Climate-Based Estimation of Hydrologic Inflow into Lake Okeechobee, Florida

JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT © ASCE / MARCH/APRIL 2005

Climate-Based Estimation of Hydrologic Inflow into Lake Okeechobee, Florida

Fernando Miralles-Wilhelm1 (Member), Paul J. Trimble2

Guillermo Podestá3, David Letson3 and Kenneth Broad3

Abstract: This paper presents a comparative evaluation of methods for climate-based estimation of the rate of net inflow rate into Lake Okeechobee, Florida. The estimated net inflow rate is used by the South Florida Water Management District (SFWMD) to support the management and operations of the Lake Okeechobee hydrologic system. The first method evaluated in this paper (Croley) uses rainfall outlooks provided by NOAA’s Climate Prediction Center (CPC) to calculate a weighed average of historical inflow values for each month. The second method evaluated in this paper (SFWMD Empirical) uses a linear regression on statistics of historical data to predict the net inflow rate. These two methods were developed and have been used operationally by the SFWMD since 2000. Three new methods are presented and comparatively evaluated to gage their ability in estimating net inflow rates. The first two of these methods are based on CPC issued forecasts in decile probability density format. The remaining method is based on a subsampling technique for “peer” wet/dry years in the historical record, and is found to yield better results in a retrospective analysis. For extreme climatic events on the historical record, CPC rainfall outlooks are found not to yield a large enough shift in probabilities for forecasts to match observed net inflow rates; this is especially noticeable during El Niño Southern Oscillation (ENSO) events. Recommendations are made for potential improvements to climate-based net inflow rate estimation methods, particularly in regard to their ability to reproduce observed results for net inflow into Lake Okeechobee in the presence of an extreme climatic event, as well as over an extended climatological period. DOI: 10.1061/(ASCE)0733-9496(2005)131:1(25) CE Database subject headings: Climate, Inflow, Okeechobee, Subsampling, SFWMD.

Introduction Regional water management systems that include large lakes and storage reservoirs with extensive tributary and water use basins can significantly benefit from climate forecasts with lead times of several months to multiple seasons [Hartmann et al., 2002; Obeysekera et al., 2000]. Such forecasts allow water resources managers to make decisions early enough to minimize adverse impacts to sensitive ecological systems, while maintaining adequate flood protection and water supply [Trimble et al., 1998]. Recent advances in the understanding of the global climate teleconnections and on linking influences of climate to hydrologic cycle processes have the potential for providing valuable seasonal and multi-seasonal hydrologic outlook forecasts and associated probabilities for risk management and decision making support. (1) Assistant Professor, Dept. of Civil, Architectural and Environmental Engineering, University of Miami, Coral Gables FL 33124 (2) Lead Engineer, Hydrologic Systems Modeling Group, South Florida Water Management District, West Palm Beach FL 33416 (3) Research Professor, Associate Professor and Assistant Professor, Rosenstiel School of Marine and Atmospheric Sciences, University of Miami, Miami FL 33149.

Although such longer-lead climate forecasts have a high uncertainty, they provide additional information for water managers who constantly have to assess the effects of current operational decisions on future water conditions of natural and human systems. Drainage of the Everglades wetlands in South Florida for the purpose of land reclamation, began in the middle 1800s and has evolved into an extensive and complex network of lakes, impoundments, canals, levees and numerous water control structures (Figure 1). Lake Okeechobee is the heart of the Central and Southern Florida (CSF) Flood Control Project, an interconnected regional aquatic ecosystem. It has multiple functions, including flood control, agricultural and urban water supply, navigation, recreation, and fish and wildlife enhancement [Obeysekera et al., 2000]. As such, operation of the Lake impacts a wide range of environmental and economic issues. Lake operations must carefully consider the entire and sometimes conflicting needs of the CSF Project. The actual flood control release made will depend on a


