1. Introduction
Lake Okeechobee, located in southern Florida, is a key component in the local and regional hydrologic system. The lake and its watershed are vital to the Kissimmee–Okeechobee–Everglades ecosystem, which ranges from the headwaters of the Kissimmee River in the north to Florida Bay in the south (Fig. 1). It is a multifaceted resource, providing drinking water to adjacent cities and towns as well as being a backup water supply for communities along the lower east coast of Florida. In addition, the lake is a major supplier of irrigation water for the surrounding agricultural areas and is a crucial supplemental water supply for the Everglades.
Currently, the U.S. Army Corp of Engineers (USACE) and the South Florida Water Management District (SFWMD) work to control the levels of Lake Okeechobee so that local water resource demands can be met. This is done through controlled releases of water through a series of man-made canals that act as outlets to the lake and that route water downstream for various uses. The Caloosahatchee River to the west and the St. Lucie Canal to the east are the main sources of surface discharge (Fig. 1), both of which are controlled; therefore, the only significant discharge from the lake that is uncontrolled is evaporation. Evaporation estimates for Lake Okeechobee are made based on solar radiation and maximum air temperature using simple empirical models (Abtew 2001).
The Kissimmee River and Fisheating Creek are the primary sources of surface water inflow into the lake (Fig. 1). Of these, only Fisheating Creek is not controlled. In addition, since Lake Okeechobee composes roughly 15% of the total area of the watershed, the volume of direct precipitation over the water surface relative to the overall volume of freshwater inflow can often reach high values.
The Southeast River Forecast Center (SERFC) has been charged with the duty of setting up and maintaining a modeling scheme for the Lake Okeechobee hydrologic system for the purpose of providing river-and lake-level forecasts. As a result, a preliminary setting including Lake Okeechobee and two of the major tributary inflows, Kissimmee River and Fisheating Creek, are currently part of the National Weather Service River Forecast System (NWSRFS). In adding new sites to the NWSRFS, especially those containing reservoirs, the process of calibration is of primary concern. Within the calibration process, model parameters are determined based on historical precipitation and discharges (NOAA/ NWS 2002a), and in smaller lakes, the approach adopted by the SERFC has been to assume that the volume of precipitation that falls directly over the lake is insignificant compared to the surface inflows. However, due to the large surface area that Lake Okeechobee represents relative to the total watershed area, this approach is not valid; therefore, special consideration will be given to the issue of precipitation estimation over the lake surface.
a. Objectives
The goal of this project is to determine the limitations and strengths of several sources of precipitation data used to compute the mean areal precipitation (MAP) over the surface of Lake Okeechobee. Data sources include gage-recorded precipitation and radar-derived multisensor precipitation estimates. Results obtained from analysis of the data will be used to determine what source of data is most suited to be used in the calibration of the Lake Okeechobee basin. Ultimately, this system will be used operationally to simulate water levels in Lake Okeechobee using computed inflows from the major tributaries, precipitation, and evaporation over the lake, as well as the most significant regulated outflows from the lake.
In addition, this project will compare the MAP estimates computed from the various data sources in order to find the relative differences between them. Due to operational issues, such as the occasional malfunction of precipitation gauges or radar, many times the mean areal precipitation estimates will need to be based on different data sources than those used for calibration; therefore, the knowledge of how these estimates compare will aid in the future forecasting of water levels in Lake Okeechobee.
2. Background
Before the precipitation data sources can be analyzed, it is important to recognize the general precipitation patterns that exist over Lake Okeechobee and south Florida. This will help in determining the importance of spatial and temporal resolution within the datasets with regard to measuring the variability of precipitation over the lake surface. Precipitation patterns in south Florida are mostly convective in nature, with strong diurnal and seasonal trends. This leads to a high spatial variability of precipitation over the region, as compared to an area dominated by stratiform precipitation events. Depending on the synoptic flow regime over the Florida peninsula at any given time, convection may be driven by synoptic forcing or through mesoscale phenomena such as sea-breeze fronts. In undisturbed conditions where synoptic forcing is not significant, Pielke (1974) discovered that sea-breeze circulations are the dominant factor in thunderstorm initiation. Cooper et al. (1982) later discovered that convection was initiated by the sea-breeze front, but subsequent thunderstorm activity was primarily a result of downdrafts from the original convection.
Under weak synoptic forcings, the sea-breeze front initially begins in the late morning along the eastern shore of the southern peninsula (Blanchard and Lopez 1985). This front moves inland due to the easterly winds brought about by the mesoscale environment. A few hours later, a lake-breeze front appears along the southeastern and eastern shore of Lake Okeechobee. This lake-breeze front has been documented by Pielke (1974) and Watson and Blanchard (1984). The sea-breeze and lake-breeze fronts interact to produce higher-intensity convection along the eastern and southeastern shores of Lake Okeechobee. At roughly the same time, a sea-breeze front sets up along the western shore of the Florida peninsula, which propagates inland before colliding with the initial sea-breeze front moving in from the east. As these fronts collide in the late afternoon, there is widespread convection over the southern peninsula; however, convection is suppressed over Lake Okeechobee due to the cooler water surface, except for the eastern and southern shores as described above. As the convection ceases in the evening and night, Lake Okeechobee remains fairly clear with lingering precipitation along the southern edge of the water surface. Michaels et al. (1987) demonstrated the significance of Lake Okeechobee in summer thunderstorm development, which is important because the day-to-day variations in thunderstorm activity over the southern peninsula vary little throughout the warm season.
