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    County forecast area of responsibility (lines) for the NWS WFO Ruskin, FL (diamond). Locations of 29 observation sites (circles), and proximity site Leesburg (square), with associated rainfall observation times (LST) are shown

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    Histogram showing the climatological frequencies of measurable rainfall occurrence as a function of the time of day (LST) from May to Sep of 1997–2000: (a) TPA, (b) FMY (1997 data not available), (c) GIF, and (d) LEE

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    Lagged autocorrelation function. (a) Daily number of stations (including 0) reporting rainfall. (b) Daily average rainfall amount reported. Dependent dataset comprising May–Sep 1997– 2000. There are 615 total cases, 608 computable first lags, each

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    Frequency of stations within the 29-site network reporting rainfall, May–Sep 1997–2000. There are 612 total days with reported measurable or 0 rainfall

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    Daily predicted (solid line–rectangles) vs observed (dashed line–diamonds) average areal coverage of measurable rainfall (%) for the independent database in 2001: (a) May, (b) Jun, (c) Jul, (d) Aug, and (e) Sep. Gaps in the graph continuity were due to missed or failed radiosonde releases for a given day. There are 149 total cases, with 29 rainfall reporting stations total

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    Daily predicted (solid line–rectangles) vs observed (dashed line–diamonds) average daily rainfall amount within the 29-site network (in.) for the independent database in 2001: (a) May, (b) Jun, (c) Jul, (d) Aug, and (e) Sep. Gaps in the graph continuity were due to missed or failed radiosonde releases for a given day. The climatological daily average rainfall (1971–2000) within the rainfall reporting network is displayed (triangular data points) for comparison. There are 149 total cases, with 29 rainfall reporting stations total

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    Scatterplot of the predicted and observed daily trends of average areal coverage for the independent sample. (a) Observed trend of increase by at least 20%, and trend direction predicted incorrectly, 0 cases; (b) observed trend of increase by at least 20%, and trend direction predicted correctly, 20 cases; (c) observed trend of decrease by at least 20%, and the trend direction predicted correctly, 19 cases; and (d) observed trend of decrease by at least 20%, and the trend direction predicted incorrectly, 0 cases. Parallel diagonal lines bound all occurrences where the predicted trend was within ±10% of the observed trend. There are 144 total cases

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    Scatterplot of predicted and observed daily trends of average rainfall amount for the independent sample. (a) Observed trend of increase by at least 0.20 in., and the trend direction predicted incorrectly, 3 cases; (b) observed trend of increase by at least 0.20 in., and trend direction predicted correctly, 14 cases; (c) observed trend of decrease by at least 0.20 in., and trend direction predicted correctly, 18 cases; and (d) observed trend of decrease by at least 0.20 in., and trend direction predicted incorrectly, 1 case. Parallel diagonal lines bound all occurrences where the predicted trend was within ±0.15 in. of the observed trend. There are 144 total cases

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The Relationship between Meteorological Parameters and Daily Summer Rainfall Amount and Coverage in West-Central Florida

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Abstract

Considerable daily variations of summer convective rainfall average areal coverage and rainfall amount were identified in west-central Florida for the period May–September 1997–2000 using a 29-site rainfall network. Pearson correlation coefficients identified the correlations to each from among 16 parameters that can be extracted directly from the 1200 UTC radiosonde data at Ruskin, Florida, and that represent moisture, stability/temperature, and flow. The highest correlations were with all of the moisture parameters—precipitable water, minimum theta- e temperature, wet-bulb zero pressure, and average dewpoints in various layers from the 850- to 500-mb height level.

Multiple linear regression analysis produced a separate prediction equation each for average areal coverage and rainfall amount, which were tested on independent data from May to September 2001. Reliable predictions of the trend direction and magnitude of the change from the observed value of the previous day occurred about 75% of the time with the average prediction error generally within ±10% (areal coverage) and ±0.10 in. (rainfall amount). When the observed trend changed by at least 20% for areal coverage (39 cases), and at least 0.20 in. for average rainfall amount (36 cases), the trend direction was correctly predicted 100% and about 90% of the time, respectively. Of these, the predictions for areal coverage underforecast both the amount of observed increase and decrease by an average of 8% and 6%. For rainfall amount, the predictions underforecast both the magnitude of observed increase and decrease by about 0.18 and 0.06 in., respectively.

Corresponding author address: Ira S. Brenner, Meteorologist In Charge, NOAA/National Weather Service, 2525 14th Ave. SE, Ruskin, FL 33570. Email: ira.brenner@noaa.gov

Abstract

Considerable daily variations of summer convective rainfall average areal coverage and rainfall amount were identified in west-central Florida for the period May–September 1997–2000 using a 29-site rainfall network. Pearson correlation coefficients identified the correlations to each from among 16 parameters that can be extracted directly from the 1200 UTC radiosonde data at Ruskin, Florida, and that represent moisture, stability/temperature, and flow. The highest correlations were with all of the moisture parameters—precipitable water, minimum theta- e temperature, wet-bulb zero pressure, and average dewpoints in various layers from the 850- to 500-mb height level.

