CRA (entity-based) verification

Beth Ebert
Bureau of Meteorology Research Centre, Melbourne, Australia


This object-oriented method verifies the properties of spatial forecasts of entities, where an entity is anything that can be defined by a closed contour. Some examples of entities, or blobs, are contiguous rain areas (CRAs, for which the method is named), convective outlook regions, and low pressure minima. For each entity that can be identified in the forecast and the observations, CRA verification uses pattern matching techniques to determine the location error, as well as errors in area, mean and maximum intensity, and spatial pattern. The total error can be decomposed into components due to location, volume, and pattern error. This is a useful property for model developers who need such information to improve the numerical weather prediction models.

In addition, the verified entities themselves may be classified as "hits", "misses", etc., according to how close the forecast location was to the observed location, and how well the maximum intensity was represented by the forecast. This event verification can be useful for monitoring forecast performance.

The CRA verification method is described below using rain forecasts as an example. The method is described in detail by Ebert and McBride (2000). Click here to download the code (written in IDL language).

1. Introduction

A good quantitative precipitation forecast (QPF) correctly predicts: Errors can occur in all of the above quantities.  However, it is difficult to determine the source(s) of error using traditional verification statistics over the model domain. Traditional verification methods  focus on matches between the forecast and observations at individual stations or gridpoints, and do not consider the spatial relationship between the points. In addition, it may be difficult to interpret the verification results for a given spatial forecast when there is more than one feature of interest in the domain.

When we verify a spatial forecast by eye, we compare the mapped forecast and observations side by side, generally focussing on one or more features of interest. The first things we notice are whether each feature was forecast to be in the right place, and whether it had the correct size, shape, and magnitude.

CRA verification is an intuitive approach that quantifies the results of "eyeball", or visual, verification. It focuses on individual weather systems as opposed to the entire domain, enabling the errors in each event to be separately assessed. It verifies the properties of the forecast entities against the properties of the corresponding observed entities. A big advantage of this approach over more traditional verification methods is that the location error of the forecast entity can be quantified.

2. Definition of CRA

A contiguous rain area (CRA) is defined as a region bounded by a user-specified isohyet (rain rate contour) in the forecast and/or the observations. It is the union of the forecast and observed entities (blobs). In Figure 1 below the CRA is defined as the entire shaded area. The forecast and observed entities need not overlap, but they must be associated with each other, which usually means that they are nearby.

Schematic of CRAThe choice of contour used to define the CRA depends on the application. For example, 1 mm hr-1 could be used to include all rain in a radar-based nowcast, while 20 mm d-1 could be used to isolate the bull’s eye in a daily rainfall forecast.

3. Calculating location errors

The location error is determined using  pattern matching. The forecast field is horizontally translated over the observed field until the best match is obtained. The location error is then simply the vector displacement of the forecast. The method does not consider amplification or distortion of features, unlike the domain-based feature verification method of Hoffman et al. (1995).

The best match can be determined in a number of ways: (a) by maximizing the correlation coefficient, (b) by minimizing the total squared error, (c) by maximizing the overlap of the two entities, and (d) by overlaying the centres of gravity of the two entities. The domain over which these statistics are calculated includes all gridpoints in the forecast and observed entities, before and after translation. When the forecast matches the observations quite well, all of the methods will give very similar location errors. However, not all forecasts are well behaved, and it may be necessary to try the various matching methods to see which one gives the most intuitively pleasing results for the particular forecast application being assessed.

4. Error decomposition

When error minimization is used to determine the best pattern match, then it is possible to decompose the total error into components due to location error, volume (intensity) error, and pattern error. The total mean squared error (MSE) can be written as:

    MSEtotal = MSEdisplacement + MSEvolume + MSEpattern

The difference between the mean square error before and after translation is the contribution to total error due to displacement,

     MSEdisplacement  = MSEtotalMSEshifted

The error component due to volume represents the bias in mean intensity,

     MSEvolume = ( F - X )2

where F and X are the CRA mean forecast and observed values after the shift. The pattern error accounts for differences in the fine structure of the forecast and observed fields,

     MSEpattern = MSEshifted - MSEvolume

Note that it may be possible to do the error decomposition when other pattern matching criteria are used. However, it is not guaranteed because the mean squared error may not decrease for the "best" match, giving in this case a negative pattern error.

5. A few examples

CRA for LAPS forecast in eastern Australia for 1 February 2001CRA verification has been used to verify 24 h QPFs from the Australian regional forecast model since mid-1999. Figure 2 shows the CRA verification for a heavy rain event on the east coast of Australia in February 2001. A contour of 20 mm d-1 was chosen to isolate the region of greatest interest. The heaviest rain was forecast slightly to the northwest of where it actually occurred, as shown by the arrow. If it had been forecast in the correct location the RMS error would have been roughly half the original value and the correlation coefficient would also have been much better. The forecast area and intensity of the rain were predicted reasonably well. For this event about 70% of the total error was associated with the error in location, and most of the remaining error was associated with the fine scale structure.
CRA verification for Autonowcaster radar-based nowcastThe second example is for a radar-based nowcast of rain in a severe storm near Sydney in November 2000. The storm moved to the left of the mean flow, leading to an error in the forecast position of about 13 km to the southwest. The nowcast overestimated the size and rain volume of the storm. In this event most of the error was split between displacement and pattern error, while 9% of the total error was due to incorrect rain volume.

When the CRA verification is applied to a large number of entities, it is possible to diagnose systematic errors in the forecasts (e.g., Ebert and McBride, 2000). An example is shown below. The dominant sources of error can also be diagnosed.
Scatterplot and 2D histogram of max RR and location errors

6. Event verification

Another way that entity-based verification can quantify visual verification is to categorize the forecasts for the events themselves as "hits", "misses", etc., depending on whether their location and intensity were well predicted.