As synoptic forcings increase in strength, the location and magnitude of the sea-breeze fronts vary; however, no matter what the scenario, Lake Okeechobee tends to effectively suppress convection, especially along its center and northwestern quadrant (Burpee and Lahiff 1984; Blanchard and Lopez 1985). Only when synoptic forcings are strong do precipitation patterns show a fairly constant depth of precipitation over the Florida peninsula, such as during tropical cyclone events or cool-season midlatitude cyclones.
In order to better compare precipitation estimates from multisensor and gage-recorded precipitation sources over Lake Okeechobee, it is advantageous to discuss the method in which the NWS and the river forecast centers develop the multisensor precipitation estimates as used in this study. At the time of writing the precipitation estimates were developed using the stage II and stage III algorithms; however, they are now being developed using the Multi-sensor Precipitation Estimator (MPE) program. These procedures will briefly be discussed here, since details can be found in Fulton et al. (1998), and also in the online documentation of the Precipitation Processing System (PPS; NOAA/NWS 2002b).
a. Precipitation Processing System and stage III
The radar precipitation estimation process begins when raw radar precipitation estimates are obtained by inputting radar reflectivity signatures through a Z–R relationship, which relates reflectivity, Z (associated with droplet size and number density), to precipitation rate, R (given in mm h−1). The basic data are integrated to produce hourly precipitation accumulations, which are output in the form of a digital precipitation array (DPA). At this point, the radar data are referred to as stage I data. Significant error can arise in this process due to inherent problems with radar precipitation observation, including beam overshoot and misrepresentation of precipitation. Since a radar beam propagates in a line-of-sight manner, high precipitation near the installation and low precipitation far away may not be measured, with obstacles such as trees, buildings, or terrain further impeding the radar by blocking the beam. In addition, different precipitation types may share the same reflectivity values (snow, rain, hail, etc.), though they may not contain equal volumes of liquid water; therefore, the inherent uncertainty in the Z–R relationship can result in significant errors. The choice of Z–R relationship used at any given time can be a significant factor in later precipitation products; however, the consistent patterns of convective precipitation over south Florida minimize this sensitivity (Steiner and Houze 1997).
After the initial stage I processing comes stage II, which includes calculating a corrective mean field gauge–radar bias and local adjustments to a multisensor precipitation field for an area within a radius of 230 km relative to a single radar installation. This area is referred to as the radar umbrella. The corrective mean-field bias is calculated using a Kalman filtering approach and is applied uniformly to all grid cell values under the radar umbrella (Smith and Krajewski 1991). Upon completion, stage II provides a multisensor precipitation field that includes both the corrective mean bias and local gauge-derived biases (NOAA/NWS 2001; Briedenbach et al. 1998).
Stage III, the final step in the multisensor precipitation processing procedure, was developed specifically for the NWS river forecast centers. Stage III takes as input the stage II multisensor precipitation fields from all radars within a given region, then creates a mosaic of coverages to form a continuous field of multisensor-estimated precipitation. Stage III products can be manually edited to remove areas of known contamination, either in the radar field or in individual rain gages, at which point stage II fields can be reprocessed to produce improved precipitation estimates. These improved radar fields are then remosaicked in stage III. In addition, in areas where two or more radar coverages overlap, the user has the option to use either mean or maximum grid values. As with stage II, stage III output includes multisensor estimates as well as radar-only fields (NOAA/NWS 2001b; Briedenbach et al. 1998).
3. Data and methodology
Within this project, data from three individual sources were utilized for comparison. These included gauge-recorded precipitation from the NWS station network and SFWMD Lake Okeechobee network, as well as hourly Weather Surveillance Radar-1988 Doppler (WSR-88D) multisensor precipitation estimates from stage III mosaics. In the area surrounding Lake Okeechobee, the NWS gauge network includes daily precipitation accumulations taken by cooperative observers. There were five such daily stations within a reasonable distance from Lake Okeechobee (<30 mi from the center of the lake), all of which contained adequate data for this project (Fig. 2). Stations that were farther away than this were not considered, since most precipitation that occurs in southern Florida is convective (occurs over a small spatial scale) and values from these sites would not reflect precipitation over the lake. The SFWMD precipitation network contains a total of 24 stations in and around Lake Okeechobee (<30 mi from the center of the lake), all of which automatically measure and record hourly precipitation.