Multiple linear regression analysis produced a separate prediction equation each for average areal coverage and rainfall amount, which were tested on independent data from May to September 2001. Reliable predictions of the trend direction and magnitude of the change from the observed value of the previous day occurred about 75% of the time with the average prediction error generally within ±10% (areal coverage) and ±0.10 in. (rainfall amount). When the observed trend changed by at least 20% for areal coverage (39 cases), and at least 0.20 in. for average rainfall amount (36 cases), the trend direction was correctly predicted 100% and about 90% of the time, respectively. Of these, the predictions for areal coverage underforecast both the amount of observed increase and decrease by an average of 8% and 6%. For rainfall amount, the predictions underforecast both the magnitude of observed increase and decrease by about 0.18 and 0.06 in., respectively.

Corresponding author address: Ira S. Brenner, Meteorologist In Charge, NOAA/National Weather Service, 2525 14th Ave. SE, Ruskin, FL 33570. Email: ira.brenner@noaa.gov

1. Introduction

The summer months of May–September offer a wide variety of daily opportunities for outdoor activities in west-central Florida. However, this is also the time of year when convective rainfall occurs nearly every day. This fact has long been acknowledged by the forecast and research community. For example, Landsburg (1958) noted that portions of peninsular Florida observe more seasonal thunderstorm activity than any other part of the United States. Rainfall, especially if associated with thunderstorms, can adversely impact travel and outdoor activities, and those affected will often wish to know if the next day will be similar or better.

National Weather Service (NWS) forecasters strive to provide information in their public products that reflect as accurately as possible any variation in the areal extent and amount of rainfall compared to the previous day. Yet, identifying this type of change in advance is often difficult, and the forecast for the upcoming day may instead indicate the familiar, “partly cloudy with scattered afternoon showers and thunderstorms.” Unfortunately, this standard forecast may not provide sufficient meaningful information to satisfy the needs of those trying to decide whether to schedule or postpone activities.

A review of the literature indicates that considerable day to day variations in the areal extent and amount of summer convective rainfall in peninsular Florida were identified over 50 yr ago, and many subsequent studies have been conducted in an attempt to better understand the various factors that govern the exact convective pattern for any given day. Byers and Rodebush (1948) noted that the considerable day to day variability could not be explained purely by thermodynamic considerations, even when moisture was taken into account. This was consistent with results from an earlier unpublished study of soundings in Florida by Baum (1947). Byers and Rodebush (1948) were first to emphasize and propose that the low-level horizontal convergence caused by the afternoon sea breezes commonly entering the peninsula from both coasts was a necessary condition for the development of summer thunderstorms.

Gentry (1950) documented his concern about the repetitive use of the standard summer forecast in south Florida, indicating it provided little additional information to the public that was not already known, and set out to investigate the issue of daily variability of rainfall. Using a network of 10 rain gauges in the Miami, Florida, area, he recorded the number receiving rain each day during five summers. His examination of the corresponding Miami soundings indicated that the lapse rate nearly always ranged between the wet- and dry- adiabatic lapse rates, yet he found little correlation between the degree of conditional instability and the number of stations in his network reporting rainfall. In fact, he found almost equal numbers of days in which no stations reported rain, 1 station reported rain, 2 stations reported rain, and so forth up to 10 stations reporting rain, thus indicating that the rainfall regime was in fact quite variable on a daily basis.

To identify and better understand the principal factors responsible for the variations in the spatial and temporal patterns of summer convective rainfall in peninsular Florida, Gentry (1950) researched parameters associated with conditions that encouraged the release (suppression) of convective instability and the increase (decrease) in moisture content of the air mass. Many of the conclusions from Gentry's work, including the significance of moisture aloft and the influence of large-scale flow patterns, appeared as recurring themes in subsequent similar studies, and served as inspiration for the current study.

For example, Day (1953) found that “wet” days tended to be associated with stronger low-level convergence. Gentry and Moore (1954), Frank et al. (1967), and Pielke (1973) established the relationship between the organization and evolution of convection over south Florida and peninsular and synoptic-scale forcing. Frank and Smith (1968) identified significant correlations between radar echo areal coverage and both moisture from 850- to 650 mb and precipitable water, indicating that showers were more likely with a deep moisture layer.

Neumann (1971) incorporated nonlinearity in his development of a system of multiple regression equations for forecasting summer thunderstorms at the Kennedy Space Center in Florida. He also noted that it may be possible to avoid discontinuities from one month to the next as well as reduce the variance further by deriving a single set of prediction equations for the entire thunderstorm season rather than using time steps of one month. Pielke (1974), Pielke and Mahrer (1978), Gannon (1978), and McCumber (1980) simulated the generation and evolution of the sea breeze and its implicit convection over south Florida, showing a strong relationship between convection, the sea breeze, and the large-scale flow.

López et al. (1984) investigated the variations in areal coverage by exploring the daily relation between the early morning sounding and the maximum echo coverage. The study results confirmed conclusions made by Gentry (1950) nearly 35 yr earlier. Blanchard and López (1985) concluded that convection on a particular day was the result of the interaction of many scales, including regional (Atlantic high pressure circulation), synoptic (waves, fronts), peninsular (sea and lake breezes), and local (surface feature variations such as soils, vegetation, etc.) in addition to cloud-scale interactions (cloud merger, outflow boundaries). They also acknowledged the continued difficulty, despite the 35 yr that had elapsed since the earlier studies, in understanding completely the myriad factors and complex interactions that determined the exact convective pattern for any given day.

