Verification Introduction Holly C. Hartmann

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Verification Introduction

Holly C. Hartmann

Department of Hydrology and Water ResourcesUniversity of Arizona

[email protected]

RFC Verification Workshop, 08/14/2007

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• General concepts of verification• Think about how to apply to your operations• Be able to respond to and influence NWS verification program• Be prepared as new tools become available• Be able to do some of their own verification • Be able to work with researchers on verification projects• Contribute to development of verification tools (e.g., look at various options)• Avoid some typical mistakes

Goals

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1. Introduction to Verification- Applications, Rationale, Basic Concepts- Data Visualization and Exploration- Deterministic Scalar measures

2. Categorical measures – KEVIN WERNER- Deterministic Forecasts- Ensemble Forecasts

3. Diagnostic Verification- Reliability- Discrimination- Conditioning/Structuring Analyses

4. Lab Session/Group Exercise- Developing Verification Strategies- Connecting to Forecast Operations and Users

Agenda

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Why Do Verification? It depends…

Administrative: logistics, selected quantitative criteria Operations: inputs, model states, outputs, quick!Research: sources of error, targeting research Users: making decisions, exploit skill, avoid mistakes

Concerns about verification?

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Need for Verification Measures

Verification statistics identify- accuracy of forecasts- sources of skill in forecasts- sources of uncertainty in forecasts- conditions where and when forecasts are

skillful or not skillful, and why

Verification statistics then can inform- improvements in terms of forecast skill

and decision making with alternate forecast sources (e.g., climatology, persistence, new forecast systems)

Adapted from: Regonda, Demargne, and Seo, 2006

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Skill versus Value

Assess quality of forecast systemi.e. determine skill and value of forecast

A forecast has skill if it predicts the observed conditions well according to some objective or subjective criteria.

A forecast has value if it helps the user to make better decisions than without knowledge of the forecast.

• Forecasts with poor skill can be valuable (e.g. extreme event forecasted in wrong place)

• Forecasts with high skill can be of little value (e.g. blue sky desert)Credit: Hagedorn (2006) and Julie Demargne

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Common across all groupsUninformed, mistaken about forecast interpretationUse of forecasts limited by lack of demonstrated forecast skillHave difficulty specifying required accuracy

Unique among stakeholdersRelevant forecast variables, regions (location & scale), seasons, lead times, performance characteristicsTechnical sophistication: base probabilities, distributions, mathRole of of forecasts in decision making

Common across many, but not all, stakeholdersHave difficulty distinguishing between “good” & “bad” productsHave difficulty placing forecasts in historical context

Stakeholder Use of HydroClimate Info & Forecasts

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Forecast evaluation conceptsAll happy families are alike;

each unhappy family is unhappy in its own way.

-- Leo Tolstoy (1876)

All perfect forecasts are alike; each imperfect forecast

is imperfect in its own way. -- Holly Hartmann (2002)

What is a Perfect Forecast?

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“Today’s high will be 76 degrees, and it will be partly cloudy, with a 30% chance of rain.”

Deterministic

Categorical

Probabilistic

Different Forecasts, Information, Evaluation

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Deterministic

Categorical

ProbabilisticProbabilisticCategoricalDeterministic

How would you evaluate each of these?


RainNo rain

30%

76°

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Deterministic

Categorical

Probabilistic


Standard hydrograph

Deterministic

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ESP Forecasts: User preferences influence verification

From: California-Nevada River Forecast Center

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Deterministic

Bias

Correlation

RMSE

• Standardized RMSE

• Nash-Sutcliffe

Linear Error in Probability Space

CategoricalHit Rate

Surprise rateThreat ScoreGerrity ScoreSuccess Ratio

Post-agreementPercent Correct

Pierce Skill ScoreGilbert Skill ScoreHeidke Skill Score

Critical Success indexPercent N-class errors

Modified Heidke Skill ScoreHannsen and Kuipers Score

Gandin and Murphy Skill Scores…

Probabilistic

Brier Score

Ranked Probability Score

Distributions-oriented Measures

• Reliability

• Discrimination

• Sharpness

So Many Evaluation Criteria!

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RFC Verification System: Metrics

CATEGORIES DETERMINISTIC FORECAST VERIFICATION METRICS

PROBABILISTIC FORECAST VERIFICATION METRICS

1. Categorical(predefined threshold, range of values)

Probability Of Detection (POD), False Alarm Ratio (FAR), Probability of False Detection (POFD)Lead Time of Detection (LTD), Critical Success Index (CSI), Pierce Skill Score (PSS), Gerrity Score (GS)

Brier Score (BS), Rank Probability Score (RPS)

2. Error (accuracy)

Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Error (ME), Bias (%), Linear Error in Probability Space (LEPS)

Continuous RPS

3. Correlation Pearson Correlation Coefficient, Ranked correlation coefficient, scatter plots

4. Distribution Properties Mean, variance, higher moments for observation and forecasts

Wilcoxon rank sum test, variance of forecasts, variance of observations, ensemble spread, Talagrand Diagram (or Rank Histogram)