The NWS and SFWMD rain gauge data were analyzed for completeness and consistency by employing a double mass analysis procedure on each data source (Kohler 1949), and stations that had an incomplete time series or consistently errant values relative to surrounding observations were removed. The double mass analysis was used only as a tool for reviewing and comparing the individual gauge time series, and no corrections were applied to the data. After reviewing the results from the analysis procedure and omitting the sites that contained errant values or an incomplete time series, all five stations were kept for the NWS network and 18 stations remained for the SFWMD network (Fig. 2). These quality control procedures were meant to check the precipitation time series for continuity and feasibility, and in no way gave any indication of the accuracy of the data.
Radar data used in this project include hourly precipitation estimates derived from WSR-88D installations, compiled and mosaicked in stage III (NOAA/ NWS 2002a,b), and archived by the NWS. As stated previously, there are errors implicit in the raw radar estimates, but by using stage III mosaicked values, this error is minimized. Lake Okeechobee is under the coverage of three radar umbrellas: Melbourne, Tampa, and Miami, Florida (Fig. 3). Under these coverages are a number of gauges used to compute the corrective radar bias, none of which are located in the immediate vicinity of Lake Okeechobee. As a result, none of the surface gauge stations used for this study was used to compute the mean field bias in the multisensor product, due to the fact that the NWS gages only recorded daily precipitation totals and the SFWMD gauges were not available to the NWS.
The study area of this project involves a 1732 km2 (669 mi2) basin, corresponding to the surface area of Lake Okeechobee as defined by the Herbert Hoover dike system; therefore, the analysis will not be done to the detail of a Hydrologic Rainfall Analysis Project (HRAP) grid cell (4 km × 4 km), such as used by Fuelberg et al. (2002) and Young et al. (2000). Instead, a similar procedure to that used by Stellman et al. (2001) will be followed, which utilized MAP estimates over a specific region. They used this method when they made a 2-yr comparison between multisensor mean areal precipitation (MAPX) and rain gauge-derived MAP for the headwater of the Flint River basin, Georgia (4744 km2).
a. Computations of mean areal precipitation
Computations of MAP are necessary to provide precipitation estimates for a lumped modeling approach, such as is used in the NWSRFS. To create a MAP, precipitation values from several gauges are used to determine a mean precipitation depth that represents a given area over a specific time. For this project, the boundary of Lake Okeechobee, as defined by the extent of the Herbert Hoover dike system, is considered a single basin; therefore, all data included in this study must be organized into a MAP time series in order to be equally compared.
1) Gauge-only MAP
When creating MAP estimates, the SERFC utilizes the Thiessen polygons method to obtain basinwide values (Linsley et al. 1975). This method was applied to both the NWS and SFWMD networks for this study. For the SFWMD gages, 3 of the 18 gages were not used in the Theissen analysis because they were either too far from the lake or did not contain adequate data. The weights used for the individual NWS and SFWMD gauge networks are included in Table 1. The largest source of error when using such a method arises due to the spatial sampling of rainfall. If the spatial sampling is insufficient, MAP estimates may be biased and have large uncertainties. This can occur when the gauge network is sparse and few gauges are located in or near the basin, or when there are an adequate number of gauges but they are concentrated in tight groups. This may cause a small sample of stations to add too large a weight relative to the overall MAP calculation. Additional error can occur if the only available gauges are located a large distance from the center of the basin, in which case the MAP value might not be well represented by the gauges. These problems are especially apparent when the local precipitation patterns are spatially varied, such as when the precipitation is dominantly a result of convective systems. This is the case in the study area of this project; therefore, the spatial distribution of the gauge networks is extremely important.
MAPs were computed using (i) the five NWS precipitation sites and (ii) the 18 SFWMD precipitation observation stations. SFWMD MAPs for two different time intervals were computed, a 1 and a 6h, while only a 6-h NWS MAP was computed. The 6-h NWS MAP was created using the 24-h cooperative observer data and 1-h NWS observations from the nearest automated stations (NOAA/NWS 2002a). This was necessary because during operations, the NWSRFS model is run on a 6-h time step due to constraints in the preprocessing software of the gauge-only rainfall data. Currently, the processing algorithms are being modified to handle a smaller time step, at which point hourly comparisons of rainfall under an operations framework can be performed. Series for both time steps were computed such that the general precipitation patterns could be determined using the 6-h time step MAP and more detailed single-event analysis could be carried out using the 1-h MAP.
2) Radar-derived MAPX
The data available from radar estimates of precipitation must be preprocessed to compute a radar-based MAPX. The inputs in this process are gridded estimates of precipitation output from stage III in the PPS, meaning the corrective mean bias and local biases have already been applied.