Over 50 yr have elapsed since the early published literature on the topic of daily variations in areal coverage and amount of convective rainfall in peninsular Florida. Yet, NWS forecasters for west-central Florida can still find it challenging at times to identify in advance, even as late as midmorning, whether that given day will experience increased or decreased average areal coverage and amount of rainfall compared to the previous day. Thus, there is still the temptation at times to provide the standard forecast, knowing that it will probably verify most of the time—especially if it is assumed that some showers occurred without measurable rain falling in some or all of the official rain gauges.

To further address this issue, an investigation spanning the months of May–September 1997–2000 was conducted with three main goals. The first goal was to use a rainfall reporting network to provide evidence that considerable daily variation in the average areal coverage and amount of convective rainfall does in fact occur in west-central Florida. The second goal was to identify meteorological parameters with high correlations to observed average areal coverage and rainfall amount within the network. The third goal was to develop a reliable objective forecast aid to predict average areal coverage and rainfall amount for the current day using input from that day's 1200 UTC unmodified radiosonde data from the NWS Forecast Office located in Ruskin, Florida (WFO Ruskin).

The results of the study would thus 1) lead to a better understanding of the meteorological parameters that contribute to daily variations of observed areal coverage and rainfall amount in west-central Florida and 2) assist the forecaster in determining whether to issue or modify certain meteorological products and information to provide a more accurate and descriptive precipitation forecast service for the public to use in planning and conducting their activities for the day.

2. Methodology

Pursuant to the first goal, a network of rainfall observation sites (Fig. 1), composed of 29 airport and NWS Cooperative Observer Program (COOP) stations and WFO Ruskin, spanning the 15 counties within the forecast area of responsibility of WFO Ruskin, was used. Observed rainfall data on each calendar day for the dependent sample of May–September 1997–2000 was entered into a database by site. The daily number of sites reporting measurable rainfall (including 0 for days when no rainfall was reported), as well as the daily average rainfall amount for all 29 sites, was calculated and accumulated in the database (612 total days). Autocorrelations and frequency analyses were then performed for each to validate the presence of considerable daily variations for the dependent period.

It is noted from Fig. 1 that the routine time of the daily rainfall observation for 17 sites was from 0000 to 0900 LST (Inverness, Weeki Wachee, Hillsborough State Park, Tampa International Airport, Lake Alfred, St. Petersburg, Parrish, Bradenton, Wauchula, Avon Park, Ona, Myakka River State Park, Desoto City, Venice, Arcadia, Archbold, and Fort Myers). Climatological frequencies of precipitation as a function of time of day are provided in Figs. 2a–d for the development period using two coastal sites [Tampa International Airport (TPA) and Fort Myers—Page Field (FMY)] and two inland sites [Winter Haven—Gilbert Field (GIF) and Leesburg Municipal Airport (LEE)]. While Fig. 1 shows Leesburg (square) to be outside the forecast area of responsibility for WFO Ruskin, it is within sufficiently close proximity to be used in validating the climatological assumptions. The histograms in Figs. 2a–d clearly show that the period from 0000 to 0900 LST for the development period was characterized by a minimum of measurable rainfall occurrences. Thus, precipitation reported at any of these 12 sites for a given day was assumed to have occurred on the previous afternoon and/or evening, and was entered into the database as such.

Figure 1 also shows that there were 12 sites for which the observation times were from 1400 to 1900 LST (Usher Tower, Bushnell, Brooksville, St. Leo, Tarpon Springs, Plant City, Lakeland, Winter Haven, Mountain Lake, Bartow, Fort Green, and Punta Gorda). From Figs. 2a–d, this time period was generally close to or within the period of maximum measurable rainfall occurrences for the dependent sample. Thus, it is possible that a precipitation event ongoing at the time of the observation at any of these seven sites may have continued beyond the time the rainfall observation was taken. In these cases, the rainfall value reported was entered into the database on that day, recognizing that it could in effect represent only a partial event total and that any accumulations beyond the observation time would be included in the database as part of the totals for the following day. This is an acknowledged problem, which is not at all unique to this study. In fact, the same data entry methodology is utilized by the National Climatic Data Center (NCDC), which is the largest active archive center of weather data in the world.

The second goal was approached by expanding the above database to include the corresponding daily values, obtained from the 1200 UTC WFO Ruskin radiosonde data, of meteorological parameters identified by the above previous studies as being physically relevant to summer convective rainfall in Florida. Pearson correlation coefficients were then computed to determine how well 1) the daily average percent (including 0) of the 29 stations within the network observing rainfall (i.e., areal coverage) and 2) the daily average rainfall amount (including 0) reported for all 29 stations correlated with each of the selected parameters.

The third goal was addressed by performing multiple linear regression analysis on the database to produce a single prediction equation each for average areal coverage and rainfall amount. The two equations were tested on an independent dataset to determine viability as a reliable objective forecast aid to predict average areal coverage and rainfall amount for the current day using input from that day's 1200 UTC unmodified radiosonde data from WFO Ruskin.

3. Daily variations in observed average areal coverage and amount of rainfall

Meteorological persistence is the tendency for weather, or a meteorological parameter, in successive time periods to be similar. For continuous variables, such as the number of stations reporting rainfall, or average amount of rainfall, persistence is typically characterized in terms of autocorrelation (also known as lagged correlations), or the correlation of the variable with its own future and past values.