number of items including: (i) minimizing impacts to the Caloosahatchee and St. Lucie estuarine systems; (ii) protecting water supply reserves available for projected agriculture and urban consumption needs and those required for the restoration of the hydroperiod of the remnant Everglades including those within the Everglades National Park; (iii) preserving and enhancing the fish and wild life within the Lake; and (iv) protecting water quality. As part of this overall scheme, the lake regulation schedule establishes ranges for regulatory releases for flood control and requires discharges to be identified based on multiple objectives in a decision tree format [Vedwan et al., 2004]. Because of its scale, the close connection between surface and groundwater, and the relatively flat regional topography, the water control system of South Florida is complex, not only in its configuration, but also in its operation. Conflicting water needs necessitate the use of appropriate water management decision tools. The ability to look into probable future responses of the system to seasonal and multi-seasonal climate variability, given the current state and future climatic forecasts, is a valuable tool for managing this complex water resources system. Linkages between climate variability at distant locations of the world are known as teleconnections [Piechota and Dracup, 1996]. One of the better known teleconnections is that associated with the linkage of regional climate variability worldwide to the El Niño-Southern Oscillation (ENSO) phenomenon. The signature of an El Niño event is the

occurrence of very warm ocean waters at low latitudes located off the west coast of South America. This region of the ocean normally has cooler sea surface temperatures due to the upwelling of the ocean. The Southern Oscillation is a quasi-periodic alternation of sea level atmospheric pressure difference between Darwin, Australia (western Pacific) and Tahiti (eastern Pacific). There is a strong connection between El Niño and the Southern Oscillation and the combined event is known as ENSO. The warm phase of ENSO is generally known as “El Niño” and the cold phase is called “La Niña.” El Niño events have been blamed for droughts in countries from India to Australia, floods from Ecuador to New Zealand, and fires in the West Africa and Brazil [Golnaraghi and Kaul, 1995]. It has also been linked to climate of specific regions of North America [Piechota and Dracup, 1996] and in particular to rainfall and drought events in the state of Florida [Hanson and Maul, 1991, Hanson et al., 2004, Mestas-Nuñez and Enfield, 2003]. In view of the current configuration of the Lake Okeechobee hydrologic system depicted in Figure 1, climate variability translates into hydrologic variability upstream through regional rainfall and consequent surface runoff rates, and propagates downstream in the form of managed flows out of the lake, which ultimately affects the water demands throughout South Florida. This translation process is illustrated in Figure 2.


Methods of Estimation for Climate-Based Inflow into Lake Okeechobee The South Florida Water Management District (SFWMD) employs the “Climate Outlook” produced by the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center (CPC) to aid operational planning efforts. The predictions of precipitation updated every month by CPC include 13 monthly windows: a one-month outlook for the next month and 12 three-month outlooks going one year into the future in overlapping one-month time steps (http://www.cpc.ncep.noaa.gov). Estimation of hydrologic net inflow to Lake Okeechobee and the resulting predictions of the lake water level and regional downstream flow over time has been performed by the SFWMD since 2000. Initially, the primary methodology applied was based on the algorithm presented in Croley [1996]. This algorithm uses a nonlinear optimization technique to compute relative weights for each CPC climate window (1 and 3 months) provided by NOAA (CPC) each month. The SFWMD Empirical method [USACE, 2000] was developed and employed by SFWMD to complement the predictions arrived at by using Croley’s method. The SFWMD Empirical method uses linear regression techniques to relate predicted to historical inflow rates [USACE, 2000]. Both of these methods use the CPC outlook probabilities expressed as tercile distributions. In this work, three new climate-based estimation methods are presented and implemented for inflow prediction into Lake Okeechobee. The first two methods are based on Croley’s and the SFWMD empirical methods using CPC outlooks in decile probability density function format. The third new method, based on subsampling of wetter/drier periods of record, allows for improved accuracy in the predictions when the CPC outlooks do not produce a large enough shift in probabilities for various types of climate events. This is especially noticeable during ENSO events, as discussed in the following section. Croley’s Method The methodology introduced by Croley [1996, 2000] has been applied by the SFWMD, using historical monthly rainfall and inflow data into Lake Okeechobee for the period 1914-1998, and the CPC outlook probabilities for rainfall on the tributary basins draining into the lake. The method is based on predicting the monthly inflow into the lake as a weighed average of historical inflow data. The weighing scheme in Croley’s method is one in which CPC issued probabilities for rainfall are used to constrain the value of the weights used to calculate in the estimated inflow. The method is essentially a weighed average of historical inflow values, updated monthly as expressed in equation (1).

In this equation, Xj is the predicted net inflow into lake Okeechobee for month j (j=1,2,…,12); n is the number of years in the observation period (n=85 in this case for the period 1914-1998); wij is the weight assigned to historical inflow for month j in year i; Xij is the historical inflow for month j in year i. The values of inflow are expressed in equivalent inches of water storage over a reference lake surface area of 467,000 acre [USACE, 2000].