Although stage III precipitation values are kept for the entire SERFC in the form of 4 km × 4 km HRAP grids, MAPX is computed for a given basin by calculating the number of HRAP grid cells in the specified area (in the case of Lake Okeechobee there were 120 grid cells) and the sum of the precipitation for all grid cells. The precipitation sum is then divided by the number of grid cells to obtain the MAPX for that basin. In this analysis, the MAPX preprocessor was executed for three time intervals: 1, 6, and 24h. It is important to note that occasionally an HRAP grid cell does not have an associated precipitation value, which can occur if a radar is not operational; however, the NWSRFS does not accept time series of precipitation data with missing values. As a result, if missing data are encountered within an HRAP grid, a missing value is replaced by 0 and the MAPX preprocessor is executed to write the time series to the processed database. The frequency and/or extent of the missing data replacements is not recorded; therefore, it is not possible to quantify the influence of the missing value substitutions within the MAPX. It is possible that precipitation occurred over areas where there are missing HRAP grid cell values, in which case the resulting MAPX may underestimate the total precipitation. It is assumed for this project that the number of missing values is small compared to the overall number of nonmissing values over Lake Okeechobee since there are three radar coverages over the lake (Fig. 3). This will act to minimize the underestimation bias.
4. Results and analysis
a. Availability of data
Clearly, the longer the time series used for calibration, the better the calibration will be, because a wider range of events and precipitation patterns are taken into account. Table 2 provides a list of all data from the sources used to compute the MAP estimates for this project, along with the general starting periods for which the data are available.
The NWS gauges provide the longest time series of available data, with four out of the five sites having observations since 1948. The SFWMD gauges range in period of record from 1988 to 1997, with seven of the SFWMD gauges providing data prior to 1997. Stage III mosaics for the Lake Okeechobee region are available since 1996; however, there are significant data gaps in the mosaic time series during that year. Based on the period of record, the NWS gauges would provide the most adequate time series for calibration since they have the longest available time series, followed by the SFWMD gauges.
b. Spatial characteristics
Figure 2 illustrates the spatial distribution of the gauges used in this study. The NWS gauges are shown to have the poorest spatial distribution of any data source, with all five stations located outside the perimeter of the lake. The SFWMD gauge network provides a much better spatial sampling of rainfall because it contains four times the number of stations, with four of the stations located over the lake surface. The stage III mosaics clearly have the best spatial coverage over Lake Okeechobee since they provide a continuous coverage over the lake surface at 4-km resolution. As a result, the stage III data are the best suited for use in calibration of direct precipitation over Lake Okeechobee based solely on spatial resolution.
In order to get a better idea of the effect of the spatial coverage of the data sources over Lake Okeechobee, precipitation climatologies were created based on the individual data sources. The period from January 1997 to December 1999 was chosen because it represents a time span in which all three data sources were available. Since the goal of these climatologies is to analyze data from several available sources that will be used for calibration, and not to actually perform a calibration, it is believed that a 3-yr period of observed gauge and radar-estimated precipitation is adequate to find general patterns and differences between the data sources.
As discussed earlier, Blanchard and Lopez (1985) showed that Lake Okeechobee has a definite effect on the precipitation over southern Florida by inhibiting convection over the water surface. The annual precipitation climatology created using the stage III mosaic grids (Fig. 4a) reflects these results by showing a lower precipitation depth over the east-central lake surface (<0.75 m) than over the western and outer edges of the lake (>0.90 m). The NWS-based annual precipitation climatology (Fig. 4b) also shows a decrease in average precipitation over the lake (1.20–1.25 m); however, the greatest values (>1.35 m) occur to the east and the minimum values occur to the southwest. This is contradictory to the results from the stage III annual precipitation climatology, the cause of which is primarily due to the significant differences in the spatial sampling for the data sources. The SFWMD annual average precipitation climatology (Fig. 4c) shows the same general trend of lower precipitation depths over the interior of Lake Okeechobee (0.95 m) and agrees with the stage III annual climatology in that the minimum depths extend to the east from the water surface.
Figures 5a–c show the summer (April–September) precipitation climatologies created using the stage III, NWS, and SFWMD data, respectively. The stage III and SFWMD climatologies show the same general pattern of higher precipitation depths in the west and southwest portions of Lake Okeechobee with lower precipitation to the east, which mirrors the annual climatology. Given that most of the precipitation that falls over Lake Okeechobee occurs during the summer season, it is reasonable to expect that the summer and annual precipitation climatologies will look similar. The NWS summer precipitation values also show a similar pattern to the annual precipitation climatology, with lower precipitation in the southern portion of the lake; however, it does not match either the stage III or SFWMD climatologies because of the lack of observations over the lake surface.
During the winter in southern Florida, precipitation is minimized due to a decrease in convection and a weakening of the sea-breeze fronts. As a result, the overall depths of average winter (October–March) precipitation, as shown in Figs. 6a–c, are lower. For the NWS and SFWMD climatologies, values over Lake Okeechobee are generally between 0.30 and 0.40 m, with SFWMD values being slightly lower than the NWS values. However, the SFWMD climatology shows a relatively homogeneous depth of precipitation over the lake surface, which agrees with the distribution of the stage III climatology. The greatest difference arises in the depth of precipitation given by the stage III climatology, with values ranging from 0.15 m in the center of the lake to 0.18–0.20 m around the periphery. The low precipitation values in the stage III estimates during the winter are due to the stratiform systems that occur in southern Florida during the winter, when radar estimates are known to underestimate precipitation depth.
