# Presentation: 425088

## Verification Introduction 

**Holly C. Hartmann**
- Department of Hydrology and Water ResourcesUniversity of Arizona
- hollyoregon@juno.com

*RFC Verification Workshop, 08/14/2007*

## Goals

-  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**

## Agenda

- 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**

## 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?***

## 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

## Skill versus Value

- Assess quality of forecast system
- i.e. determine skill and value of forecast

- Credit: Hagedorn (2006) and Julie Demargne

## Stakeholder Use of HydroClimate Info & Forecasts

- Uninformed, mistaken about forecast interpretation
- Use of forecasts limited by lack of demonstrated forecast skill
- Have difficulty specifying required accuracy

***Unique among stakeholders***
- Relevant forecast variables, regions (location & scale), seasons, lead times, performance characteristics
- Technical sophistication: base probabilities, distributions, math
- Role of of forecasts in decision making

***Common across many, but not all, stakeholders***
- Have difficulty distinguishing between “good” & “bad” products
- Have difficulty placing forecasts in historical context

**Stakeholder Use of HydroClimate Info & Forecasts**

## Forecast evaluation concepts

**All 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?**

## Deterministic

**with a ****30% chance of rain****.”**

**Deterministic**
**Categorical**
**Probabilistic**

**Different Forecasts, Information, Evaluation**

## Deterministic 

**with a ****30% chance of rain****.”**

**Deterministic **
**Categorical**
**Probabilistic**

***Probabilistic***

***Categorical***

***Deterministic***

***How would you evaluate each of these?***

**Different Forecasts, Information, Evaluation**

***Rain***

*No rain*

***30%***

***76******°***

## Deterministic

**with a ****30% chance of rain****.”**

**Deterministic**
**Categorical**
**Probabilistic**

**Different Forecasts, Information, Evaluation**

**Deterministic**

## ESP Forecasts: User preferences influence verification 

**ESP Forecasts: User preferences influence verification **

- From: California-Nevada River Forecast Center

## ESP Forecasts: User preferences influence verification 

**ESP Forecasts: User preferences influence verification **

- From: California-Nevada River Forecast Center

## ESP Forecasts: User preferences influence verification 

**ESP Forecasts: User preferences influence verification **

- From: California-Nevada River Forecast Center

## ESP Forecasts: User preferences influence verification 

**ESP Forecasts: User preferences influence verification **

- From: California-Nevada River Forecast Center

## So Many Evaluation Criteria! 

**Bias**
**Correlation**
**RMSE**
** ****Standardized RMSE**
** ****Nash-Sutcliffe**
**Linear Error in Probability Space**

_**Categorical**_
**Hit Rate**
**Surprise rate**
**Threat Score**
**Gerrity Score**
**Success Ratio**
**Post-agreement**
**Percent Correct**
**Pierce Skill Score**
**Gilbert Skill Score**
**Heidke Skill Score**
**Critical Success index**
**Percent N-class errors**
**Modified Heidke Skill Score**
**Hannsen and Kuipers Score**
**Gandin and Murphy Skill Scores...**

_**Probabilistic**_
**Brier Score**
**Ranked Probability Score**
**Distributions-oriented Measures**
** ****Reliability**
** ****Discrimination**
** ****Sharpness**

**So Many Evaluation Criteria! **

## 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

**Notes:**
Highlighted in “Blue” color are used by us!

## 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

**Notes:**
Highlighted in “Blue” color are used by us!

## Possible Performance Criteria

**Bias - *****difference between average forecast and average observation  ***
**Consistency - *****forecasts don’t waffle around***

**Possible Performance Criteria**

**Good consistency**

## Possible Performance Criteria

**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**

## 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 and
observations | Association |
| Forecast should be more accurate than low-skilled reference forecasts (e.g., random chance, persistence,  or climatology) | Skill |

- Adapted from : Ebert (2003)

## 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)

## Forecasting Tradeoffs

- warning 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**

## Skill Score: (0.50 – 0.54)/(1.00-0.54) = -8.6%

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

**Skill Score =**

**S****Forecast**** – S****Baseline**
**S****Perfect**** – S****Baseline**

**How Good? Compared to What?**

**What is the appropriate Baseline?**

**= 1 - **

**S****Forecast**
**S****Baseline**

## Graphical

**Forecast Evaluation**

## Historical seasonal water supply outlooks

***Historical seasonal water supply outlooks***
***Colorado River Basin***

***Basic Data Display***

- Morrill, Hartmann, and Bales, 2007

## Historical seasonal water supply outlooks

***Historical seasonal water supply outlooks***
***Colorado River Basin***

***Scatter plots***

- Morrill, Hartmann, and Bales, 2007

## Historical seasonal water supply outlooks

***Historical seasonal water supply outlooks***
***Colorado River Basin***

***Histograms***

- Morrill, Hartmann, and Bales, 2007

## IVP Scatterplot Example

**IVP Scatterplot Example**

- Source: H. Herr

## Cumulative Distribution Function (CDF): IVP

- 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

## Probability Density Function (PDF): IVP

- Cat 1 = No Observed Precipitation
- Cat 2 = Observed Precipitation (>0.001”)

- Empirical distribution for 10 bins for IVP GUI

- Goal: Widely separated PDFs

- Source: H. Herr, IVP Charting Examples, 2007

## “Box-plots”: Quantiles and Extremes

**“****Box-plots”: Quantiles and Extremes**

- Based on summarizing CDF computation and plot

- Goal: Widely separated box-plots

- Cat 1 = No Observed Precipitation
- Cat 2 = Observed Precipitation (>0.001”)

- Source: H. Herr, IVP Charting Examples, 2007

## Scalar

**Forecast Evaluation**

## Bias

**Bias**
- Mean forecast = Mean observed
**Correlation Coefficient**
- Variance shared between forecast and observed (r2)
- Says nothing about bias or whether
-    forecast variance = observed variance
- Pearson correlation coefficient: assumes normal distribution, can be + or – (Rank r: only +, non-normal ok)
**Root Mean Squared Error**
- Distance between forecast/observation values
- Better than correlation, poor when error is   heteroscedastic
- Emphasizes performance for high flows
- Alternative: Mean Absolute Error (MAE)

***fcst***

***obs***

- Observed

- Forecast

**Standard Scalar Measures**

## Standard Scalar Measures (with Scatterplot)

**1943-99 April 1 Forecasts for **
**Apr-Sept Streamflow a****t **
**Stehekin R at Stehekin, WA**

**Forecast (1000’s ac-ft)**

**Observed (1000’s ac-ft)**

**Observed (1000’s ac-ft)**

**1954-97 January 1 Forecasts for **
**Jan-May Streamflow a****t **
**Verde R blw Tangle Crk, AZ**

***Bias = 22***
***Corr = 0.92***
***RMSE = 74.4***

***Bias = -87.5***
***Corr = 0.58***
***RMSE = 228.3***

**Standard Scalar Measures (with Scatterplot)**

## IVP: Deterministic Scalar Measures

**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

- Source: H. Herr, IVP Charting Examples, 2007

## IVP: RMSE – Skill Scores

- Skill compared to Persistence Forecast

- Source: H. Herr, IVP Charting Examples, 2007