!

X j =1

nwijXij

i=1

n

"

(1) For each month j, the computation of the n weights (i=1, 2, …n) in this method involve solving the least squares optimization problem [Croley, 1996]:

[ ]2

1

1!=

"n

i

ijwMIN

(2) subject to the constraints:

!=

=

n

i

ij nw

1

(2a)

!"#

=

=

n

i

i

jij

j

nPw

1

(2b) Here, Pj are CPC outlook probabilities issued for month j; Wj is the subset of years in which historical rainfall for month j (1 mo- and 3 mo- windows) falls within the upper tercile (above normal conditions) or within the lower tercile (below normal conditions) of the historical rainfall distribution for that month. The historical rainfall data over the Lake Okeechobee and its tributary area is used to define the Wj subsets. The methodology currently implemented by the SFWMD uses the CPC outlook probabilities issued as a tercile distribution, where outlooks for rainfall are expressed as probabilities of rainfall being above (A) or below (B) normal conditions; the probability of occurrence of normal conditions is the complement. Since tercile probabilities are used, the calculation of the net inflow for each month involves solving for n weights (85 in this case) using the optimization problem posed in (2) subject to 27 constraints: one is expressed in (2a) and 26 are expressed in (2b), 13 probability windows for each of above (A) and below (B) conditions. Details of the optimization procedure used to solve (2, 2a, 2b) are presented in Croley [1996], and the implementation to the Lake Okeechobee system is described in Cadavid [1999]. It is quite frequent that the optimization procedure produces negative weights, which have no physical meaning. We have chosen here to

https://www.researchgate.net/publication/245286682_Using_NOAA's_New_Climate_Outlooks_in_Operational_Hydrology?el=1_x_8&enrichId=rgreq-1527c0e6-3f93-42b4-add1-91f09f8fbef2&enrichSource=Y292ZXJQYWdlOzI0MTMxNjA3NDtBUzoxMDE0NjI0MzY3NDUyMTdAMTQwMTIwMTkzODE1NQ==


introduce additional non-negativity constraints into (2) to eliminate this problem, as suggested by Croley [1996].

0!ijw (2c)

Once the Croley weights are found, the seasonal (6-month total, starting at month j) net inflow into Lake Okeechobee, XSj, is then found as follows:

!+

=

=

5j

ji

jSj XX

(3) It is important to note that this method derives the weights based on rainfall data, but the weights are applied to predict net inflow data (rainfall over the lake plus surface runoff minus evaporation). So, the CPC outlook probabilities for rainfall are used as surrogates for those of net inflow into the lake. In the case of Lake Okeechobee, this assumption is justified by the correlation of rainfall and net inflow data, as illustrated in Figure 3.

Fig.3. Correlation between rainfall and net inflow into Lake Okeechobee over the period 1914-1998. Above: Time series format. Below: Scatter plot format. Note that a negative value of net inflow indicates that evaporation from the lake exceeds the combined direct rainfall and surface runoff into the lake.

SFWMD Empirical Method This method was developed by the SFWMD as an alternative method to improve predictions of net inflow into the lake in cases where the least-squares optimality of the solution to (2) found from Croley’s method is significantly reduced by the constraints posed in (2a), (2b) and (2c). This method is based on a linear regression of net inflow historical data for the same period of 1914-1998. The SFWMD Empirical method uses the following equation to calculate the seasonal (6-month total, starting at month j) net inflow into the lake, in units of equivalent inches over a lake area of 467,000 acre [USACE, 2000]:

!

XSj = A0

+ A1E X

j CPC[ ] + A2E Z

j CPC[ ]+A

3E Z

j+1CPC[ ] + A4E Z

j+2CPC[ ]+A

5E Z

j+3CPC[ ] + A6E Z

j+4 CPC[ ] (4)

In this equation, Xk and Zk are the historical values of the 1-month and 3-month net inflow totals into Lake Okeechobee. The coefficients of the linear regression are given as follows: A0 = -0.1768; A1 = 0.5915; A2 = A5 = 0.484; A3 = A4 = 0.308; A6 = 0.2369. If the month indices in equations (3) and (4) take values greater than 12, it should be noted that new indices should be obtained by subtracting 12 from the old values. The expected values E[.] in equation (4) are calculated based on the CPC issued probabilities for month j, and thus calculated as follows:

!