Regarding spatial resolution and the stage III multisensor precipitation estimates, the continuous radar coverage over Lake Okeechobee will more accurately represent the relative variations in precipitation that occur over the water surface. The annual and seasonal comparisons described above attest to this fact, in that the climatologies created from the radar data give a better representation of the spatial extent and variability of precipitation depth in and around the lake. This does not necessarily mean that the stage III precipitation estimates are inherently more accurate. However, if the biases within the data could be accounted for, the radar-derived precipitation products would most certainly provide for the most accurate precipitation estimates.
c. Comparison of MAP time series
Since calibration of direct precipitation over Lake Okeechobee will be done using mean areal values of precipitation, it is necessary to compare the MAP and MAPX time series in order to ascertain the relative differences between them. Often, operational forecasters are forced to use other sources of data than those used for calibration, such as when gauges or radars malfunction or provide erroneous observations; therefore, knowing the relationship between the data sources is useful if one data source must be used in place of another. Comparing the time series of MAP and MAPX will also give information regarding the biases and trends of different data sources given certain precipitation patterns, which will help in deciding which data source is better suited for use in calibration.
Looking at the patterns of cumulative precipitation between the SFWMD MAP, the NWS MAP, and the MAPX over the entire study period using a double mass analysis, the relative difference between the magnitudes of each were found (Fig. 7). Since the beginning of the study period, the NWS MAP was consistently greater than either the SFWMD MAP or MAPX, while the SFWMD MAP was greater than the MAPX. This can be seen by slopes of the three lines in Fig. 7, all of which are positive relative to the reference line. The reasons for the low MAPX estimates may be due to a systematic underestimation of precipitation, which has been found to occur in radar precipitation products since the WSR-88Ds were first deployed (NOAA/NWS 2001). This underestimation was found to be a result of the cumulative effects of mathematical truncations occurring during the summation of rainfall totals. It is suspected that these truncation errors may partially explain the tendency for precipitation underestimation observed in WSR-88D products, such as the stage III-derived MAPX (the truncation error was corrected in 2001). However, the differences between the MAP estimates may not be limited to only sensor accuracy, equipment sensitivity or bias, but may be attributable to the location of specific observation stations for the surface networks in regard to overall precipitation distribution. The latter may especially be true regarding the NWS gauge network, as discussed previously with the precipitation climatologies.
Figure 8 provides a graph of the relative differences between the SFWMD MAP, NWS MAP, and MAPX over the 3-yr study period. (This comparison was not begun until August 1997, because the cumulative depths of precipitation up to that point were not large enough. For smaller values, any added precipitation changed the MAP biases exceedingly quickly, and falsely, because of the instability with the calculations.) It can be seen that the SFWMD MAP and NWS MAP followed nearly the same pattern relative to the MAPX throughout the study period, although the NWS MAP had a greater average difference than did the SFWMD MAP. This difference ranged between 1.2 and 1.3, as can be seen by the line showing the relative differences between the NWS MAP and SFWMD MAP. This similarity in pattern, despite the difference in overall depth of estimated precipitation, shows that the gauge networks recorded the same general changes in precipitation throughout the period. This indicates that the two networks would give relatively similar results for MAP over Lake Okeechobee if adjusted to correct for biases since the bias remains fairly homogeneous.
For the MAPX, the final cumulative difference from the SFWMD MAP was 1.21, while for the NWS MAP it was 1.54. In the progression of relative differences over the study period (Fig. 8), there is little change in the relative difference between the MAPX and the NWS or SFWMD MAP after 1997, showing that the differences between the precipitation estimations remain fairly consistent. It is not until the summer of 1999 that the differences involving MAPX drop significantly as the MAPX progression converges toward the MAP estimates given by the NWS and SFWMD gauge networks.
As shown by the precipitation climatologies discussed previously (Figs. 4–6), there are definite maximum and minimum areas of precipitation over the surface of Lake Okeechobee and adjacent areas, based on both the radar stage III estimates and the SFWMD and NWS station data. For the surface observation stations, such as the NWS and SFWMD networks, the specific location of stations is important when estimating mean areal precipitation. This is especially true for the NWS stations due to the poor spatial distribution and lack of data over the water surface. Since the precipitation over the center of Lake Okeechobee is shown to be lower than the precipitation near the periphery of the lake (Figs. 4a– c), there is a high probability that the NWS gauge estimates are biased toward a higher MAP than the SFWMD MAP or the MAPX. The same problem could theoretically be true for the SFWMD data as well; however, the greater number of stations and significantly improved spatial distribution should reduce such an effect.
To better illustrate the differences between the estimates of mean areal precipitation over Lake Okeechobee, yearly accumulations were calculated individually so that any significant interannual distinctions could be noted. The accumulations for 1997 (Fig. 9a) show that the NWS and SFWMD MAPs remained fairly close in values until late May, at which time the NWS MAP increased sharply by 0.16 m. The SFWMD MAP and MAPX also showed a significant increase during this time (0.10 and 0.09 m, respectively), but the accumulations do not show as rapid an increase as in the NWS MAP. After this brief period of divergence, the difference in MAP estimates remains consistent until October, at which point the gauge-based MAPs begin to show higher accumulations than the MAPX.
