THE SCAN 0-1 HOUR RAINFALL FORECAST ALGORITHM


David H. Kitzmiller, Michael E. Churma, and M. Thomas Filiaggi


Techniques Development Laboratory

Office of Systems Development

National Weather Service


INTRODUCTION

DATA USED IN DEVELOPMENT AND VALIDATION

DERIVATION OF STORM MOTION VECTORS

EXPRESSIONS FOR RAINFALL PROBABILITIES

SKILL OF CATEGORICAL (YES/NO) FORECASTS DERIVED FROM PROBABILITIES

CONVERTING PROBABILISTIC FORECASTS TO ISOHYETS

GRIDDED RAINFALL FORECAST DISPLAYS

FORECASTS OF 1-INCH RAINFALL AMOUNTS ASSOCIATED WITH INDIVIDUAL STORM CELLS

REQUIRED INPUT PRODUCTS

IMPLICATIONS FOR OPERATIONAL USE

1. INTRODUCTION


The System for Convection Analysis and Nowcasting (SCAN), a suite of algorithms within the Advanced Weather Interactive Processing System (AWIPS), features a variety of automated radar interpretation products. The SCAN 0-1 Hour Rainfall algorithm (SRAIN1) produces the following products for nowcasting convective rainfall:

gridded probabilities that 0-1 h rainfall will reach or exceed 0.1, 0.25, 0.5, and 0.75 inch (approximately 2.5, 6.25, 12.5, and 18.75 mm);

a 0-1 h gridded forecast rainfall amount;

storm-cell-based probabilities that 0-1 h rainfall will exceed one inch anywhere in the immediate vicinity of convective storms.

The gridded probabilities and amounts are valid within each box of a 4-km grid covering the central portion of the radar umbrella. The nowcasting algorithm is based on an extrapolative-statistical method, first tested conceptually by Saffle and Elvander (1981).

This technique was developed by correlating purely extrapolative forecasts of radar reflectivity and vertically-integrated liquid (VIL) with analyses of observed rainfall over many historical cases. The relationships between the purely extrapolative forecasts and the observed amounts are now used in interpreting real-time extrapolative forecasts in terms of rainfall probability and amount. The historical development data consist of base reflectivity observations from WSR-88D units in Oklahoma and Kansas, and coincident WSR-88D Stage III radar-gauge rainfall estimate fields.

The resulting extrapolative-statistical approach to rainfall forecasting implicitly accounts for echo decay and uncertainty in the extrapolation process, and is a form of the Model Output Statistics technique often used to produce forecasts of sensible weather from numerical weather prediction model output. Because it incorporates input from a variety of statistical predictors, the extrapolative-statistical approach yields improvements over a purely extrapolative one, at the expense of a modest increase in computing time. The improvement is greatest for rainfall amounts of 0.5 inch and greater.

This note contains a brief explanation of the development methodology and operational skill of the algorithm. A more complete summary of the methodology, as applied to an earlier version of the technique, was prepared by Kitzmiller (1996). A summary of the development for the SCAN version is contained in Kitzmiller and Churma (1999).

2. DATA USED IN DEVELOPMENT AND VALIDATION


The radar data used in development were collected at the WSR-88D sites at Twin Lakes, Oklahoma (KTLX), Tulsa, Oklahoma (KINX), and Wichita, Kansas (KICT) during the 1994 and 1995 warm seasons. Each case featured at least some convective storms, since our primary interest was forecasting the location of the heaviest rainfall within regions affected by thunderstorms. Base reflectivity data were objectively interpolated to a 4-km local grid oriented north-south and covering a 230-km umbrella centered on the radar site. The default WSR-88D Z-R and Z-M relationships were used to derive rainrates from the reflectivity field at the lowest antenna elevation, and VIL from volumetric reflectivity.