E Xj CPC[ ] = XL , jPB , j + XU , jPA , j + XM , j (1" PA , j " PB , j )

(5)

!

E Zj CPC[ ] = ZL , jPB , j + ZU , jPA , j + ZM , j (1" PA , j " PB , j )

(6) In equations (5) and (6), PA,j and PB,j are the CPC probabilities for rainfall in month j (1 mo- or 3 mo- totals) being in the upper tercile (A) or bottom tercile (B) of the historical rainfall distribution statistics for the period 1914-1998. The values of XL,j , XU,j , XM,j, ZU,j , ZL,j , and ZM,j are the mid points of the lower (L), upper (U) and middle (M) terciles of the net inflow historical distribution for the period 1914-1998. These values are


found from distributing monthly historical values of hydrologic inflows (1-month and 3-month totals) into percentiles (upper, middle and lower terciles in this case), and calculating the arithmetic mean of the values of inflow in each percentile. It is worth noting that in terms of computational effort, the SFWMD empirical method is easier to implement and less intensive, since it does not involve an optimization procedure which requires large matrix inversions for each monthly prediction (112 x 112 matrices, month to month). Along the same lines, the simplicity of this method stems from the fact that the for a given month, the predicted seasonal net inflow into Lake Okeechobee is affected by a subset of historical inflows (one 1-mo and five 3-mo windows), as opposed to Croley’s method, which every month considers all 13 windows of rainfall outlook probabilities issued by CPC. Methods Based on CPC Outlooks in Decile Format The CPC issues improved resolution rainfall and temperature outlooks which contain exceedence threshold values for given probability levels: 98, 95, 90, 80, 70, 60, 50, 40, 30, 20, 10, 5, and 2 percentile levels. This section incorporates these probabilities into Croley’s and the SFWMD empirical methods to quantify the effect of better resolved climatological outlooks on predictions of hydrologic variables, the net inflow into Lake Okeechobee in this case. As a first step, the exceedence threshold values issued by CPC need to be converted into probabilities, essentially in the form of a probability density function. This is done by taking the numerical derivative of the exceedence threshold curves and normalizing the resulting curve so that the probability density function integrates to unity. This procedure yields the equivalent of CPC probabilities issued as terciles, but in a more distributed format (14 probability intervals), which is referred here as “decile” format for simplicity. These probabilities can then be applied to the Croley and SFWMD Empirical methods, to study the effect of a higher resolution climate outlook on the predicted net inflow rates into Lake Okeechobee. To implement these higher resolution probabilities into Croley’s method, the constraints in (2b) are augmented from 26 in the case of CPC issued terciles to 169 (13 monthly windows x 13 probability windows; the remaining probability window is complementary). This increases the matrix size used for Croley weight estimation to (255 x 255). Other than the added computational effort, the implementation procedure is the same as that of Croley [1996, 2000]. To implement these higher resolution probabilities into the SFWMD empirical method, the expressions for expected values of 1-mo and 3-mo total net inflows into Lake Okeechobee, presented in (5) and (6) above, need to be

modified to account for the distributed probability density function, as follows:

[ ] !=

=

14

1

,,

k

jkjkCPCj PXXE

(7)

[ ] !=

=

14

1

,,

k

jkjkCPCj PXZE

(8) Note, as indicated above, that there are now 14 intervals in the probability density function issued by CPC in the form of exceedence threshold curves: 0-2, 2-5, 5-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70, 70-80, 80-90, 90-95, 95-98, 98-100. There are 3 such intervals in the tercile format used in the SFWMD empirical method. Application of Croley and SFWMD Empirical Methods to Lake Okeechobee 1995-2001 Net Inflow Time History The Croley and SFWMD Empirical methods, using CPC probabilities in tercile and decile formats, were implemented to calculate the net inflow into Lake Okeechobee for the seven year period January 1995 – June 2001. This period was chosen because it covered the start of CPC forecasts being issued by NOAA (since Dec 1994), and because it contained significant climate variability, most noticeably the 1997-1998 ENSO event. The purpose of this implementation is to observe the net inflow predicted by each of the methods, and how the predictions deviate from the historical data of the same hydrologic variable. This comparison also allows identification of potential modification to such methods that can be used for improved predictions of Lake Okeechobee net inflow, and the resulting impact of climate variability on water flows in the South Florida hydrologic system. Figure 4 shows results of the application of Croley’s method, using CPC climate outlooks for rainfall in tercile and decile formats. The method is able to reproduce the seasonal cycle of net inflow variation between highs during the wet season and lows during the dry season. However, it is clear that the method is unable to capture the extreme high and low values of net inflows that occur during the observation period. It is also noticeable that the implementation of tercile and decile formats of CPC forecasts does not offer significant differences. Visual inspection of Figure 4 does not allow to assess an improvement of the predictive capabilities of Croley’s method when using a higher resolution probability distribution in the CPC climate outlook. This assessment is approached through the results shown on Figure 5. For


