Statistical Weather Forecasting

Statistical Weather Forecasting Statistical Weather Forecasting - Start

2015-09-21 93K 93 0 0

Statistical Weather Forecasting - Description

Independent Study. Daria. . Kluver. From Statistical Methods in the Atmospheric Sciences by Daniel . Wilks. Perfect . Prog. and MOS. Classical statistical forecasts for projections over a few days are not used. Current dynamical NWP models are more accurate.. ID: 136208 Download Presentation

Download Presentation

Statistical Weather Forecasting

Download Presentation - The PPT/PDF document "Statistical Weather Forecasting" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.

Presentations text content in Statistical Weather Forecasting


Statistical Weather Forecasting

Independent Study



From Statistical Methods in the Atmospheric Sciences by Daniel



Perfect Prog and MOS

Classical statistical forecasts for projections over a few days are not used. Current dynamical NWP models are more accurate.

2 types of classical statistical


forecasting are used to improve aspects of NWP forecasts. (by post-processing the NWP data)

Both methods used large multiple regression equations.


3 reasons why statistical reinterpretation of dynamical NWP output is useful for practical weather forecasting:

1. NWP models simplify and homogenize



Statistical relationships can be developed


NWP output and desired forecast quantities.

NWP model forecasts are subject to error. To the extent that these errors are systematic, statistical forecasts based on NWP info can correct forecast biases.

3. NWP models are deterministic. Using NWP info in conjunction with statistical methods allows quantification of the uncertainty associated with different forecast situations.


1st Statistical approach for dealing with forecasts from NWP

Perfect Prog (Klein et al. 1959)Takes NWP model forecasts for future atmosphere assuming them to be perfectPerfect prog regression equations are similar to classical regression equations except they do not incorporate any time lag.


equations specifying tomorrows


are developed using tomorrow’s predictor values.

If the NWP forecasts for tomorrow’s predictors

really are

perfect, the perfect-


regression equations should provide very good forecasts.


2nd Statistical approach

Model Output Statistics (MOS)Preferred because it can include directly in the regression eqns the influences of specific characteristics of different NWP models at different projections into the future. To get MOS forecast eqns you need a developmental data set with historical records of predictand, and records of the forecasts by NWP model.Separate MOS forecast equations must by made for different forecast projections.



is tomorrows 1000-800mb thickness as forecast today by a certain NWP model.


Advantages and Disadvantages of Perfect-


and MOS:


Perfect Prog


Large developmental sample (fit using historical climate data)

Equations developed without NWP info, so changes to NWP models don’t require changes in regression equations

Improving NWP models will improve forecasts

Same equations can be used with any NWP models


Potential predictors must be well forecast by the NWP model



Advantages:Model-calculated, but un-observed quantities can be predictorsSystematic errors in the NWP model are accounted forDifferent MOS equations required for different projection timesMethod of choice when practicalDisadvantages:Requires archived records (several years) of forecast from NWP model to develop, and models regularly undergo changes. Different MOS equations required for different NWP models


Operational MOS Forecasts

Example: FOUS14MOS equations underlying the FOUS14 forecasts are seasonally stratified: warm season (Apr- Sep) and cool season (Oct-Mar).A finer stratification is preferable with sufficient developmental dataForecast equations (except t, td and winds) are regionalized. Some MOS equations contain predictors representing local climatological valuesSome equations are developed simultaneously to enhance consistency (example: a td higher than t doesn’t make sense)


Ensemble Forecasting


First, lets talk about the birth of Chaos…

LorenzRoyal McBeeSensitive dependence on initial conditions

Lorenz’s data


What does Chaos have to do with NWP?

The atmosphere can never be completely observed

A NWP model will always begin calculating forecasts from a state slightly different from the real atmosphere.

These models have the property of sensitive dependence on initial conditions.


Stochastic Dynamical Systems in Phase Space

Stochastic dynamic prediction-

physical laws are deterministic, but the equations that describe these laws must operate on initial values not known with certainty

can be described by a joint probability distribution.

This process yields, as forecasts, probability distributions describing uncertainty about the future state of the atmos.


Phase space

Phase space is used to visualize the initial and forecast probability distributions

Phase space

– geometrical representation of the hypothetically possible states of a dynamical system, where each of the coordinate axes defining this geometry pertains to one of the forecast variables of the system.


Pendulum Animation

Lorenz attractor and the



Phase space of a atmospheric model has many more dimensions.

Simple model has 8 dimensions!

Operational NWP models have a million dimensions

More Complications:

The trajectory is not attracted to a single point like the pendulum

Pendulum did not have sensitive dependence to initial conditions.


Uncertainty about initial state of the atmosphere can be conceived of as a probability distribution in phase space.

The shape of the initial distribution is stretched and distorted at longer forecast projections.

Also, remember there is no single attractor.

A single point in phase space is a unique weather situation.

The collection of possible points that equal the attractor can be interpreted as the climate of the NWP model.