Our development effort was focused on this area because it was among the first to be covered by WSR-88D Stage III precipitation analyses (Breidenbach et al. 1998), prepared operationally at the NWS River Forecast Center in Tulsa, Oklahoma. These analyses incorporate both radar and gauge data. One-hour rainfall estimates are interpolated to a polar stereographic grid with a spacing of approximately 4 km over the central United States. Some manual editing of the analyses is done to remove erroneous gauge reports and other artefacts such as hail contamination of rainfall estimates.

An independent sample was collected from 72 events during the 1996 warm season, at 27 WSR-88D sites in the United States east of the Rocky Mountains. The 1996 data were not used in the initial development effort itself because it includes some radar precipitation estimates with no gauge bias adjustment. These data are still useful in testing the reliability of the forecast algorithm in different geographic regions.

To prepare data for the development or training sample, we obtained 113 sequences of volumetric radar scans that were continuous for at least 25 minutes, and included a scan beginning 54-59 minutes into the hour. For each sequence, a single storm motion vector (SMV) was derived by using a binary pattern-matching method. Forecasts of the reflectivity and VIL fields were made at 10-minute intervals through 60 minutes. For the sake of simplicity, reflectivity was converted to nominal rainrates and integrated to create rainfall amounts. The VIL forecasts were temporally averaged over the 1-hour forecast period.

The statistical predictor/predictand sample was created by drawing the predictor values and the verifying rainfall value from every ninth box in each of the analysis grids. Only boxes between 20 and 90 nm from the radar were included, since the radar is unable to detect higher-altitude echoes close to the radar and lower-altitude echoes at longer ranges. We obtained a development sample of forecasts and verifying observations from 6886 individual grid boxes.

3. DERIVATION OF STORM MOTION VECTORS


A binary-correlation pattern-matching technique was used to estimate the storm motion vector (SMV) for each historical case. This method, described by Saffle and Elvander (1981) and by Ciccione and Pircher (1984), is computationally efficient and works well when the entire echo region does not change size or shape appreciably between images. The method reduces two radar grid maps to all "0" or "1" points according to some reflectivity criterion, in this case 30 dBZ. The grids are separated by 20-35 minutes in time. The earlier grid is shifted relative to the later one until the binary correlation coefficient between the two is maximized; the vector displacement divided by the time lag represents a velocity estimate.

In real-time operations, the lag-correlation method described above is used in stratiform rainfall situations; in situations with convective storms present, the average cell motion output in the Storm Track Information (STI) product is used. The SMV is set equal to the 700-mb wind vector when the echo pattern is too small or is evolving too rapidly for either of these approaches to work effectively.

4. EXPRESSIONS FOR RAINFALL PROBABILITIES


We obtained expressions relating the various predictors to the probability of reaching rainfall thresholds by a forward-selection linear screening regression procedure. In the expressions below, rainfall amounts are in mm and VIL is in kg m-2. For the 0.1-in predictand, the best fit to the dependent data was realized by the following expression:


     P( 0.1) = 0.412 + 3.517 [VILFCST]AVG3 + 0.704 [VILINIT]MAX7

             + 0.98 [NREFL24]3X3                                        (1)

where P is probability in per cent. The VIL-based predictors are defined: [VILFCST]AVG3 is the local average of the 0-60 minute time-average VIL forecast, [VILINIT]MAX7 is the maximum of VIL within the local 7x7 box region. The final predictor, [NREFL24]3X3, is defined as the sum of the number of occurrences of 24-dBZ reflectivity within the local 3x3 box region over all 7 forecast intervals within the 0-60 minute period. This predictor ranges in value from 0 to 63 (9 boxes times 7 forecast intervals beginning at 0 minutes). It indicates the fraction of the local area and time that is forecasted to experience 24-dBZ or greater reflectivity. The 0.1-inch rainfall threshold was exceeded in 16.3% of the cases. This expression explained 47% of the predictand variance within the dependent data sample.