The collection of autocorrelations computed for various numbers of lags is called the autocorrelation function, which can be displayed graphically with the autocorrelations plotted as a function of lag. Figures 3a and 3b each show the first seven values of the autocorrelation function for the daily number of stations reporting rainfall, and for the daily average rainfall amount, respectively, from May to September composited over the four dependent years. Since any unshifted series of data will exhibit perfect correlation with itself, the 0 lag is not shown. Note that the autocorrelation function decays toward 0 with higher lag value, reflecting the generally weaker statistical relationships between data points further removed from each other in time. From a meteorological perspective, if the autocorrelation function did not decay toward 0 after a few lags, persistence would be a reasonably accurate prediction for the parameter from the current observation out several (or more) days. Thus, Figs. 3a and 3b indicate daily variability in both average areal coverage and rainfall amount for the dependent data.

Additionally, a frequency distribution for the occurrence of rainfall (Fig. 4) shows that spatially, daily rainfall across this region of Florida was highly variable for the dependent sample. Of relevance is that the general trend in Fig. 4 decreases from left to right; that is as the number of stations reporting rainfall increases, the number of occurrences decreases, with relatively few occurrences of 27–29 stations reporting rainfall.

4. Correlations of meteorological parameters to daily observed average areal coverage and amount of rainfall

The second goal in the study was to investigate how well daily average areal coverage and amount of rainfall each correlated with certain meteorological parameters. The studies referenced earlier identified the key meteorological quantities most relevant to the production of daily summer convective precipitation in Florida as being moisture, stability/temperature, and flow. Among these, specific parameters that can be extracted directly from the sounding data were chosen for the current study. This resulted in the selection of 16 parameters (Table 1), of which 7 were moisture parameters, 5 were related to stability/temperature, and 4 were wind flow parameters.

Included among the moisture parameters was precipitable water (PW), which is a measurement of the depth (in.) of liquid water at the surface that would result after precipitating all of the water vapor in a vertical column extending from the surface to 300 mb. Additional moisture parameters included the average dewpoint from 850 to 700 mb (ATD87), 850 to 500 mb (ATD85), 850 to 400 mb (ATD84), and 700 to 500 mb (ATD75). Included also was the minimum theta-e temperature (MNTHTEK), which describes the relative dryness or wetness of the atmosphere by representing the minimum temperature (K) a parcel of air would have if all of its moisture were condensed out through adiabatic ascent, and then the parcel descended dry adiabatically to 1000 mb. Last among the moisture parameters was wet-bulb zero pressure (WBZPRES). Being a function of moisture, the pressure (mb) at which the wet-bulb temperature is 0 (°C) increases as moisture decreases.

The difference between the 850- and 700-mb temperatures (T8MINT7), and between the 700- and 500- mb temperatures (T7MINT5), were among the group of five stability/temperature parameters. As indicators of convection, the K Index (K) and SWEAT Index (SWEAT) were also included. The average of the 850- and 700-mb temperatures (A87) was also added, recognizing that high values would relate to potential instability because of the higher potential low-level moisture content, and the higher potential moisture content might itself also be related to rainfall coverage and especially amounts. Thus, even though the process of averaging may at times smooth out the actual effect of the temperatures at each level (e.g., when there was a steep lapse rate between the two levels), the parameter was included.

The included wind flow parameters were the 0–3-km AGL mean wind direction (MNDIR3) and speed (MNSPD3), and the 0–6-km AGL mean wind direction (MNDIR6) and speed (MNSPD6). There was some concern regarding the separating of wind direction and speed for use as flow predictors, as this could potentially risk diluting the effects of the flow regimes. However, given the large geographic size of the area used in the study, rain will usually occur somewhere regardless of the direction of the flow, suggesting that the flow direction may not be as important as the wind speed. Therefore, the wind direction and speed were maintained as separate parameters.

The Skew-T/Hodograph Analysis and Research Program (SHARP; Hart and Korotky 1991) software application was used to extract daily values for the 16 parameters from the 1200 UTC WFO Ruskin radiosonde data. The data were then included in the dependent database. As background, the SHARP application is particularly useful to meteorologists because it allows qualitative diagnosis of data provided by radiosonde releases. It has been utilized successfully in other studies to identify meteorological event predictors. For example, Hagemeyer and Matney (1993), in attempting to ascertain whether multiple indices have value as event predictors for severe thunderstorms and tornadoes, noted that data output by SHARP had a distinct advantage over pattern matching using mean soundings derived by category of event. Goss and Moore (1995) modified the 1200 UTC radiosonde data for surface conditions in an attempt to use SHARP to predict severe thunderstorm potential in the spring season in northern Texas. Maglaras and LaPenta (1997) performed regression analysis on SHARP output to develop an equation that provided guidance on forecasting tornadic, nontornadic but severe, and nonsevere thunderstorm days in New York State. The follow-up study by Maglaras and LaPenta (2000) involved the development of objective statistical guidance based on regression analysis using SHARP output to discriminate between major and minor hail days in New York State.

