Methodologies for converting NWP outputs into QPF and PQPF
 Norman (Wes) Junker National Centers for Environmental Prediction Hydrometeorological Prediction Center Camp Springs, MD

PQPF
 Is there one best way to do PQPF? Keep man in the loop? Statistical methods applied to model output Calibrated probabilities from Enembles? Point versus the probability of occurrence within some area?

Krzysztofowicz approach
 Relies on calibration of subjective forecasts of probability. Need rain/no rain probability Uses conditional exceedence fractiles: The X50, or amount where there is an equal chance of getting more or less precipitation that that number the X25,  amount the forecaster thinks there is a 25% percent chance of exceeding that value. Can then use curve to set probabilities for any amount.

MODEL OUTPUT STATISTICAL METHODS THAT CAN BE USED TO DEVELOP PROBABILITIES
 LINEAR REGRESSION (MDL MOS) LOGISTIC REGRESSION (NON LINEAR) USES SAME TYPE OF FUNCTIONAL RELATIONSHIPS AS NEURAL NETWORKS BUT HAS NO HIDDEN LAYERS DISCRIMINANT ANALYSIS NEURAL NETWORKS (NON LINEAR) CLASSIFIER SYSTEM (IF THEN STATEMENTS, SURVIVAL OF THE FITTEST)

Brier skill scores for six statistical methods for 3 precipitation thresholds

Non linear techniques like logistic regression improve forecasts for the higher probabilities (figures from Applequist et al.)

VERY USEFUL FOR LIGHTER THRESHOLDS BUT TREND TOWARDS CLIMATOLOGY AT LONGER RANGES

STATISTICS METHODS

Ensemble forecasting
 Another way to assess probabilities for various thresholds. Provides a method to take into account the predictability of the pattern. Need to perturb initial conditions and model physics. You assume each member has equal skill this might be an incorrect assumption, if you are not careful how you perturb the physics.

Bias (Forecast precipitation/Observed precipitation) for various models during September 2000 for northeast

Perfect Prog approach, Assume members  are unbiased. Can show where at least 60% of the members exceeded a threshold.

Man-machine mix

A better way of using enemble forecasts to generate probability forecasts
 Develop rank histograms based on the precipitation forecast by each of the members. however the shape of the  histograms change significantly based on the variability of the ensemble members. So separate histograms need to be developed for high, medium and low variability cases. How do you handle the heaviest 10%, the extreme rainfall events?

The brier scores for higher thresholds were higher for forecasts applying various statistical methods to ensemble forecasts than those from the NGM MOS

If ensemble forecasts are used, which more cost effective
 More members with lower resolution? Fewer members with higher resolution?

Slide 16

Accuracy of model forecasts decreases rapidly as threshold increases and as the scale of the event decreases

Because higher amounts or thresholds are relatively rare, it is difficult getting a big enough sample to calibrate forecasts using traditional statistical techniques. Verification of 24 hour QPF for various thresholds

For extreme events is there a better way?

Or is it?  How Good Are the Forecasts?

What about assessing probability of precipitation occurring anywhere within a circle or hexagon? The probabilities would be influenced by the density of observations,  but your probabilities might be high enough to allow emergency managers to assess the risk within their area.

Then how do we approach forecasting QPF , Probabilistically?
 For lighter, more frequent events. MOS-type non-linear statistical approaches MAKE SENSE. Provide WELL CALIBRATED  probabilities. Calibrated ensemble methods also work well may be more computationally expensive in long run. Statistical-man mix may be an option. Since a forecaster might be able to take into account the predictability of the pattern. a person might be able to combine information from ensemble and statistical methods to adjust POPS (this is already being done at HPC in the 3-7 day range).

For high end, rare events
 point probabilities may not always make sense.  Point probabilities will always be very low,  possibly too low for emergency managers to act. Other methods need to be explored. One possibility- develop probabilities of various thresholds within a circle of some radius.  Such forecasts might be useful to emergency managers helping them decide when to put their staffs on alert Ensemble forecasts, combined with statistical methods might be able to provide such probabilities and might be used to determine the size of the circle.   or A single non-hydrostatic model run might provide enough guidance to develop such probabilities if the radius of the circle is based on error characteristics of the model. The phase error helps determine size of circle. the magnitude of the precipitation forecast be used to help determine probabilities of occurrence within the circle for various thresholds.