The MAP accumulations for 1998 (Fig. 9b) show the gauge-based MAPs to remain close in value, similar to the pattern in 1997 (Fig. 9a); however, the MAPs show a diverging pattern relative to the MAPX, with the highest levels of divergence occurring during the winter months. In early November 1998, there is a distinct event in which the SFWMD increases by 0.15 m. The NWS MAP and MAPX show increases of 0.08 and 0.02 m, respectively, resulting in a further divergence between the gauge-based MAPs and the MAPX, as well as a slight convergence between the NWS MAP and the SFWMD MAP.
The MAP accumulations during 1999 (Fig. 9c) are surprising in that the SFWMD MAP and MAPX remain at nearly the same values throughout the entire year. This change in relationship between the SFWMD MAP and MAPX during 1999 is evidenced in Fig. 7 by the change in slope of the double mass line comparing SFWMD MAP and MAPX values. Where the line previously sloped positively away from the 1:1 reference line, it now slopes slightly negatively relative to the reference line. Similar to the previous years, however, the NWS MAP continuously diverges from the other MAP estimates toward higher values. The change in patterns for this particular year for the relationship between the SFWMD MAP and the MAPX is of special concern. Reasons why the SFWMD MAP and MAPX began to have similar values during 1999 could be a result of enhancements in the Z–R relationship or PPS algorithms in one or more of the radars used in this study. These are likely possibilities, since there is a continuing effort to improve radar-derived precipitation estimates (Fulton 2002). This does not necessarily explain the change in pattern between the MAP accumulations, however, and does not imply that later years would show the same similarity in observed values. Only by studying the relationship between MAPX and the gauge-based MAPs over a longer time period, and by carefully investigating the specifics of the radar algorithms used, will these changes be better understood.
d. Statistical analysis
It is important to know the basic statistical characteristics of the mean areal precipitation time series used in this project in order to better understand how the data behave over time, be it monthly, seasonally, or annually. Knowledge of how each data source acts individually as well as how it compares to other data sources will yield information regarding how the resulting time series will perform over a given calibration period.
Figure 10 presents the monthly mean precipitation and associated standard deviations of the precipitation observations given by the SFWMD MAP, NWS MAP, and MAPX. For nearly all time periods the NWS MAP shows the highest mean monthly precipitation, with November being the only exception when the SFWMD MAP is slightly higher. Despite this, the monthly standard deviations of the NWS MAP data closely match those of the SFWMD MAP, which is based on a surface network with much better spatial coverage. It is only during June and December that the standard deviations of the NWS MAP are higher than those of the SFWMD MAP. Throughout most of the period, the SFWMD MAP estimates are larger than the associated MAPX estimates, with the exception of June and July. This difference is most noticeable from October through March, when the MAPX estimates are roughly 50% lower than the SFWMD estimates. The reason for this difference may be due to the more stratiform nature of precipitation events over the area during the cooler fall, winter, and early spring seasons, when the sparse surface gauge networks are better able to accurately sample the homogeneous precipitation depth. During the wet summer season, however, when most precipitation results from convective storm systems, the MAPX more closely matches the SFWMD estimates, ranging from a 16% overestimation (June) to a 10% underestimation (September). These results showing a strong seasonal bias closely match those of Stellman et al. (2001).
Regarding the monthly average standard deviations, the seasonal bias can still be seen through lower values during the winter and higher values during the spring, summer, and fall. The low standard deviations in the winter correspond with consistently lower and more uniform precipitation estimates; however, convective events lead to higher variations in precipitation and consequently higher standard deviations. The exception is the month of July, when standard deviations drop substantially due to low variation in July precipitation totals over the study period. This decrease in standard deviation may perhaps be a statistical anomaly relevant only to the data from the 3-yr period chosen for this study, or it may be due to a physically based phenomenon in which the rainfall estimates are unrelated to the convective or uniform nature of the precipitation. Only by performing a future study when more data are available for analysis can this anomaly be better understood.
Figure 11 presents the average number of hourly precipitation estimates greater than 0 given by the SFWMD and MAPX for each month, which more clearly shows the distinct wet and dry seasons that are prominent over southern Florida and Lake Okeechobee. Additionally, Fig. 11 shows the linear correlation coefficient between the data sources (based on periods when precipitation was recorded). This correlation remains low for nearly all months, illustrating that although it is possible for average precipitation values from different data sources to match closely, the timing of the precipitation may not necessarily agree. Especially with high-resolution hourly data, it is unlikely that both the MAPX and SFWMD MAP would result in precipitation estimates at the same hour due to their different spatial sampling and/or observation abilities. The exception to this is a correlation of 60% during March, which is a statistical coincidence with little physical relevance: the relatively high value arises due to a small number of large hourly accumulation observations inflating the correlation.
