Verification of Rainfall in City Forecasts

This blog post is the first in a three-part series discussing verification of MetService forecasts. Here, we present the method used for verifying rainfall in city forecasts, along with some recent examples.

Verification Scheme

Four times daily (around 11:15am, 4:15pm, 10:50pm and 3:45am) MetService issues city forecasts for more than 40 locations. Currently, for 32 of these (and soon for most of the remainder), the forecasts of tomorrow’s precipitation from today’s late morning issue are verified against observations from a nearby automatic weather station.
Counts of precipitation forecasts and corresponding observations are made using a categorical forecast verification system. The principle is described in the contingency table below. Over a given period (typically, a month), for each location, the number of times an event was

  • A: Forecast and observed
  • B: Forecast and not observed
  • C: Not forecast but observed
  • … are recorded.

2 x 2 Contingency Table Event Observed
Yes No
Event Forecast Yes A B
No C D

From these, indications of accuracy are readily obtained:

Probability Of Detection (POD) Ratio of the number of times rainfall was successfully forecast to the total number of times it was observed Probability of Detection
False Alarm Ratio (FAR) Ratio of the number of times rainfall was forecast but not observed to the total number of times it was forecast False Alarm Ratio
Success Ratio (SR) Ratio of the number of times rainfall was successfully forecast to the total number of times it was forecast
Critical Success Index (CSI) Ratio of the number of times rainfall was successfully forecast to the number of times it was either forecast (successfully or not) or observed Critical Success Index
Bias Ratio of the total number of times rainfall was forecast to the total number of times it was observed Bias

For good forecasts, POD, SR, Bias and CSI approach a value of 1.

In the verification scheme:

  • “Tomorrow” is the 24-hour period between midnight tonight and midnight tomorrow
  • The forecast is considered to be of precipitation when the accompanying icon (as it appears, for example, in the city forecast for Auckland) is any one of “Rain”, “Showers”, “Hail”, “Thunder”, “Drizzle”, “Snow”, or “Few Showers”
  • Precipitation is considered to have fallen if the automatic weather station records any precipitation amount greater than zero.

The scheme operates automatically – that is, there is no input by MetService staff.

Some Results

POD, SR, Bias and CSI can be geometrically represented in a single diagram, and therefore simultaneously visualised.
The diagram below shows the accuracy of the forecasts issued late morning, for tomorrow, of precipitation, for the 32 cities verified, during September 2010.
Urban Rainfall September 2010

North and west of North Island (NWNI) East and south of North Island (SENI) North and east of South Island (NESI) West and south of South Island (WSSI)
WR Whangarei
AA Auckland
WT Whitianga
HN Hamilton
RO Rotorua
TG Tauranga
WK Whakatane
NP New Plymouth
WU Wanganui
AP Taupo
GS Gisborne
HS Hastings
NR Napier
TM Taumarunui
MS Masterton
PM Palmerston North
LV Levin
WG Wellington
NS Nelson
WB Blenheim
KI Kaikoura
CH Christchurch
AS Ashburton
OU Oamaru
TU Timaru
WS Westport
HK Hokitika
QN Queenstown
WF Wanaka
DN Dunedin
GC Gore
NV Invercargill

From the above diagram, for example:

  • The forecast for Auckland scores well, with Probability of Detection, Success Ratio and Bias all close to 1
  • The forecast for Timaru scores not as well: Probability of Detection around 0.75 is compromised by a Success Ratio just under 0.4 and a Bias of 2. In other words, during September 2010, the precipitation icon accompanying the late morning issue of the city forecast for Timaru for tomorrow, was too often one of “Rain”, “Showers”, “Hail”, “Thunder”, “Drizzle”, “Snow”, or “Few Showers”.

It’s also useful to see performance when the cities are grouped into the geographical areas described in the key above and overall. The diagram below shows the accuracy of the forecasts issued late morning, for tomorrow, of precipitation, for the 32 cities verified, during September 2010.

In this particular case, forecasts for the group of cities comprising the north and east of South Island (“NESI”) didn’t verify as well as for other places, with a Probability of Detection of about 0.75 and a False Alarm Ratio of about 0.3.