Source: Verification Group, courtesy J. Demargne

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RFC Verification System: Metrics

CATEGORIES DETERMINISTIC FORECAST VERIFICATION METRICS

PROBABILISTIC FORECAST VERIFICATION METRICS

5. Skill Scores (relative accuracy over reference forecast)

Root Mean Squared Error Skill Score (SS-RMSE) (with reference to persistence, climatology, lagged persistence), Wilson Score (WS), Linear Error in Probability Space Skill Score (SS-LEPS)

Rank Probability Skill Score, Brier Skill Score (with reference to persistence, climatology, lagged persistence)

6. Conditional Statistics (based on occurrence of specific events)

Relative Operating Characteristic (ROC), reliability measures, discrimination diagram, other discrimination measures

ROC and ROC Area, other resolution measures, reliability diagram, discrimination diagram, other discrimination measures

7. Confidence (metric uncertainty)

Sample size, Confidence Interval (CI)

Ensemble size, sample size, Confidence Interval (CI)

Source: Verification Group, courtesy J. Demargne

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Accuracy - overall correspondence between forecasts and observations

Bias - difference between average forecast and average observation

Consistency - forecasts don’t waffle around

Possible Performance Criteria

Good consistency

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Accuracy - overall correspondence between forecasts and observations

Bias - difference between average forecast and average observation

Consistency - forecasts don’t waffle around

Sharpness/Refinement – ability to make bullish forecast statements

Not Sharp

Sharp

Possible Performance Criteria

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What makes a forecast “good”?

Forecasts should agree with observations, with few large errors

Accuracy

Forecast mean should agree with observed mean Bias

Linear relationship between forecasts andobservations

Association

Forecast should be more accurate than low-skilled reference forecasts (e.g., random chance, persistence, or climatology)

Skill

Adapted from : Ebert (2003)

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What makes a forecast “good”?

Binned forecast values should agree with binned observations (agreement between categories)

Reliability

Forecast can discriminate between events & non-events

Resolution

Forecast can predict with strong probabilities (i.e., 100% for event, 0% for non-event)

Sharpness

Forecast represents the associated uncertainty Spread (Variability)

Adapted from : Ebert (2003)

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False Alarms Surpriseswarning without event event without warning

No fire

“False Alarm Ratio” “Probability of Detection”A forecaster’s fundamental challenge

is balancing these two. Which is more important?

Depends on the specific decision context…

Forecasting Tradeoffs

Forecast performance is multi-faceted

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Skill Score: (0.50 – 0.54)/(1.00-0.54) = -8.6%~worse than guessing~

Skill Score =SForecast – SBaseline

SPerfect – SBaseline

How Good? Compared to What?

What is the appropriate Baseline?

= 1 - SForecast

SBaseline

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GraphicalForecast Evaluation

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Historical seasonal water supply outlooks

Colorado River Basin

Basic Data Display

Morrill, Hartmann, and Bales, 2007

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Scatter plots


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Histograms


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IVP Scatterplot Example

Source: H. Herr

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Empirical distribution of forecast probabilities for different observations categories

Goal: Widely separated CDFs

Cumulative Distribution Function (CDF): IVP

Cat 1 = No Observed Precipitation

Cat 2 = Observed Precipitation (>0.001”)

Source: H. Herr, IVP Charting Examples, 2007

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Probability Density Function (PDF): IVP



Empirical distribution for 10 bins for IVP GUI

Goal: Widely separated PDFs


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“Box-plots”: Quantiles and Extremes

Based on summarizing CDF computation and plot

Goal: Widely separated box-plots




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ScalarForecast Evaluation

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BiasMean forecast = Mean observed

Correlation CoefficientVariance shared between forecast and observed (r2)Says nothing about bias or whether forecast variance = observed variancePearson correlation coefficient: assumes normal distribution, can be + or – (Rank r: only +, non-normal ok)

Root Mean Squared ErrorDistance between forecast/observation valuesBetter than correlation, poor when error is heteroscedasticEmphasizes performance for high flows Alternative: Mean Absolute Error (MAE)

fcstobs

Observed

Fore

cast

Standard Scalar Measures

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1943-99 April 1 Forecasts for Apr-Sept Streamflow at

Stehekin R at Stehekin, WA

Fore

cast

(100

0’s a

c-ft

)

Observed (1000’s ac-ft) Observed (1000’s ac-ft)

1954-97 January 1 Forecasts for Jan-May Streamflow at

Verde R blw Tangle Crk, AZ

Bias = 22Corr = 0.92RMSE = 74.4

Bias = -87.5Corr = 0.58RMSE = 228.3

Standard Scalar Measures (with Scatterplot)

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IVP: Deterministic Scalar Measures

ME: smallest; + and – errors cancel

MAE vs. RMSE: RMSE influenced by large errors for large events

MAXERR: largest

Sample Size: small samples have large uncertainty


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IVP: RMSE – Skill Scores

Skill compared to Persistence Forecast


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Verification Introduction Holly C. Hartmann