The number of 6-h precipitation estimates greater than 0 (Fig. 12) is roughly half those from the 1-h estimates (Fig. 11); however, the overall pattern remains the same with the MAPX showing more values in the summer than the SFWMD MAP and fewer in the winter. The NWS MAP shows the lowest number of estimates greater than 0 for all months, averaging roughly half those from the MAPX during all but the winter months. This, combined with the fact that the NWS MAP provides for the highest mean precipitation estimates (Fig. 12), shows that the NWS MAP gives substantially higher values of precipitation than either the SFWMD MAP or MAPX whenever precipitation is reported.
The correlations between the data sources using the 6-h data (Fig. 12) are much higher than those for the 1-h data (Fig. 11). This is due to the lower temporal resolution of the data allowing for a greater probability that precipitation will be accounted for during the same time period. Although the correlation values are relatively low and show significant fluctuation between months, there is a slight seasonal effect with lower correlation values in the summer. This might be explained by the fact that summer convective precipitation events are more variable, both spatially and temporally, than stratiform events that occur in the winter months.
5. Summary and conclusions
In this study, three independent mean areal precipitation (MAP) estimates derived from NWS precipitation sites, SFWMD precipitation sites, and multisensor radar estimates (MAP developed using this data is referred to as MAPX) were analyzed in order to test the utility of each for calibration of NWSRFS flow and runoff parameters within the Lake Okeechobee forecast scheme. In the analysis, issues of data availability (length and completeness of precipitation record), spatial distribution, and characteristics of computed mean areal precipitation estimates were considered.
It was determined that limitations in station location and spatial distribution led to large biases in the NWS MAP computed using NWS cooperative observing sites around Lake Okeechobee. The NWS MAP consistently showed 20%–30% more precipitation over the lake surface then the SFWMD MAP, and 40%–60% more precipitation than the MAPX. However, despite the bias toward higher precipitation amounts, the NWS and SFWMD MAP estimates showed roughly the same pattern regardless of the differences in spatial coverage of the gauge networks. The major advantage of the NWS gauges is the long periods of record, which extend back to the late 1940s and early 1950s, depending on the station. If the bias were removed from the MAP values computed using this data source, then it would be the longest and most stable source for MAP estimates; however, the major drawback with the NWS data is the lack of hourly observations, which limits the use of the data. Although the SERFC currently runs the NWSRFS at 6-h temporal resolution, the model is capable of running at a 1-h time step; therefore, it is advantageous to have a data source that is flexible enough to produce both a 1- and 6-h MAPs over Lake Okeechobee, such as the SFWMD surface gauge network or the multisensor precipitation estimates.
The SFWMD MAPs tended to display roughly 10%– 30% more precipitation than the MAPX; however, during 1999 the two MAP estimates agreed closely. This may be due to a change in the precipitation processing algorithms. In general, however, the pattern of precipitation over the surface of Lake Okeechobee matched relatively well between the data sources, despite the fact that the multisensor estimates have a superior spatial coverage. The major disadvantage with the SFWMD MAP and MAPX, in terms of usefulness for calibration, is the short periods of record, which extend to roughly 1997 and 1996, respectively (Table 2). In addition, a number of changes in the precipitation processing algorithms throughout the time period lead to inconsistencies in the data, which translates into variable bias in the MAPX.
For all the MAP data sources, there is a distinct seasonality regarding the overall mean monthly precipitation, with June–September having substantially more precipitation than all other months, and December and January having substantially less. Overall, however, the NWS MAP continually estimates a greater depth of precipitation than either the SFWMD MAP or MAPX. The overall variability of the data sources, as defined by the monthly standard deviations, does not show a strong seasonal trend except for slightly lower values during December and January. In comparing the MAP data sources with the linear correlation of nonzero precipitation estimates, it was found that there were higher correlations during winter when stratiform precipitation dominated. Since precipitation of this type is generally more spatially and temporally consistent than precipitation from convective storms, which are characteristic of summer conditions, there is more agreement as to which time period the precipitation is accounted for. Overall, correlations involving MAPX were the highest during the summer months since the superior spatial sampling inherent in the radar-based precipitation estimates will best capture and reflect the timing of precipitation over Lake Okeechobee, if not necessarily the depth. To this effect, it would be advantageous to use MAPX for calibration of model parameters, especially at higher temporal resolutions.
Clearly, a data source that can estimate accurate depths of precipitation over an area such as Lake Okeechobee is most suitable for calibration purposes, but the importance of recognizing spatial and temporal variations in precipitation is also critical. In many cases, the spatial variability determines whether or not the precipitation estimates from a data source are useful. The NWS gauge network, for example, may provide reasonable values of MAP over Lake Okeechobee, but the fact that the five-gauge network cannot adequately sample spatial variations results in more variable (and uncertain) MAP estimates. Given this, radar-based precipitation estimates ultimately have the greatest potential for providing accurate observations and values of MAP.