The specific criteria for what constitutes "well predicted" depends on the needs of the user. For example, for spatial 24 h rain forecasts Ebert and McBride (2000) specified that (a) the location error must be within one effective radius of the rain system, but not more than 5 degrees latitude/longitude, and (b) the forecast maximum rain rate must be within one category of the observed (categories bounded by 1, 2, 5, 10, 20, 50, 100, 150, and 200 mm d-1).

Based on the designated location and intensity criteria, an event contingency table can be constructed:
Too little Approx. correct Too much
Location Close Underestimate Hit Overestimate
Far Missed Event Missed location False alarm

A missed event can also occur when an entity was observed but not predicted at all. Similarly, a false alarm can occur when an entity was predicted but did not occur. While in these cases it is impossible to determine a location or intensity error, it is still important to include them in the event verification.

Event verification for a large number of CRAs can give useful information on the nature of the forecast errors. These descriptions could prove a useful tool for monitoring forecast performance over time.

An example for the Australian regional model is shown below, where the results are stratified according to the observed maximum intensity of the events. For all events together (threshold of 0 mm d-1) the event hit rate was close to 50%, while the most common type of error was a missed location. The event hit rate improves slightly as the rain events become more intense, then rapidly drops when the observed intensity exceeds 100 mm d-1. Although the forecast location was good for these very heavy rain events, their intensity was underestimated by the model.
CRA event verification categories as a function of max rain rate

7. Strengths and weaknesses of CRA verification

The entity-based CRA verification method has a number of attractive features:
(a) It is intuitive, quantifying what we can see by eye
(b) it estimates the location error in the forecast,
(c) the total error can be decomposed into contributions from location, intensity, and pattern,
(d) forecast events can be categorized as hits, misses, etc. These descriptions could prove a useful tool for monitoring forecast performance over time.
There are also some drawbacks to this approach:
(a) Because it depends on pattern matching, it must be possible to associate entities in the forecast with entities in the observations. This means that the forecast must be halfway decent. The verification results for a large number of CRAs will be biased toward the "decent" forecasts, i.e., those for which location and intensity errors could reliably be determined.
(b) The user must choose the pattern matching method as well as the isoline used to define the entities. The verification results will be somewhat dependent on these choices.
(c) When a forecast and/or observed entity extends across the boundary of the domain it is not possible to be sure whether the pattern match is optimal. If the CRA has a reasonably large area still within the domain then the probability of a good match is high. Ebert and McBride (2000) suggest applying a minimum area criterion to address this issue.
The CRA verification methodology has so far been successfully applied to numerical model forecasts of 6- and 24-hourly accumulations (Ebert and McBride, 2000; Ebert et al., 2003; Loughe et al., 2002; Grams et al., 2004), radar-based rainfall nowcasts (Ebert et al., 2004), convective outlooks, and satellite precipitation estimates (Ebert, 2002). The approach is now beginning to be used to evaluate ensemble forecasts (Ebert 2009; Gallus 2010) and even climatological precipitation features in climate model output.

8. References

Ebert, E.E., 2002: Verifying satellite precipitation estimates for weather and hydrological applications. 1st Intl. Precipitation Working Group (IPWG) Workshop, Madrid, Spain, 23-27 September 2002.
Ebert, E., 2009: Feature-specific verification of ensemble forecasts. 4th Intl Verification Methods Workshop, Helsinki, Finland, 8-10 June 2009. Available online at
Ebert, E.E. and W.A. Gallus, 2009: Toward better understanding of the contiguous rain area (CRA) verification method. Wea. Forecasting, 24, 1401-1415.
Ebert, E.E. and J.L. McBride, 2000: Verification of precipitation in weather systems: Determination of systematic errors.  J. Hydrology, 239, 179-202.
Ebert, E.E., U. Damrath, W. Wergen and M.E. Baldwin, 2003: The WGNE assessment of short-term quantitative precipitation forecasts (QPFs) from operational numerical weather prediction models. Bull. Amer. Met. Soc., 84, 481-492.
Ebert, E., L.J. Wilson, B.G. Brown, P. Nurmi, H.E. Brooks, J. Bally, and M. Jaeneke, 2004: Verification of nowcasts from the WWRP Sydney 2000 Forecast Demonstration Project. Wea. Forecasting, 19, 73-96.
Gallus, W.A. Jr., 2010: Application of object-based verification techniques to ensemble precipitation forecasts. Wea. Forecasting, 25, 144-158.
Grams, J.S., W.A. Gallus, L.S. Wharton, S. Koch, E.E. Ebert and A. Loughe, 2004: Use of a modified Ebert-McBride technique to verify IHOP QPF as a function of convective system morphology. 20th Conf. Wea. Analysis & Forecasting, Amer. Met. Soc., Seattle, 11-15 January 2004.
Hoffman, R.N., Z. Liu, J.-F. Louis, and C. Grassotti, 1995: Distortion representation of forecast errors. Mon. Wea. Rev., 123, 2758-2770.
Loughe, A.F., L.S. Wharton, J.L. Mahoney, and E.I. Tollerud, 2002: Real-time quantitative precipitation forecast verification during IHOP (May-June, 2002). Workshop on Making Verification More Meaningful, Boulder, 30 July-1 August 2002.

Go to Forecast Verification - Issues, Methods, and FAQ

For more information on this method, contact Beth Ebert, Centre for Australian Weather and Climate Research, Bureau of Meteorology, GPO Box 1289, Melbourne, Vic., Australia 3001.