System and method for forecasting snowfall probability distributions
Currently available weather forecasts, which include a specific snowfall accumulation or range, do not convey the probability that snowfall will be within the forecasted snowfall accumulation range, probabilities of other snowfall accumulation amounts, or a forecaster's level of confidence. A snowfall probability distribution forecasting system is disclosed that uses a rules-based process to leverage third party weather forecasts, including members of ensemble forecasts, to generate snowfall probability distributions forecasting the most likely snowfall accumulation range, the probability that snowfall accumulation will be within the most likely snowfall accumulation range, and probabilities that snowfall accumulation will be outside of the most likely snowfall accumulation range. To ensure consistency with the deterministic forecast, the snowfall probability distribution may be shifted based on a deterministic forecast. Because third party weather forecasts can produce a non-normal distribution of snowfall accumulation forecasts, the snowfall probability distribution may be normalized.
1. A method of forecasting snowfall accumulation, the method comprising:
identifying a predicted location and a predicted time period of a snowstorm;
receiving a plurality of weather forecasts for the predicted time period in the predicted location;
for each of the plurality of weather forecasts, determining a snowfall accumulation forecast;
forming an ensemble histogram by identifying a series of consecutive, non-overlapping snowfall accumulation ranges and determining how many of the snowfall accumulation forecasts are in each of the snowfall accumulation ranges;
calculating a probability density function representing the relative likelihood of snowfall accumulation amounts based on the ensemble histogram;
forming a snowfall probability distribution based on the probability density function, the snowfall probability distribution including:
a most likely snowfall accumulation range and a probability that snowfall accumulation in the predicted location over the predicted time period will be within the most likely snowfall accumulation range;
at least one higher snowfall accumulation range and a probability that snowfall accumulation in the predicted location over the predicted time period will be within the higher snowfall accumulation range; and
at least one lower snowfall accumulation range and a probability that snowfall accumulation in the predicted location over the predicted time period will be within the lower snowfall accumulation range;
generating a snowfall probability forecast that includes the most likely snowfall accumulation range and the probability that snowfall accumulation in the predicted location over the predicted time period will be within the most likely snowfall accumulation range; and
outputting the snowfall probability forecast.
2. The method of claim 1 , further comprising:
identifying a deterministic snowfall accumulation forecast for the predicted location over the time period;
creating an adjusted probability density function by:
making a mode of the adjusted probability density function equal to the deterministic snowfall accumulation forecast;
calculating a difference between a mean of the probability density function and the deterministic snowfall accumulation forecast; and
shifting the probability density function based on the difference between the mean of the probability density function and the deterministic snowfall accumulation forecast, wherein the snowfall probability forecast is based on the adjusted probability density function.
3. The method of claim 1 , further comprising:
creating a normalized probability density function by moving data points from far tails of the probability density function toward the mean of the probability density function until the probabilities of each snowfall accumulation range decrease from the most likely snowfall accumulation range to the tails of the snowfall probability distribution,
wherein the snowfall probability forecast is based on the normalized probability density function.
4. The method of claim 1 , wherein the snowfall probability forecast further includes:
the higher snowfall accumulation range and the probability that snowfall accumulation in the predicted location over the predicted time period will be within the higher snowfall accumulation range; and
the lower snowfall accumulation range and the probability that snowfall accumulation in the predicted location over the predicted time period will be within the lower snowfall accumulation range.
5. The method of claim 4 , wherein the snowfall probability forecast further includes: a highest snowfall accumulation range and the probability that snowfall accumulation in a predicted location over the predicted time period will be within the highest snowfall accumulation range; and a lowest snowfall accumulation range and a probability that snowfall accumulation in the predicted location over the predicted time period will be within the lowest snowfall accumulation range.
6. The method of claim 1 , wherein the snowfall accumulation forecasts are determined based on the plurality of weather forecasts using a Cobb method.
7. The method of claim 6 , wherein:
each of the plurality of weather forecasts include a forecasted precipitation amount, a forecast forecasted temperature, a forecasted vertical motion, and a forecasted relative humidity; and
the snowfall accumulation forecasts are determined by:
calculating a snow-to-liquid ratio based on the forecasted temperature, the forecasted vertical motion, and the forecasted relative humidity; and
multiplying the forecast precipitation amount by the snow-to-liquid ratio.
8. The method of claim 1 , wherein the snowfall probability forecast is output to a remote device for display to a user via a graphical user interface.
9. The method of claim 1 , wherein the snowfall probability forecast is output to control a remote device.
10. The method of claim 1 , wherein the plurality of weather forecasts includes at least one of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS), one or more members of the Global Ensemble Forecast System (GEFS), one or more members of the NCEP Short Range Ensemble Forecast (SREF), or one or more members of the European Centre for Medium-Range Weather (ECMWF) ensemble.