A similar expression was derived for the probability of rain exceeding 0.25 inch:


     P( 0.25) = -0.331 + 2.701 [VILFCST]AVG3 + 0.469 [VILINIT]MAX7

              + 0.230 [NREFL24]3X3 + 0.090 [RAINFCST]AVG3    (2)
 

where [RAINFCST]AVG3 is the local average of the 0-30 minute extrapolation rainfall forecast. The 0.25-inch rainfall threshold was exceeded in 7.6% of the cases, and this regression equation explains 34% of the predictand variance.

For the two highest thresholds, the following expressions were derived:


     P( 0.5) = 0.144 + 2.074 [VILFCST]AVG3 + 0.063 [RAINFCST]AVG3 (3)

     P( 0.75) = 0.112 + 1.125 [VILFCST]AVG3 + 1.905 [NVIL10]3X3   (4)

where [NVIL10]3X3 is the number of boxes in the local 3x3 box region in which initial-time VIL exceeds 10 kg m-2. This last predictor indicates the presence of larger convection cells. Within the dependent sample, 2.8% of the cases had rainfall 0.5 inch, and 1.1% had rainfall 0.75 inch. The expression in (3) explained 19.4% of the predictand variance, and the expression in (4) explained 9.5%

5. SKILL OF CATEGORICAL (YES/NO) FORECASTS DERIVED FROM PROBABILITIES


An informative method of assessing the skill of the probability forecasts obtained from (1)-(4) involves scoring categorical (yes/no) forecasts derived from the probabilities. The most common method of deriving categorical forecasts from probabilities is by applying a threshold value: all probabilities below the threshold are interpreted as "no," those at and above the threshold as "yes." Such forecasts can be scored in terms of probability of detection (POD), false alarm ratio (FAR), and critical success index (CSI). The calculation and characteristics of these scores have been discussed by Donaldson et al. (1975) and by Schaefer (1990). Another measure of forecast utility is bias, which is the ratio of the number of "yes" forecasts to "yes" observations.

Scores for each of the four probability equations appear in Figs. 1-4. The POD, FAR, CSI, and bias are shown for all probability thresholds from 1% to 30% or higher. For example, for the P( 0.1) equation (Fig. 1), a yes/no threshold of 20% yields a POD of 0.82 and an FAR of 0.42. That is, 82% of all observed 0.1-inch precipitation events were covered by "yes" forecasts, and 42% of all "yes" forecasts were false alarms in which the observed rainfall was less than 0.1 inch. The bias at this threshold is about 1.6, meaning that here were 60% more "yes" forecasts than were observed. Alternatively, this bias indicates that on average the forecasted 0.1-inch isohyets enclose 60% more area than do the observed isohyets. Of course, all of the forecast scores are based on performance over many different events, and will vary substantially from case to case.

As is apparent from the POD and FAR curves, it is possible to achieve large POD's at the expense of high FAR and bias, or to achieve very low FAR's by accepting low POD's. The CSI represents a measure of how well the FAR and POD can be balanced between too many false alarms and too few event detections. For the 0.1-inch forecasts, the highest CSI, 0.56, is reached at a threshold of 35%, where the POD is 0.7, the FAR is 0.3., and the bias is 1.1.

Forecast skill is lower for the higher rainfall thresholds. The peak CSI values are lower: 0.43 for 0.25 inch (Fig. 2), 0.30 for 0.5 inch (Fig. 3), and 0.14 for 0.75 inch (Fig. 4). It is also apparent that, as higher rainfall amounts are considered, it is necessary to accept a higher FAR and bias in order to achieve any value of the POD. For example, in order to detect 70% of events (POD=0.7), one must accept an FAR of 0.3 for the 0.1-inch threshold, but an FAR of 0.78 for the 0.5-inch threshold and an FAR of 0.89 for the 0.75-inch threshold.