Ensemble Forecasts

The ensemble forecast procedure begins by drawing a finite sample from the probability distribution describing the uncertainty of the initial state of the atmos.Members of the point cloud surrounding the mean estimated atmospheric state are picked randomlyThese are the ensemble of initial conditionsThe movement of the initial-state probability distribution through phase space is approximated by this sample’s trajectoriesEach point provides the initial conditions for a separate run of the NWP model.


Ensemble Average and Ensemble Dispersion

To obtain a forecast more accurate than 1 model run with the best estimate of the initial state of the atmosphere, members of the ensemble are averaged.

The atmospheric state corresponding to the center of the ensemble in phase space will approximate the center of the stochastic dynamic probability distribution at the future time.

Doing this with weather models averages out elements of disagreement and emphasizes shared features.

Over long time periods, the average smoothes out and looks like climatology.

We get an idea of the uncertainty

More confidence if the dispersion is small

Formally calculated by ensemble standard deviation


Graphical Display of Ensemble Forecast Information

Current practice includes 3 general types of graphics:

displays of raw ensemble output,

displays of statistics summarizing the ensemble distribution, and

displays of ensemble relative frequencies for selected predictands.






Effects of Model Errors

2 types of model errors:1. models operate at a lower resolution than reality2. certain physical processes- predominantly those operating at scales smaller than the model resolution- are represented incorrectly.To represent the residuals of fig 6.31, random numbers can be added to the parameterization function. Called “stochastic physics” and used at ECMRF

The parameterization (smooth curve) does not fully capture the range of behaviors for the parameterized process that are actually possible (scatter of points)


Statistical Postprocessing: Ensemble MOS

You can do MOS post processing on the ensemble mean:

There is still research on how best to do this.

Multiple ways, which involve probability distributions, which will not be discussed here.


Subjective Probability Forecasts

The nature of subjective forecasts:Subjective integration and interpretation of objective forecast info forecast guidance.Includes deterministic forecast info from NWP, MOS, current obs, radar, sat, persistence info, climate data, individual previous experiences.Subjective forecasting – the distillation by a human forecaster of disparate and sometimes conflicting info.A subjective forecast- one formulated on the basis of the judgment of 1 or more individuals. Good one will have some measure of uncertainty.


Assessing Discrete Probabilities

Tricks forecasters can use, like spinning wheels or playing betting games.


Chapter 7: Forecast Verification


Purposes of Forecast Verification

Forecast verification-

the process of assessing the quality of forecasts.

Any given verification data set consists of a collection of forecast/observation pairs whose joint behavior can be characterized in terms of the relative frequencies of the possible combinations of forecast/observation outcomes.

This is an empirical joint distribution

It is important to do verification to improve methods, evaluate forecasters, estimate error characteristics.


The Joint Distribution of Forecasts and Observations

Forecast = Observation = The joint distribution of the forecasts and observations is denotedThis is a discrete bivariate probability distribution function associating a probability with each of the IxJ possible combinations of forecast and observation.


The joint distribution can be factored in two ways, the one used in a forecasting setting is:

Called calibration-refinement factorizationThe refinement of a set of forecasts refers to the dispersion of the distribution p(yi)

If y


has occurred, this is the probability of o

j happening.Specifies how often each possible weather event occurred on those occasions when the single forecast yi was issued, or how well each forecast is calibrated.

The unconditional distribution, which specifies the relative frequencies of use of each of the forecast values yi sometimes called the refinement of a forecast.


Scalar Attributes of Forecast Performance

Partial list of scalar aspects, or attributes, of forecast quality


Average correspondence between individual forecasts and the events they predict.


The correspondence between the average forecast and the average observed value of the




Pertains to the relationship of the forecast to the average observation,

for specific values of the forecast.


The degree to which the forecasts sort the observed events into groups that are different from each other.


Converse of resolution, pertains to differences between the conditional averages of the forecasts for different values of the observation.



the unconditional distribution (relative frequencies of use) of the forecasts.


Forecast Skill

Forecast skill- the relative accuracy of a set of forecasts, wrt some set of standard control, or reference, forecast (like climatological average, persistence forecasts, random forecasts based on climatological relative frequencies)Skill score- a percentage improvement over reference forecast.


Accuracy of reference

Accuracy that would be achieved by a perfect forecast.


Next time

Continue to talk about forecast verificationLooking at some forecast dataNWS vs vs climatology2x2 contingency tablesConversion from probabilistic to nonprobabilisticQuantile plotsProbability forecasts of discrete predicandsProbability forecasts for continuous predictandsAccuracy measures, Skill scores, Brier Score, MSEMulti-category events

About DocSlides
DocSlides allows users to easily upload and share presentations, PDF documents, and images.Share your documents with the world , watch,share and upload any time you want. How can you benefit from using DocSlides? DocSlides consists documents from individuals and organizations on topics ranging from technology and business to travel, health, and education. Find and search for what interests you, and learn from people and more. You can also download DocSlides to read or reference later.