overall impact of snowstorms, it is a useful context in which to examine
several operationally important issues that are not completely addressed by the usual
statistics.
Details of the methodology are presented in the Appendix. An overview follows.
The core mission for municipal snow removal is to insure that the roadways are cleared
and safe for travel. Whatever amount that is required to achieve this is ultimately spent
(sometimes with adverse consequences to the overall budget). If the roads are not cleared,
then the core mission has been failed. As a result, individuals in this arena are risk averse
(e.g., Stewart et al. 2004).
Accordingly, the measure that we employ incorporates costs, but does so in the
context of what we term forecast “credibility.” The first step is to compute an estimate of
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