We verified that the categorical forecast skill was similar within the 1996 independent case sample. In Figs. 5-8, POD and FAR are shown for both the dependent and independent samples, with bold lines for the dependent data and fine lines for the independent. For the three lower thresholds (Fig. 5 for 0.1 inch, Fig. 6 for 0.25 inch, and Fig. 7 for 0.5 inch), the POD's are very similar for both samples except at threshold probabilities > 40%, while the FAR in the independent sample is somewhat larger than in the dependent. This is logical, since the probability equations on which the categorical forecasts were based were tuned for skill in the dependent sample.

At higher threshold probabilities, the POD's were actually higher in the independent sample. Also, skill for forecasting 0.75-inch amounts was actually higher in the independent sample, i.e., POD was generally higher and FAR lower (Fig. 8). This result is likely to be a consequence of the rarity of the event, and thus due to chance. However, the verification experiment strongly suggests that the forecast algorithm will perform stably in most trials with a reasonably large number of cases.

6. CONVERTING PROBABILISTIC FORECASTS TO RAINFALL FORECASTS


The discussion in the previous section focused on simple yes/no forecasts, considering only whether one rainfall threshold would be exceeded. For many purposes, it is desireable to derive a forecast isohyet field from the probabilities. A simple method for carrying out this conversion is to assign a rainfall amount to a grid box after considering the probabilities for all threshold amounts.

In the present application, this is done by applying a fixed set of thresholds, and forecasting the rainfall category to be the highest one for which the threshold is exceeded.

The set of probability thresholds were selected to be those which produced the highest CSI within the dependent sample. These probabilities were 33%, 30%, 22%, and 14%, for the 0.1-, 0.25-, 0.5-, and 0.75-inch thresholds respectively. Thus for any grid box, if P( 0.1) is < 33%, the categorical rainfall amount is forecasted to be less the 0.1 inch. If P( 0.1) > 32%, the categorical amount is forecasted to be at least 0.1 inch. If P( 0.1) > 32% and P( 0.25)  > 29%, the amount is forecasted to be at least 0.25 inch, and so on.

We have found that this procedure yields forecast fields with a noticeable bias toward higher amounts, but which capture a substantial portion of the higher rainfall observations and forecast the shape of the isohyet field well. A tabulation of forecasts and obervations by category for the dependent sample appears in Table 1. The columns represent forecast categories and the rows, observed categories. Of the 6886 cases, 1370 were forecasted to have rainfall  0.1 inch, while 1125 actually did so, indicating a bias of 1.2 for the precipitation area as a whole. For all cases in which rain was forecasted, 34% fell into the correct observed category and 86% fell within one category of the correct one.

Within the independent 1996 sample (Table 2) we found similar results. The bias in overall rainfall area  0.1 inch was somewhat higher (1.44 compared to 1.2), while 23% of the rainfall forecasts fell into the correct category and 79% fell within one category of the correct one.

In practice, the categorical forecasts are transformed to continuous rainfall amounts in the range 0.1-0.7 inch, and contoured at 0.1-inch intervals in the output graphical display. This was done by treating the boxes at boundaries between categories as if they contained the lowest rainfall amount within the category; the amounts within all remaining boxes were then estimated by interpolation.

7. GRIDDED RAINFALL FORECAST PRODUCT DISPLAYS


These products are displayable through the local radar product menu within D2D. To be seen at the proper scale, they should be accessed through the WFO-scale (local-scale) map display.

In AWIPS Build 4.1, the following command sequence accesses SCAN quantitative precipitation forecast (QPF) products:

1) Left click on the WSR-88D identifier on the menu bar above the map display;

2) Left click and hold on the QPF products line of the local radar product pull-down menu;

3) Drag the cursor to the right into the QPF products menu, down to the desired product, then release the left button.

The product (if available) will then appear. When the full-sized WFO map is displayed, only every other probability isopleth will appear (i.e. 10%, 30%, 50%, ...). On magnification, intermediate isopleths will appear. Similarly, at full scale only a limited range of forecast isohyets will appear, with isohyets appearing at every 0.1 inch on magnification.