Prior to determining correlations, the assumption was established that the overall air mass represented by the 1200 UTC WFO Ruskin radiosonde data did not change significantly during the day. From the dependent database, Pearson correlation coefficients (Wilks 1995) were calculated (Table 2). Asterisks indicate where they are significantly different from 0 at the 0.01 and 0.05 significance level. Only days with no missing values for all 16 variables were included so as to avoid correlations computed from substantially different subsets of the cases. This resulted in 515 of the 536 cases being applied. The significance tests assumed 514 degrees of freedom.

Table 2 lists the Pearson correlation coefficients between each parameter from Table 1 and the predictands average areal coverage and rainfall amount. Table 2 shows that all seven moisture parameters provided the highest correlations with each predictand, significant at the 0.01 level (two tailed). This was not unexpected, as the summer convective rainfall process in this region taps the nearly always present low-level moisture, and is further enhanced by the presence of midlevel moisture. Since PW is a direct measure of the available moisture in the atmospheric column to 300 mb, it was not surprising that it yielded the highest correlations.

It is also interesting to note from Table 2 that WBZPRES was negatively correlated with both average areal coverage and rainfall amount (−0.665 and −0.486, respectively). Thus, in the dependent sample, higher (lower) values of WBZPRES correlated with lower (greater) average areal coverage and rainfall amount. Indeed, being a function of moisture, as WBZPRES increases, moisture decreases.

Among the stability/temperature parameters in Table 2, it is noted that for both predictands, K and SWEAT, and T7MINT5 yielded correlations that were significant at the 0.01 level (two tailed). Additionally, Table 2 shows that for average areal coverage, T8MINT7 was also significant at the 0.01 level (two tailed). Nevertheless, the individual correlations of the stability/temperature parameters with each predictand were all lower than the respective moisture parameters. With the summer Florida atmosphere being nearly always conditionally unstable in this region, it thus appears that stability is of lesser importance when compared with moisture, as a contributor to the variability factor.

Among the flow parameters in Table 2, the correlations with both predictands for the low-level flow MNDIR3 and MNSPD3 were each very low and not significant at either the 0.01 or 0.05 levels (two tailed). This is not necessarily in conflict with research presented earlier, which identified a relationship between the patterns and locations of Florida summertime convective rainfall and the wind flow at low levels. Rather, it may be more a result of these flow parameters being entered in the default output format of direction and speed that is generated by SHARP, which, for linear correlation, results in a discontinuity at 0° and 360°. An additional partial explanation may be that the area selected for the current study was large enough to have rainfall occur from both low-level easterly and westerly flow regimes, therefore making low-level flow appear less important in the linear correlation results.

It is also noted in Table 2 that the correlations between MNDIR6 and both predictands were very low and not significant at either the 0.01 (two tailed) or the 0.05 levels (two tailed). However, the correlations for MNSPD6 were identified as significant at the 0.01 level (two tailed), but the low values are generally considered to be in the noise range in terms of meteorological significance (especially since the degrees of freedom are overestimated in this case). Nevertheless, since it is known from previous studies that the summertime convective rainfall process is further enhanced by the presence of midlevel moisture (in addition to the nearly always present moisture at low levels), these results may also suggest the relative importance of the advection of moisture at midlevels (between 3 and 6 km) generally from any directional source.

5. Multiple linear regression analysis and results

The third goal involved performing multiple linear regression analysis on the dependent database to produce a single prediction equation each for the average areal coverage and rainfall amount. The resultant equations would then be tested on an independent dataset to determine their viability as an objective forecast aid.

The multiple linear regression analysis performed was that of the stepwise predictor selection method (Draper and Smith 1998), using the statistical analysis software application SPSS for Windows version 10.1. The first variable considered for entry into the equation was the one with the largest positive or negative correlation with the dependent variable. The variable was then checked for significance as a prerequisite to searching for the second predictor variable to enter into the equation. At each step, a variable was entered into the model if the significance level of its F statistic was less than the “entry” value, and was removed if the significance level was greater than the “removal” value. The F statistic is used for variance ratio tests, especially in the analysis of variance. The alpha values of 0.05 and 0.10 for the limits of significance of the F statistic were used for entry and removal, respectively, as these were the SPSS default criterion, as well as the values recommended by Draper and Smith (1998). Note that lower (higher) values of the threshold alpha are associated with higher (lower) significance of the selected predictor. The method terminated when no more variables were eligible for inclusion or removal.

As expected, PW was the first selected variable in each resultant equation (Table 3). For both equations, the next two selected predictors included A87 and MNSPD6. It is noted that despite their high positioning in the equations (Table 3), these two predictors actually had lower correlations with the predictands (Table 2) than any of the remaining selected predictors in each equation. Sometimes predictors that display lower correlation with the predictand are preferred if they also are relatively uncorrelated with predictors already in the equation.

The adjusted R2 for the daily percent average areal coverage prediction equation, Eq. (1) in Table 3, was 0.630, and the standard error of the estimate was 16.2. The adjusted R2 for the daily average rainfall amount prediction equation, Eq. (2), was only 0.391, and the standard error of the estimate was 0.22.

6. Independent data sample analysis and discussion

The database content for the independent dataset, composed of the months of May–September 2001, was developed to be consistent with that of the dependent sample. Observed rainfall was available for 153 days, and the 1200 UTC WFO Ruskin radiosonde data were available on 149 days.