To this end, as a longer record of radar-derived precipitation estimates becomes available, the new data should be incorporated in an effort to validate the findings regarding different sources of MAP and MAPX estimates. It is extremely likely that with successive improvements in the radar Z–R relationships, PPS algorithms, and multisensor precipitation estimation procedures, radar precipitation estimates will soon be able to provide accurate and continuous coverages of precipitation depth over any area. This would greatly enhance all hydrologic simulations that require such fields for calibration and operational use, as is the case for the Lake Okeechobee hydrologic system. In addition, although the radar-based precipitation estimates may not be completely accurate due to inherent biases, radar does provide continuous spatial coverage over the lake. As a result, any variations in precipitation over the lake would be reflected in the radar precipitation product. It is possible to compute and adjust for these biases, allowing the MAPX to be used for calibration and operationally; however, there is considerable difficulty in doing so. First, there must be a long enough time series of MAPX values to compute the bias, and second, the time series must be homogeneous enough to make the bias useful operationally. Currently, neither of these limitations are met.
Despite these inherent biases in multisensor precipitation estimates due to problems associated with truncation error, location of surface observations stations used to compute local biases, missing grid values due to radar malfunctions, or misrepresentation of precipitation type and intensity, improvements are constantly being made and applied to the radar and multisensor product. These improved bias calculations and processing algorithms may heighten the accuracy of the radar precipitation estimates, allowing the radar-derived products to be used reliably in future calibration and operational procedures.
Acknowledgments
We thank Sharon Peterkin and Scott Huebner of the South Florida Water Management District for providing the precipitation data used in this study. We also greatly appreciate the suggestions and assistance of Dr. Henry Fuelberg (The Florida State University), Rusty Pfost (National Weather Service Forecast Office, Miami, Florida), Dr. Luis Cadavid (South Florida Water Management District), Richard Fulton (National Weather Service Headquarters), Judi Bradberry (Southeast River Forecast Center), and anonymous reviewer C.
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Map of south Florida showing primary surface inflows and outflows to Lake Okeechobee
Citation: Weather and Forecasting 19, 6; 10.1175/824.1
Locations of SFWMD and NWS precipitation observation sites relative to Lake Okeechobee. Stations marked with an asterisk (*) denote those used in the Theissen polygon analysis
Citation: Weather and Forecasting 19, 6; 10.1175/824.1
Radar umbrellas over southern Florida used in the stage III mosaic in relation to Lake Okeechobee. The X's show stations used to compute stage II multisensor fields from the Melbourne, FL, radar
Citation: Weather and Forecasting 19, 6; 10.1175/824.1
Annual mean precipitation (m) for (a) stage III multisensor field values, (b) NWS surface observation gauges, and (c) SFWMD surface observation gauges. Asterisks represent the NWS and SFWMD gauge locations, respectively
Citation: Weather and Forecasting 19, 6; 10.1175/824.1
Summer (Apr–Sep) mean precipitation (m) for (a) stage III multisensor field values, (b) NWS surface observation gauges, and (c) SFWMD surface observation gauges. Asterisks represent the NWS and SFWMD gauge locations, respectively
Citation: Weather and Forecasting 19, 6; 10.1175/824.1
Winter (Oct–Mar) mean precipitation (m) for (a) stage III multisensor field values, (b) NWS surface observation gauges, and (c) SFWMD surface observation gauges. Asterisks represent the NWS and SFWMD gauge locations, respectively
Citation: Weather and Forecasting 19, 6; 10.1175/824.1
Double mass curves comparing the SFWMD MAP, NWS MAP, and MAPX data over the period 1997–99
Citation: Weather and Forecasting 19, 6; 10.1175/824.1
Computed differences between SFWMD MAP, NWS MAP, and MAPX values. Time period is from Aug 1997 to Dec 1999
Citation: Weather and Forecasting 19, 6; 10.1175/824.1
Cumulative plots of SFWMD MAP, NWS MAP, and MAPX for (a) 1997, (b) 1998, and (c) 1999
Citation: Weather and Forecasting 19, 6; 10.1175/824.1
Monthly mean precipitation (mm) and standard deviation over Lake Okeechobee for Jan 1997–Dec 1999
Citation: Weather and Forecasting 19, 6; 10.1175/824.1
Monthly average number of hourly MAP precipitation estimates greater than 0 over Lake Okeechobee, along with average linear correlation values between data sources, for the period Jan 1997–Dec 1999
Citation: Weather and Forecasting 19, 6; 10.1175/824.1
Monthly average number of 6-h MAP precipitation estimates greater than 0 over Lake Okeechobee, along with average linear correlation values between data sources, for the period Jan 1997–Dec 1999
Citation: Weather and Forecasting 19, 6; 10.1175/824.1
List of NWS and SFWMD gauges and their associated Thiessen polygon weights used in the MAP calculations
Individual data sources and their respective dates at which the periods of record begin. All periods of record extend to the present. Stations marked with an asterisk (*) denote those used in the Theissen polygon analysis