The relationship between rainfall forecasts and initial-time base reflectivity fields is illustrated in Figs. 11-12. In the situation shown here (1724 UTC, 18 August 1998), the storms over southern Pennsylvania were moving slowly east; thus the highest probabilities for 0.1 inch (Fig. 11) and the highest rainfall amount forecasts (Fig. 12) lie just east of the convective cell centroids.

In another similar situation (7-8 September 1998), the forecasts showed basically good agreement with the mesoscale organization of the observed precipitation. Radar observations were from the WSR-88D unit at Sterling, VA. At 2357 UTC, thunderstorms and showers over southern Pennsylvania, western Maryland, and northwestern Virginia were moving slowly to the east-southeast. The likeliest areas for significant rainfall during the subsequent 0000-0100 UTC period are indicated by the probabilities of 0.1 (Fig. 13), 0.25 (Fig. 14), and 0.5 inch (Fig. 15). The very highest probabilities were over south-central Pennsylvania, as were the highest rainfall amount forecasts (Fig. 16).

The Stage I radar-estimated rainfall field for the period 0000-0100 UTC (Fig. 17) indicated that the heaviest amounts did occur there, with a few values of 0.4 inch. The overall shape of the forecast fields agrees with that of the observed, though the forecasts did not completely capture the precipitation over and to the west of Baltimore City.

8. FORECASTS OF 1-INCH RAINFALL AMOUNTS ASSOCIATED WITH

INDIVIDUAL STORM CELLS


We found that within the development data sample, our techniques were inadequate to skillfully forecast the location of 1-hour rainfall amounts in excess of one inch. These are especially rare event (in terms of specific locations within a 4-km grid) and our predictors could not differentiate between rainfall amounts of 0.5-0.99 inch and amounts 1 inch.

However, the extrapolative-statistical method yields useful indications as to whether or not a storm cell will produce 1-inch rainfall at some place near the path of the cell centroid. Formally, these cell-associated probabilities are valid within a square region 28 km on a side, immediately in the path of the storm reflectivity centroid. Such forecasts are analogous to the output of the SCAN Severe Weather Detection and SCAN Severe Hail Detection algorithms (Kitzmiller and Breidenbach 1993 and 1995; Kitzmiller et al. 1999).

The probability that an individual storm cell will produce one inch of rain is given by:

 
      P( 1.0) = 2.19 x MXVILFCST - 5.76                                  (5)

where P( 1.0) is the probability in percent and MXVILFCST is the maximum value of the time-average VIL forecast (kg m-2) in the path of the associated storm cell centroid. Operationally, the probability is truncated at 40%, since we found that the observed event relative frequency remains near that value even when (5) evaluates to larger values.

In practice, we must determine P(1.0) for storm cells already defined in the STI product. Therefore, local maxima in the MXVILFCST field are associated with current cell centroids by finding the centroid closest to the point reached when the VIL maximum is moved backward 30 minutes at the current average cell velocity.

Categorical (yes/no) forecast skill scores within the dependent data sample are shown in Fig. 18. The CSI is maximized near a threshold probability of 17%, where the POD is 0.55 and the bias is about 1.7.

The output of this algorithm appears in the Thunderstorm Product popup box, along with other storm characteristics such as maximum VIL, severe weather and large hail probability, and lightning strike count. The probability number is located under "HVY" (Fig. 19).

To obtain the popup box for any identified storm cell in the Thunderstorm Product display, in AWIPS Build 4.1:

1) Select Storm Cells/Site Storm Threat from the local radar menu;

2) Position the cursor over the "Thunderstorm Popup" text identifier at the lower right part of the screen, and middle click. This makes the product "editable";

3) Position the cursor within a cell circle and right-click to bring up the box for that cell.

9. REQUIRED INPUT PRODUCTS


In order for the rainfall forecasts to be generated in real time, AWIPS must ingest the following products from the WSR-88D Radar Product Generator (RPG):

Z (base reflectivity, product 19, 0.5 elevation, 1-km resolution, 16 data levels)

VIL (product 57)

STI (Storm Track Index, product 58)

These must be included in the Routine Product Set (RPS) list.

