eTRaP combines TRaP forecasts from multiple scans and multiple sensors.

• Weighted averaging reduces the random error in the deterministic forecast, leading to more accurate rain amounts and better placement of rain maxima.
• Probabilistic forecasts of rain exceeding critical thresholds provides important uncertainty information to support decision makers.

Why an ensemble of TRaPs?

First, some background on TRaP...  NOAA/NESDIS produces operational areal Tropical Rainfall Potential (TRaP) forecasts of rainfall for landfalling tropical cyclones. TRaP forecasts are essentially 24-hour extrapolation forecasts of satellite rain rates derived from passive microwave observations from polar orbiting satellites. Sensors include the Advanced Microwave Sounder Unit (AMSU), Special Sensor Microwave Imager (SSM/I), and Tropical Rainfall Monitoring Mission (TRMM) Microwave Imager.

TRaP rainfall accumulations are predicted every 6 hours out to 24 hours following three basic assumptions: (a) the satellite rain rate estimates are accurate, (b) the forecasts of cyclone track are accurate, and (c) the rain rates over a 24 h period can be approximated as steady state following the cyclone path. Errors in these assumptions lead to errors in TRaP rainfall predictions.

One way to reduce the random error is to average several TRaPs together in a "poor man's ensemble". This smooths the rain field, with associated advantages and disadvantages. The mean field is less likely to produce very large errors when compared to the observations; however, the averaging dampens the high rain intensities, which were the original motivation for making TRaP forecasts!

A more intelligent approach is to retain information on the distribution of forecasts within the ensemble, making use of the uncertainty (variability) among the TRaP forecasts. One can generate probabilistic forecasts of rain exceeding certain critical thresholds in locations of interest, an approach very amenable to risk management and mitigation strategies.

How is eTRaP generated?

eTRaP is made up of TRaP forecasts based on observations from several microwave sensors, initialized at several observation times, using several different track forecasts. 6-hour TRaP segments are combined in multiple permutations to make an ensemble of TRaP forecasts for 6 h, 12 h, and 24 h accumulations. Here is a step-by-step guide to how eTRaP is made:

1. Select all available 6h TRaP segments with valid (final) times within the accumulation period of interest

TRaPs are assigned to the nearest synoptic time of 00, 06, 12, or 18 UTC. 6-hour TRaP "segments" refer to the 0-6 h, 6-12 h, 12-18 h and 18-24 h rainfall accumulations within a given TRaP forecast. Select all 6-hour TRaP segments with accumulation times ending within the next 24 hours. Normally there will be more segments early in the period since they could originate from TRaPs made 18 hours ago, 12 hours ago, 6 hours ago, and now. The last 6 hours of the 24 h forecast can only use the most recent TRaPs.

2. Assign each TRaP segment a weight

The weight w_i depends on both the latency of the scan on which the TRaP is based (i.e., how old the scan is relative to the current time) and the relative accuracy of sensor in determining rain rates:

The scan weights were assigned subjectively on the expectation that steady state rainfall is a more valid assumption early in the forecast period than later. The sensor weights have been estimated from previous validation studies (Ferraro et al. 2005, Ebert et al. 2005):

3. Using permutations of 6h segments, combine TRaP forecasts to make ensemble members with the desired accumulation

For example, if there are five 6-hour TRaPs available for the first six hours of a 24 h forecast, four TRaPs for the second six hour segment, four TRaPs for the third segment, and two TRaPs for the fourth segment, then the number of ensemble members comprising the 24 h forecast is 5 x 4 x 4 x 2 = 160. The weight associated with each ensemble member is the sum of the weights of its 6-hour segments. Frequently there are more than a thousand potential ensemble members, in which case 500 are randomly selected to speed up the eTRaP processing.

4. Generate deterministic forecasts as the weighted ensemble mean and weighted probability-matched ensemble mean

The ensemble mean areal rainfall R is simply the weighted average of the ensemble members at every grid box in the domain.

We perform a further post-processing step to obtain the probability-matched ensemble mean, which has the same relative spatial distribution of rain as the ensemble mean but the intensity distribution is transformed using probability (histogram) matching to have the same intensity distribution as the full ensemble. The purpose of this transformation is to remove most of the excess light rain caused by the averaging process, and to restore the heavy rain accumulations that may have been lost during averaging. For heavy rain events this can be an important correction.

5. Generate probabilistic forecasts using weighted polling

The probabilistic forecast P of rain exceeding a given threshold is weighted to give greater influence to the ensemble members with greater expected accuracy:

where R_T is a threshold rain amount and the quantity (TRaP_i ≥ R_T) is either 0 or 1. The thresholds chosen for computing probabilistic forecasts are 25, 50, 75, and 100 mm for 6 h and 12 h forecasts, and 50, 100, 150, and 200 mm for 24 h forecasts.

Example eTRaP for Hurricane Rita

The ensemble mean, probability-matched mean, and probabilities of rain exceeding 50, 100, 150, and 200 mm, valid for the 24 h ending at 18 UTC on 24 September 2005, are shown below:

Comparing first the simple ensemble mean and the probability-matched ensemble mean, note how the latter has higher rain intensities in the center of the storm, and reduced extent of the lightest rainfall. The rain probabilities suggest a broad area with greater than 50% likelihood of at least 50 mm. There is non-negligible (>50%) chance of rain exceeding 200 mm along the border region.

Verification of the probability-matched mean against Stage IV radar-gauge totals (below) suggest that the deterministic forecast was quite good in most respects.

Although the maximum rain rate was still underestimated, the placement of the maximum was within a few tens of kilometers of where it was observed and the overall rain pattern was well predicted.

Comparison of TRaPs and experimental eTRaPs for several tropical cyclones over the United States and Australia has shown the following:

• eTRaP provide spatial forecasts with greater accuracy and realism (less streakiness)
• eTRaP give better placement and intensity of the rain maximum
• eTRaP probabilistic forecasts of rain exceeding critical amounts provide uncertainty information to aid in risk assessment and decision making.

References

Ebert, E., S. Kusselson and M. Turk, 2005: Validation of NESDIS operational tropical rainfall potential (TRaP) forecasts for Australian tropical cyclones. Aust. Meteorol. Mag., 54, 121-135.

Ferraro, R., P. Pellegrino, M. Turk, W. Chen, S. Qiu, R. Kuligowski, S. Kusselson, A. Irving, S. Kidder and J. Knaff, 2005: The Tropical Rainfall Potential (TRaP) technique. Part 2: Validation. Wea. Forecasting, 20, 465-475.

Kidder, S.Q., S.J. Kusselson, J.A. Knaff, R.R. Ferraro, R.J. Kuligowski, and M. Turk 2005: The Tropical Rainfall Potential (TRaP) technique. Part 1: Description and examples. Wea. Forecasting, 20, 456-464.