this set of observations, the decile forecast based predictions do not appear to offer improvement over their tercile based counterparts. This is explained by the central tendency nature of the Croley and SFWMD Empirical methods. A higher resolution probability density function will actually tend to be more accurate in forecasting central tendency, and thus less able to forecast those inflow values that deviate the most from the average, i.e., inflow values such as those observed during extreme climatic events. So, we are finding that the inability of these methods to go to extreme values is not due to the resolution of the probability density functions used in the calculation, but rather on the averaging (central tendency) nature of the methods.

Fig. 4. Comparison of predicted net inflow into Lake Okeechobee using Croley’s method with historical data for the period Jan 1995 – Jun 2001.

Fig. 5. Correlation between predicted and observed net inflow into Lake Okeechobee, using Croley’s method. Above: CPC outlooks in tercile. Below: CPC outlooks in decile format.

A similar set of results is found by comparing the predicted vs. observed net inflow into Lake Okeechobee using the SFWMD Empirical method. These results are shown on Figure 6. These results are consistent with our assertion that since Croley's and the SFWMD Empirical methods are based on expected values of rainfall/net inflow, they forecast central tendency in the distributions and do not go to the extremes. Independently of the shifts that may be reflected in the climate outlooks towards wetter or drier conditions, both of these methods seem to predict a very similar seasonality year after year. Even when CPC outlooks show large anomalies, as is the case in the 1997-1998 ENSO season, these methods do not react to such large changes. For example, the tercile CPC outlook probabilities for rainfall issued on Nov 1997 were: 0.086 (dry), 0.238 (normal) and 0.676 (wet), indicating over twice as much chance of rainfall being above average; average conditions would use a 1/3:1/3:1/3 probability distribution. However, the predicted net inflow does not deviate from the seasonal trend shown in Figure 4 and Figure 6. In addition to this, as is the case for Croley’s method, it does not seem that using a higher resolution CPC outlook in these methods results in better predictions, as shown on Figure 7.

Fig. 6. Comparison of predicted net inflow into Lake Okeechobee using the SFWMD Empirical method with historical data for the period Jan 1995 – Jun 2001. Improving Predictive Methods: Subsampling and Other Climate Phenomena in Addition to ENSO The tendency towards averages observed in the predicted values for net inflow using the Croley and SFWMD Empirical methods can be expected, given the fact that these methods are both based on weighed averages of long term net inflow data. The net inflow predicted by these methods is essentially a weighed average of the entire historical data in the observation period, and thus cannot reproduce the hydrologic response of the system to extreme climate events, which by definition imply significant deviations from the historical averages. Because of this, two predictive exercises were implemented using selected subsampling of the historical


Fig. 7. Correlation between predicted and observed net inflow into Lake Okeechobee, using the SFWMD Empirical method. Above: CPC outlooks in tercile. Below: CPC outlooks in decile format.