The system also ingests numerical model input data for the 700-mb wind vector. These data could be from the Eta or the RUC models.

10. IMPLICATIONS FOR OPERATIONAL USE


Users should note that the gridded products forecast rainfall as averaged over 16-km2 regions, the resolution of the Digital Precipitation Array (DPA) product. This resolution is coarser than that of the One Hour Precipitation (OHP) product, which shows averages for 1 x 2 km regions. Therefore the peak amounts appearing in the forecasts are generally lower than those in the corresponding OHP. However, any numerical value appearing in one box of the DPA represents a substantially larger volume of water than does the same value appearing in one box of the OHP. Stage III estimates were used during development in preference to higher-resolution data because they had already received quality control, were spatially continuous over fairly large areas, and were likely to feature fewer range degradation effects than were OHP products taken one umbrella at a time.

The cell-based 1-inch rainfall probability algorithm monitors storm development and motion to identify cells that have particularly large water loads and are moving slowly enough to produce locally-heavy rainfall. Of course, the heavy rainfall potential of a storm is often significantly different from its severe weather potential. The SCAN suite has been constructed to identify both types of events.

ACKNOWLEDGEMENTS


Robert Saffle and Robert Elvander provided the initial impetus for this work, and gave helpful advice about getting it underway. Jeffrey Ator and Bryon Lawrence created the computer code for binary pattern matching and extrapolation forecasting. Mark Lilly selected the validation cases and provided assistance in data processing. The WSR-88D Operational Support Facility provided a copy of the algorithm for calculating gridded VIL from the Archive Level II radar data, which was then coded by Douglas Rankin.

REFERENCES


Breidenbach, J. P., D. J. Seo, and R. A. Fulton, 1998: Stage II and Stage III post processing of NEXRAD precipitation estimates in the modernized Weather Service. Preprints, 14th International Conf. on Interactive Information Processing Systems, Phoenix, Amer. Meteor. Soc., 263-266.

Ciccione, M., and V. Pircher, 1984: Preliminary assessment of very short term forecasting of rain from single radar data. Proceedings Second International Symposium on Nowcasting, Norrkoping, European Space Agency, 241-246.

Donaldson, R. J., R. M. Dyer and M. J. Kraus, 1975: An objective evaluator of techniques for predicting severe weather events. Preprints Ninth Conference on Severe Local Storms, Norman, Amer. Meteor. Soc., 321-326.

Kitzmiller, D. H., and J. P. Breidenbach, 1993: Probabilistic nowcasts of large hail based on volumetric reflectivity and storm environment characteristics. Preprints 26th International Conference on Radar Meteorology, Norman, Amer. Meteor. Soc., 157-159.

_____, and _____, 1995: Detection of severe local storm phenomena by automated interpretation of radar and storm environment data. NOAA Technical Memorandum NWS TDL 82, National Weather Service, NOAA, U.S. Department of Commerce, 33 pp. [Available from Techniques Development Laboratory, W/OSD2, National Weather Service, 1325 East West Highway, Silver Spring, Md.]

_____, and M. E. Churma, 1999: The AWIPS 0-1 hour rainfall forecast algorithm. Preprints, 15th International Conf. on Interactive Information Processing Systems, Dallas, Amer. Meteor. Soc.

_____, _____, and M. T. Filiaggi, 1999: Severe local storm and large hail probability algorithms in the System for Convection Analysis and Nowcasting. [Accessible at http://www.nws.noaa.gov/tdl/scan/scan2.html]

Saffle, R. E., and R. C. Elvander, 1981: Use of digital radar in automated short range estimates of severe weather probability and radar reflectivity. Preprints Seventh Conference on Probability and Statistics in Atmospheric Sciences, Monterey, Amer. Meteor. Soc., 192-199.

Schaefer, J. T., 1990: The critical success index as an indicator of warning skill. Wea. Forecasting, 5, 570-575.