For each of the 149 cases, the predicted daily average areal coverage and rainfall amount were calculated using the appropriate equation from Table 3, and subsequently displayed graphically, by month (Figs. 5a–e and 6a–e), with the corresponding observed data for visual comparison (dashed lines). The combined climatological daily average rainfall within the 29-site rainfall reporting network for sites where a full 30 yr of records were available (all but Archbold and Ona) is also displayed in Figs. 6a–e (triangular data points) for comparison. While visual inspection of Figs. 5a–e and 6a– e appears to reveal a correlation between the predicted and observed magnitudes and trends, a more specific analysis of the error patterns for the predictions was developed (Table 4).

Examining the values for areal coverage first, Table 4 (above the dashed line) shows that among the 149 total predictions, 11 (7.4%) verified exactly, and there was an equal division (69 of 149 total, or 46.3% each) between predictions that were higher and lower than the observed areal coverage, with the overall average errors being in the range of 8%–10%. Of greater importance for operational use is how well the predictions forecasted the trend direction from the observed percent average areal coverage of the previous day, along with the associated average error. There were 144 predictions for which values for the trend types indicated in Table 4 (below the dashed line) could be calculated.

The first four trend types for areal coverage represent when the predicted trends of increase or decrease (not including predictions of no change) were in the correct direction when compared with the observed trend (excluding for now those cases where the magnitude of the trend prediction was exactly forecast). These composed 99 (68.8%) of the 144 total predictions, with the predictions averaging within ±10% of the observed value.

The next six trend types represented situations where the predicted and corresponding observed trends for areal coverage did not match, and consisted of 35 (24.3%) of the 144 total occurrences. In most of these occurrences, the data showed that the observed 1200 UTC value of one or more of the moisture parameters in Eq. (1) changed considerably from the previous day (contributing to a corresponding change in the predicted areal coverage trend). Additionally, a comparable or even larger change in these same parameters in the opposite direction (i.e., a rebound) was noted in the data from the 1200 UTC radiosonde release the following day.

This pattern allows speculation that the rebound may have actually begun on the same day that the 1200 UTC radiosonde release initially showed the changed moisture values, but subsequent to that release. Thus, the amount of observed areal coverage for that day could potentially be influenced by the early rebound in a manner not reflected appropriately in the prediction for that day from Eq. (1).

The three remaining trend types in Table 4 for areal coverage reflected the situations of no change (persistence) in the predicted and observed trend, and when a predicted trend of increase or decrease from the observed value of the previous day was accurately forecast for the trend direction, and also exactly forecast for the magnitude of the change. Table 4 shows that 10 (6.9%) of the 144 occurrences met the criteria for these trend types.

Combining the number of occurrences within the first four and last three trends in Table 4, Eq. (1) was a reliable predictor of the trend direction 75.7% (109 cases of 144 total) of the time, with the associated average error generally within ±10% of the observed value, for the independent sample.

Upon a similar review of the results in Table 4 based upon using Eq. (2) for predictions of average rainfall amount, Eq. (2) was found to be a reliable predictor of the trend direction 77.1% (111 cases of 144 total) of the time, with the associated average error generally within ±0.10 in. of the observed value, for the independent sample.

However, for average rainfall amount, it is also noted from Table 4 that the average error when a decreasing trend was predicted but an increase occurred was over twice that in magnitude of when an increasing trend was predicted but a decrease occurred. An examination of the data revealed that this larger average error was associated with widespread and excessive rainfall on 13 September 2001 and particularly on 14 September 2001, when Tropical Storm Gabrielle directly affected west- central Florida. The rainfall total for all 29 rainfall sites in the study network on 14 September 2001 was 96.32 in.! Thus, the average rainfall was 3.32 in. While the equation predicted 1.11 in., which was the highest prediction made during the entire 5 months of the independent sample, it nonetheless fell significantly short of the observed value, contributing to the large average error.

Furthermore, that prediction of 1.11 in. was less than the observed average rainfall of the previous day, which was 1.36 in. (total rainfall in the network was 39.38 in.), also due to the widespread heavy rainfall in advance of the approaching tropical storm. (Note from Fig. 6e that the equation did correctly predict an increase for 13 September 2001 from the previous day's observed with a prediction of 0.97 in., which was the second highest prediction made for the entire independent sample.) But despite predicting the highest value of the independent sample for 14 September 2001, a large error for magnitude was incurred, and the proper direction of the trend was missed as well, due to the excessive observed rainfall the previous day. As a point of interest, removing just the 14 September 2001 rainfall anomaly from the tabulation in Table 4 reduced the average error for the trend “decreasing trend forecasted, increasing trend observed” from 0.35 to 0.18 in., and the average error for the trend “underforecast of increasing trend” from 0.14 to 0.11 in.

To further the investigation regarding the performance of Eqs. (1) and (2) when tested on the independent dataset, an analysis of the error patterns was conducted for predictions when observed trend changes of larger magnitude were observed. For average areal coverage, this was defined as a change of at least 20% in the observed areal coverage compared to the observed value of the previous day. For average rainfall amount, it was a change of at least 0.20 in. in the observed amount.