Fig. 8. Total annual rainfall amounts and comparison with El Niño (above) and not El Niño (below) seasons within the period of rainfall record (1914-1998). data in the predictive methods. The first of such exercises involved subsampling ENSO seasons from the historical data, using data compiled by the Center for Ocean-Atmospheric Prediction Studies (COAPS) at Florida State University

(http://www.coaps.fsu.edu). In this exercise, only El Niño (warm phase of ENSO) seasons (Oct-Sep) were used to calculate the predicted net inflow into Lake Okeechobee during months contained within the El Niño seasons; the same approach was followed with La Niña months (cold phase of ENSO). The seasons subsampled for El Niño were the October-September periods starting in the years: 1918, 1925, 1929, 1930, 1940, 1951, 1957, 1963, 1965, 1969, 1972, 1976, 1982, 1986, 1987, 1991 and 1997, following the information presented in http://www.coaps.fsu.edu/research/jma_index1.shtml. This subsampling approach did not yield improvements on the predictions of net inflow, because the central tendency of the Croley and SFWMD Empirical methods did not vary significantly with the subsampling of the ENSO seasons in the historical data for rainfall and net inflow. This is explained by the results in Figure 8, which show that the seventeen El Niño seasons in the period of rainfall/net inflow observation do not correspond exactly to the highs in rainfall/net inflow, i.e., some higher than average rainfall values are not included among El Niño seasons subsampled; and conversely, not all El Niño seasons subsampled correspond to higher than average rainfall. Similar results apply to the analysis of La Niña seasons, i.e., some lower than average rainfall values are not included among La Niña seasons subsampled; and conversely, not all La Niña seasons subsampled correspond to lower than average rainfall. Research into the role of other climate indicators that may be useful for predicting hydrologic flows in the Lake Okeechobee system suggests climate phenomena other than ENSO that may be useful for predicting south Florida hydrology. These include solar sunspot activity and fluctuations in geomagnetic field [Labitzke and van Loon, 1993], the Atlantic Multi-decadal Oscillation (AMO) [Enfield et al, 2001] and the Pacific Decadal Oscillation (PDO) [Mantua et al., 1997]. One future research avenue which may offer potential improvements of climate based estimation methods is the use of Artificial Neural Network (ANN) models. ANN models have been developed for predicting net inflow volumes into Lake Okeechobee using ENSO and other climatic indices [Zhang and Trimble, 1996; Trimble et al., 1997; Trimble and Trimble, 1998]. These models are based on improving the identification of a wet/dry season in advance, based on a set of climate indices (ENSO, AMO, PDO and others) that are combined in such a way that the predictive algorithm is “trained to learn” from reproducing historical data. A second exercise consisted of subsampling of wetter than normal months in the net inflow data record for prediction of net inflow into Lake Okeechobee during months that are predicted to be wetter, with the same rationale applying to drier than normal months. In this


exercise, months that are predicted to be wetter than normal subsample the upper 20 percent of the historical net inflow data, while months that are predicted to be drier than normal subsample the lower 20 percent of the same data. This percentage cut is an arbitrary choice for this exercise, used solely for the purposes of demonstrating the potential benefits of subsampling procedures. The results of this exercise are shown in Figure 9.

Fig. 9. Comparison of predicted net inflow into Lake Okeechobee using the SFWMD Empirical method with subsampling of historical data for the period Jan 1995 – Jun 2001. For these results, this subsampling approach is implemented in the SFWMD Empirical method, though it could be done with Croley’s method as well. The results show a better match of predictions to the historical data, and also an ability of the method to break away from the constant seasonal pattern displayed in Figure 4 and Figure 6. This improvement in the prediction abilities of the method is brought by the fact that wetter month net inflows are predicted with “peer” wetter than normal historical months; the same applies to drier month net inflow prediction. It is important to note that the applicability of this method hinges on two implementation factors, (i): the ability of climate information to yield a reliable prediction of wetter/drier conditions with lead times that can be incorporated in quantitative predictive tools; and (ii): the criteria for subsampling. In regard to (i), this exercise assumes that wetter/drier than normal conditions are known a priori, which implies that a climate indicator such as ENSO would need to be complemented with additional information, in producing a more reliable wetter/drier predictor; this could be achieved, for instance, with methods such as ANN models, as explained above. Wilks [2000] has noted the limited applicability of the overlapping forecasts produced by CPC, as they may imply physically unrealistic monthly values for the forecasted climatic variable (precipitation in this case), and thus not provide a consistent approach to producing reliable forecasts over an extended period of time. In regard to (ii), methodologies for direct subsampling of historical data, i.e., no use of climate forecasts, can be used for better accuracy hydrologic predictions. In view of this, methodologies such as the K-Nearest Neighbor subsampling [Lall and Sharma, Rajagopalan and Lall, 1999, Yates et al., 2003] and parametric weighed forecasting [Croley, 2003] are currently being investigated by the authors for potentially improved predictive