Further, it’s interesting to look at results dating from the implementation of this particular scheme in March 2009 through to 28 October 2010. Probability of Detection hovers at around 0.8 ± 0.15 (80% ± 15% in the graph immediately below). The False Alarm Ratio has shown a steady decline – in other words, predictions of rainfall in the city forecasts have improved in accuracy over the last year.
POD time series

FAR time series

Performance Target

MetService’s performance target for the forecast of precipitation in city forecasts is a combined POD greater than 0.77 for the 2010/11 financial year, increasing to 0.80 for the 2011/12 financial year.


Even across small distances, there can be significant variations in rainfall during the course of a day. Thus, the observation point used to verify the forecast for a given place may or may not fairly represent the rainfall there – or may be a good indication in some weather situations but not in others. MetService observation sites are commonly at airports, which in general are at least some distance from the city or town they serve.


Finally, there is much literature about forecast verification. If you’d like to know more about it, try these:
Doswell Charles A., 2004: Weather forecasting by humans—Heuristics and decision making. Weather and Forecasting, 19, 1115–1126.
Doswell, Charles A., Robert Davies-Jones, David L. Keller, 1990: On Summary Measures of Skill in Rare Event Forecasting Based on Contingency Tables. Weather and Forecasting, 5, 576–585.
Hammond K. R., 1996: Human Judgment and Social Policy. Oxford University Press, 436 pp.
Roebber, Paul J., 2009: Visualizing Multiple Measures of Forecast Quality. Weather and Forecasting, 24, 601–608.
Stephenson, David B., 2000: Use of the “odds ratio” for diagnosing forecast skill. Weather and Forecasting, 15, 221–232.

Published by

Peter Kreft

Peter has a BSc(Hons) in mathematics and has been a meteorologist for over 30 years. He's spent about half of this time working in the National Forecast Centre, as both a forecaster and a manager, and the other half recruiting and training New Zealand's meteorologists. These days, Peter gets his practical weather experience by trying to estimate the wind strength while trying to run up Wellington's hills. Peter's particular area of expertise is broad-scale weather systems and he has been an honorary teaching associate at Victoria University of Wellington. He is Chief Forecaster at Meteorological Service of New Zealand Limited.

4 thoughts on “Verification of Rainfall in City Forecasts”

  1. I found the accuracy rate for Tauranga very high compared to my experience, and I watch the predictions closely for the washing (with 3 small children) and work. We always ignore the MetService prediction for precipitation whenever the system is coming from the westerly quarter because the Kaimai Ranges tend to capture most of the moisture before it reaches town, whereas predictions for systems coming from the north or east are generally accurate. Southerlies tend to depend on whether they are SE or SW, with SE being more likely to get the rain predicted. Actually the rural forecasts tend to be more accurate for Tauranga than the Tauranga forecast. But we agree that the rainfall can vary from one place to another across town, and can watch dramatic lightning and rainfall at sea and at Papamoa but get not a drop in the city.

  2. I have to think the wet winter has contributed to these recent better results – if it rained most days it is hard to have a false alarm and pretty easy to get a hit. PODs and FARs are really targeted at verifying rare events (like Mr Doswell says) – which might have been sunny days this last winter!

  3. “Precipitation is considered to have fallen if the automatic weather station records any precipitation amount greater than zero.” Though convenient, it’s not really very relevant. In my Auckland, it can be a *really nice day* with two or three slight showers adding to the sparkling clarity and freshness, or dull, overcast, and either cold or muggy, with no showers at all.

    Do meteorologists anywhere try to capture something like this?

    1. Measuring how successfully the “niceness of the day” was forecast is rather more challenging. In short, our experiences with schemes for this are (a) they take a lot more time and effort and are therefore not easily extensible to a large number of places, (b) they require a degree of subjectivity, which we try to avoid when verifying forecasts, and (c) they tend not to provide much more information.

      As you suggest, the verification “error” that may occur on marginal days cuts both ways. We are happy to accept that some forecasts will be marked incorrectly, but overall, and in the long run, the scheme will accurately represent the success of forecasts of rain or not.

      The results from this automated scheme are consistent with an earlier manual verification scheme we operated. If we started over or under forecasting rain, the effect of it would soon show up in the verification results even when such simple methods are used.

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