Figure 7 provides a scatterplot of the predicted and observed daily trends of areal coverage for the independent sample. Figure 7 also shows that for cases when the observed amount of areal coverage constituted a trend change of at least 20% (areas a–d), Eq. (1) correctly predicted the trend direction (areas b, c) in 39 of 39 total occurrences (100.0%). The overall average trend prediction error for the 20 total occurrences within area b of Fig. 7 was about 8%, indicating that Eq. (1) tended to underforecast the magnitude of the increasing trend by about 8% on the average. Similarly, the overall average prediction error for the 19 total occurrences within area c was 5.66%, indicating that Eq. (1) tended to underforecast the amount of the decrease by about 6%. Note also that the plots for 23 of these 39 specific occurrences (59%) fell along or between the portions of the two parallel diagonal lines that were within areas b and c, indicating that the individual prediction for each occurrence was within ±10% of the observed value. Additionally, Fig. 7 shows that for all 144 total trend occurrences, 91 (63%) fell within the dual parallel lines, indicating that the individual prediction for each was within ±10% of the observed value.

Figure 8 is a similar scatterplot for average rainfall amount. From areas a–d, it is seen that when the observed trend for rainfall amount changed by at least 0.20 in., Eq. (2) correctly predicted the trend direction (areas b, c) in 32 of 36 total occurrences (88.9%). For the 14 occurrences plotted within area b of Fig. 8, Eq. (2) tended to underforecast the magnitude of the increasing trend by about 0.18 in. on the average. The overall average prediction error for the 18 total occurrences within area c was 0.06 in., indicating the average amount that Eq. (2) tended to underforecast the magnitude of the decrease. The portions of the dual parallel diagonal lines within areas b and c of Fig. 8 show that for 18 of these 32 specific occurrences (56%) the individual prediction for each was within ±0.15 in. of the observed value. Finally, Fig. 8 shows that 98 of the 144 total trend occurrences (68%) were plotted within the dual parallel lines, signifying that the individual prediction for each was within ±0.15 in. of the observed value.

7. Summary and conclusions

Considerable daily variations of average areal coverage and rainfall amount occurred in west-central Florida during the dependent period (May–September 1997– 2000). Pearson correlation coefficients calculated from a dependent dataset consisting of observed daily rainfall within a 29-site rainfall network and corresponding daily values of 16 selected meteorological parameters taken directly from the 1200 UTC radiosonde data at WFO Ruskin, in Florida, and representing moisture, stability/ temperature, and flow, identified the highest correlations to daily average areal coverage and amount of rainfall to be all the included moisture parameters. The specific moisture parameters identified were precipitable water, minimum theta-e temperature, wet-bulb zero pressure, and average dewpoints in various layers from the 850- to the 500-mb height levels.

Multiple linear regression analysis yielded a single equation each for the prediction of average areal coverage and rainfall amount, which were then tested on an independent sample for the period from May to September 2001. Both equations were reliable predictors of the trend direction from the observed value of the previous day, and of the magnitude of the change, about 75% of the time with the associated average errors generally within ±10% (area coverage) and ±0.10 in. (average rainfall amount), respectively. The equations can especially serve the forecaster in predicting trends of larger magnitudes (at least 20% and 0.20 in. for average areal coverage and rainfall amount, respectively), as even higher reliability (100% and about 90%, respectively) was indicated in the verification of those cases, with associated average errors similar to those indicated above.

The above results, while considered good, were nevertheless obtained from multiple linear regression analysis based on several assumptions that cannot be expected to be valid on all days. For example, the radiosonde data were technically only a limited temporal sample of the atmosphere at and just subsequent to balloon release through a single ascent line, and contrary to the assumption used in the study, are not representative of the true nonstatic nature of the atmosphere. Additionally, the study included assumptions basing the day that the daily observed rainfall was entered into the database for each station within the 29-site rainfall network upon the time of day that the respective daily precipitation measurements were taken. Therefore, while it may be possible that other and/or additional parameters could further improve the results, significant additional improvement using the present methodology may be difficult to achieve unless these limitations are addressed.

In conclusion, the overall accuracy of the equation predictions when tested upon an independent dataset should allow the forecaster to dependably utilize the equations in determining whether to issue, modify, and/ or fine-tune certain meteorological products and information (e.g., zone forecasts, area forecast discussions, hazardous weather outlooks, etc.) for the midmorning forecast update, which would be in time for residents and visitors to take the updated information into account for their planning of the day's activities.

Acknowledgments

Many thanks are due (posthumously) to Annegret Cornell, administrative support assistant, and forecaster Paul Close, at WFO Ruskin. Their help in tirelessly compiling the observed rainfall data, along with many associated calculations, was crucial to this project and its timely completion. A debt of gratitude is also owed to the HMT staff at WFO Ruskin for recording 1200 UTC meteorological parameters on a daily basis from May through September for each of the years 1997 through 2000, allowing the author to incorporate this information into this study. Mr. Anthony Harper, IT at WFO Ruskin, is also recognized for automating the process of storing the daily 1200 UTC radiosonde data from Tampa, Florida, in a SHARP-compatible format. The author is also indebted to the reviewers for their valuable comments and infinite patience.

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Fig. 1.
Fig. 1.

County forecast area of responsibility (lines) for the NWS WFO Ruskin, FL (diamond). Locations of 29 observation sites (circles), and proximity site Leesburg (square), with associated rainfall observation times (LST) are shown

Citation: Weather and Forecasting 19, 2; 10.1175/1520-0434(2004)019<0286:TRBMPA>2.0.CO;2

Fig. 2.
Fig. 2.

