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Realtime forecasting of snowfall using a neural Realtime forecasting of snowfall using a neural network Paul J. Roebber, Melissa R. Butt and Sarah J. Reinke Atmospheric Science Group,

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  • 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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