methods for net inflow into Lake Okeechobee and regional south Florida hydrologic flows. Summary This paper provides a summary and evaluation of climate-based methods to incorporate climate information into the prediction of net inflow into Lake Okeechobee, Florida. The scope of this investigation is twofold, (i) introduce the Lake Okeechobee hydrologic system as a case study in incorporating climate information into water resources management; (ii) present the specifics of how climate information is used to predict the net hydrologic inflow into Lake Okeechobee and comparatively evaluate methods used for this purpose. In particular, overall performance and performance during extreme events (e.g., 1997-1998 El Niño) is evaluated, and potential improvements to methods currently utilized by the water resources management agency (SFWMD) are assessed. The first methodology applied by the SFWMD to predict net inflow into Lake Okeechobee was that of Croley [1996]. This method assigns relative weights to each climate window (1 and 3 months) provided by NOAA (CPC) each month; these weights are computed via a least-squares optimization procedure which is constrained by the CPC issued probabilities for rainfall over the basin tributary to the lake. The SFWMD Empirical method has been developed and employed by SFWMD as an alternative to improve predictions of net inflow into the lake in cases where the optimality of the solution provided by Croley’s method is significantly reduced by the constraints posed in the optimization procedure. Both of these methods utilize the CPC outlook probabilities expressed as tercile distributions. In this work, two additional methods have been presented and implemented based on Croley and the SFWMD empirical methods using CPC outlooks in decile format. In addition to this, a subsampling approach based on the SFWMD empirical method is developed and implemented, which allows for improved accuracy in the predictions when the CPC outlooks do not produce a large enough shift in probabilities in the presence of extreme climatic phenomena. This is especially noticeable during ENSO events. A comparison of historical data of net inflows into Lake Okeechobee for the period January 1995 – June 2001 with predictions generated by using Croley’s and the SFWMD Empirical methods indicates their ability to reproduce the seasonal cycle of net inflow variation between highs during the wet season and lows during the dry season. However, it is clear that these method are unable to capture the extreme high and low values of net inflows that occur during the observation period in response to extreme climatic events, e.g., 1997-1998 ENSO. These


results are consistent with the fact that Croley's and the SFWMD Empirical methods are based on expected values of rainfall/net inflow, so they forecast central tendency in the distributions and do not go to the extremes. Even when CPC outlooks show large anomalies, as is the case in the 1997-1998 ENSO season, these methods do not react to such large changes. The implementation of CPC climate outlooks, expressed as discrete (decile) probability density functions rather than its currently implemented tercile format is found to accentuate the central tendency of these two methods and does not offer any improvement in the predictive capabilities of these two methods. Subsampling of historical data based on an ability to predict wetter/drier than average conditions results in a better match of predictions to the historical data, and also an ability of the methods to break away from a constant seasonal pattern. This improvement in the prediction abilities of the methods is brought by the fact that wetter month net inflows are predicted with “peer” wetter than normal historical months; the same applies to drier month net inflow prediction. It is important to note that the applicability of this method hinges on two implementation factors, (i) the ability of climate information to yield a reliable prediction of wetter/drier conditions with lead times that can be incorporated in quantitative predictive tools; and (ii) the criteria for and implementation of subsampling of historical data. These two factors are the subject of ongoing investigation in developing improved predictive methods for net inflow into Lake Okeechobee and regional south Florida hydrologic flows. Acknowledgements This work is funded by the National Oceanographic and Atmospheric Administration (NOAA), Office of Global Programs’ Research Integrated Science Assessments References Cadavid, L.G., Van Zee, R., White, C., Trimble, P. and Obeysekera, J. (1999), Operational hydrology in South Florida using climate forecast, American Geophysical Union, 19th annual Hydrology Days, August 16-20. Croley, T.E. (1996), Using NOAA’s new climate outlook in operational hydrology. Journal of Hydrologic Eng , ASCE 1(3), 93-102. Croley, T.E. (2000), Using meteorology probability forecasts in operational hydrology, ASCE Press, American Society of Civil Engineers, Reston, VA. Croley, T.E. (2003), Weighed Climate Parametric Hydrologic Forecasting, Journal of Hydrologic Eng , ASCE 8(4), 171-180.

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Climate-Based Estimation of Hydrologic Inflow into Lake Okeechobee, Florida

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