Histogram showing the climatological frequencies of measurable rainfall occurrence as a function of the time of day (LST) from May to Sep of 1997–2000: (a) TPA, (b) FMY (1997 data not available), (c) GIF, and (d) LEE

Citation: Weather and Forecasting 19, 2; 10.1175/1520-0434(2004)019<0286:TRBMPA>2.0.CO;2

Fig. 3.
Fig. 3.

Lagged autocorrelation function. (a) Daily number of stations (including 0) reporting rainfall. (b) Daily average rainfall amount reported. Dependent dataset comprising May–Sep 1997– 2000. There are 615 total cases, 608 computable first lags, each

Citation: Weather and Forecasting 19, 2; 10.1175/1520-0434(2004)019<0286:TRBMPA>2.0.CO;2

Fig. 4.
Fig. 4.

Frequency of stations within the 29-site network reporting rainfall, May–Sep 1997–2000. There are 612 total days with reported measurable or 0 rainfall

Citation: Weather and Forecasting 19, 2; 10.1175/1520-0434(2004)019<0286:TRBMPA>2.0.CO;2

Fig. 5.
Fig. 5.

Daily predicted (solid line–rectangles) vs observed (dashed line–diamonds) average areal coverage of measurable rainfall (%) for the independent database in 2001: (a) May, (b) Jun, (c) Jul, (d) Aug, and (e) Sep. Gaps in the graph continuity were due to missed or failed radiosonde releases for a given day. There are 149 total cases, with 29 rainfall reporting stations total

Citation: Weather and Forecasting 19, 2; 10.1175/1520-0434(2004)019<0286:TRBMPA>2.0.CO;2

Fig. 6.
Fig. 6.

Daily predicted (solid line–rectangles) vs observed (dashed line–diamonds) average daily rainfall amount within the 29-site network (in.) for the independent database in 2001: (a) May, (b) Jun, (c) Jul, (d) Aug, and (e) Sep. Gaps in the graph continuity were due to missed or failed radiosonde releases for a given day. The climatological daily average rainfall (1971–2000) within the rainfall reporting network is displayed (triangular data points) for comparison. There are 149 total cases, with 29 rainfall reporting stations total

Citation: Weather and Forecasting 19, 2; 10.1175/1520-0434(2004)019<0286:TRBMPA>2.0.CO;2

Fig. 7.
Fig. 7.

Scatterplot of the predicted and observed daily trends of average areal coverage for the independent sample. (a) Observed trend of increase by at least 20%, and trend direction predicted incorrectly, 0 cases; (b) observed trend of increase by at least 20%, and trend direction predicted correctly, 20 cases; (c) observed trend of decrease by at least 20%, and the trend direction predicted correctly, 19 cases; and (d) observed trend of decrease by at least 20%, and the trend direction predicted incorrectly, 0 cases. Parallel diagonal lines bound all occurrences where the predicted trend was within ±10% of the observed trend. There are 144 total cases

Citation: Weather and Forecasting 19, 2; 10.1175/1520-0434(2004)019<0286:TRBMPA>2.0.CO;2

Fig. 8.
Fig. 8.

Scatterplot of predicted and observed daily trends of average rainfall amount for the independent sample. (a) Observed trend of increase by at least 0.20 in., and the trend direction predicted incorrectly, 3 cases; (b) observed trend of increase by at least 0.20 in., and trend direction predicted correctly, 14 cases; (c) observed trend of decrease by at least 0.20 in., and trend direction predicted correctly, 18 cases; and (d) observed trend of decrease by at least 0.20 in., and trend direction predicted incorrectly, 1 case. Parallel diagonal lines bound all occurrences where the predicted trend was within ±0.15 in. of the observed trend. There are 144 total cases

Citation: Weather and Forecasting 19, 2; 10.1175/1520-0434(2004)019<0286:TRBMPA>2.0.CO;2

Table 1.

Description of the 16 meteorological parameters with physical relevance to daily summer convective rainfall, along with the parameter name used in the correlations and multiple linear re gression analysis

Table 1.
Table 2.

Pearson correlation coefficients for correlations between 16 meteorological parameters and the predictands average areal coverage of rainfall (%) and average rainfall amount (in.) from May to Sep 1997–2000. There are 515 cases with no missing values for all 16 parameters. Correlation significant at the 0.01 level (two tailed) is shown with a double asterisk. Correlation significant at the 0.05 level (two tailed) is shown with an asterisk

Table 2.
Table 2.

(Extended)

Table 2.
Table 3.

Resultant multiple linear regression (stepwise) equations for May–Sep 1997–2000, for the predicted daily average areal coverage, Eq. (1), and the predicted daily average rainfall amount among the 29 rainfall reporting sites, Eq. (2)

Table 3.
Table 4.

Analysis of the average errors for average areal coverage and rainfall amount within the May–Sep 2001 independent dataset for predictions that were too high, too low, and exact when compared to the observed value (above the dashed line), as well as a breakdown for various predicted trends (below the dashed line). Number of occurrences in parentheses. There are 149 total cases. Trends were determined for 144 cases

Table 4.
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