11. A system, comprising:
a forecast database that stores a plurality of weather forecasts;
an analysis unit that:
identifies a predicted location and a predicted time period of a snowstorm;
for each of the plurality of weather forecasts, determines a snowfall accumulation forecast;
forms an ensemble histogram by identifying a series of consecutive, non-overlapping snowfall accumulation ranges and determining how many of the snowfall accumulation forecasts are in each of the snowfall accumulation ranges;
calculates a probability density function representing the relative likelihood of snowfall accumulation amounts based on the ensemble histogram;
forms a snowfall probability distribution based on the probability density function, the snowfall probability distribution including:
a most likely snowfall accumulation range and a probability that snowfall accumulation in the predicted location over the predicted time period will be within the most likely snowfall accumulation range;
at least one higher snowfall accumulation range and a probability that snowfall accumulation in the predicted location over the predicted time period will be within the higher snowfall accumulation range; and
at least one lower snowfall accumulation range and a probability that snowfall accumulation in the predicted location over the predicted time period will be within the lower snowfall accumulation range;
generates a snowfall probability forecast that includes the most likely snowfall accumulation range and the probability that snowfall accumulation in the predicted location over the predicted time period will be within the most likely snowfall accumulation range; and
outputs the snowfall probability forecast.
12. The system of claim 11 , wherein:
the forecast database further includes a deterministic snowfall accumulation forecast for the predicted location over the time period; and
the analysis unit is further configured to:
create an adjusted probability density function by:
making a mode of the adjusted probability density function equal to the deterministic snowfall accumulation forecast;
calculating a difference between a mean of the probability density function and the deterministic snowfall accumulation forecast; and
shifting the probability density function based on the difference between the mean of the probability density function and the deterministic snowfall accumulation forecast,
wherein the snowfall probability forecast is based on the adjusted probability density function.
13. The system of claim 11 , wherein the analysis unit is further configured to:
create a normalized probability density function by moving data points from far tails of the probability density function toward the mean of the probability density function until the probabilities of each snowfall accumulation range decrease from the most likely snowfall accumulation range to the tails of the snowfall probability distribution,
wherein the snowfall probability forecast is based on the normalized probability density function.
14. The system of claim 11 , wherein the snowfall probability forecast further includes:
the higher snowfall accumulation range and the probability that snowfall accumulation in the predicted location over the predicted time period will be within the higher snowfall accumulation range; and
the lower snowfall accumulation range and the probability that snowfall accumulation in the predicted location over the predicted time period will be within the lower snowfall accumulation range.
15. The system of claim 14 , wherein the snowfall probability forecast further includes:
a highest snowfall accumulation range and a probability that snowfall accumulation in the predicted location over the predicted time period will be within the highest snowfall accumulation range; and
a lowest snowfall accumulation range and a probability that snowfall accumulation in the predicted location over the predicted time period will be within the lowest snowfall accumulation range.
16. The method of claim 11 , wherein the analysis unit is further configured to determine the snowfall accumulation forecasts based on the plurality of weather forecasts using a Cobb method.
17. The method of claim 16 , wherein:
each of the plurality of weather forecasts include a forecasted precipitation amount, a forecast forecasted temperature, a forecasted vertical motion, and a forecasted relative humidity; and
the analysis unit is configured to determine the snowfall accumulation forecasts by:
calculating a snow-to-liquid ratio based on the forecasted temperature, the forecasted vertical motion, and the forecasted relative humidity; and
multiplying the forecast precipitation amount by the snow-to-liquid ratio.
18. The method of claim 11 , wherein the analysis unit outputs the snowfall probability forecast to a remote device for display to a user via a graphical user interface.
19. The method of claim 11 , wherein the analysis unit outputs the snowfall probability forecast to control a remote device.
20. The method of claim 11 , wherein the plurality of weather forecasts includes at least one of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS), one or more members of the Global Ensemble Forecast System (GEFS), one or more members of the NCEP Short Range Ensemble Forecast (SREF), or one or more members of the European Centre for Medium-Range Weather (ECMWF) ensemble.
21. A non-transitory computer readable storage medium storing instructions that, when executed by a computer processor, cause a computing system to:
identify a predicted location and a predicted time period of a snowstorm;
receive a plurality of weather forecasts for the predicted time period in the predicted location;
for each of the plurality of weather forecasts, determine a snowfall accumulation forecast;
form an ensemble histogram by identifying a series of consecutive, non-overlapping snowfall accumulation ranges and determining how many of the snowfall accumulation forecasts are in each of the snowfall accumulation ranges;
calculate a probability density function representing the relative likelihood of snowfall accumulation amounts based on the ensemble histogram;
form a snowfall probability distribution based on the probability density function, the snowfall probability distribution including:
a most likely snowfall accumulation range and a probability that snowfall accumulation in the predicted location over the predicted time period will be within the most likely snowfall accumulation range;
at least one higher snowfall accumulation range and a probability that snowfall accumulation in the predicted location over the predicted time period will be within the higher snowfall accumulation range; and
at least one lower snowfall accumulation range and a probability that snowfall accumulation in the predicted location over the predicted time period will be within the lower snowfall accumulation range;
generate a snowfall probability forecast that includes the most likely snowfall accumulation range and the probability that snowfall accumulation in the predicted location over the predicted time period will be within the most likely snowfall accumulation range; and
output the snowfall probability forecast.