1

WSC-Category 2 Collaborative: Robust Decision-Making

For South Florida Water Resources

by Ecosystem Service Valuation,

Hydro-Economic Optimization, and

Conflict Resolution Modeling

Task 1: Economic Analyses of Urban and Agricultural

Water Use1

Florida State University

Center for Economic Forecasting and Analysis (CEFA)

P.I. Julie Harrington, Ph.D.

3200 Commonwealth Blvd.

Tallahassee, Fl. 32303

(850) 644-7357 phone

jharrington@cefa.fsu.edu

September 18, 2014

1 The research work pertaining to Agriculture was supported by a grant from the Agriculture and Food Research Initiative of the USDA National institute of Food and Agriculture (NIFA), grant number # 2012-67003-19862.

2

Summary Report

Value of Using Irrigation Water in South Florida Agriculture

Yuki Takatsukaa, Martijn Niekusa, Julie Harringtona, Jeffrey Czajkowskib, Jessica Bolsonb, Victor Engelc,

Michael Sukopd

a Center for Economic Forecasting and Analysis, Florida State University, Tallahassee, FL

b Wharton Risk Management and Decision Processes Center, University of Pennsylvania, Philadelphia, PA

c United States Geological Survey (USGS), Gainesville, FL

d School of Environment, Arts and Society, Florida International University, Miami, FL

Preliminary Findings:

Penalties (economic loss) caused by changing surface and ground water usage in cropland are

increasing from years 2000 to 2010 in the Lower East Coast (LEC) and Upper East Coast (UEC) in

the South Florida Water Management District (SFWMD).

Among four regions in SFWMD cropland, the highest penalty is imposed to Kissimmee Basin (KB).

There is approximately $2,300 of economic loss per one million gallons per day (MGD) of surface

water reduction. This result indicates that if surface water is available in all regions, trading

surface water to the KB from other regions is profitable for the entire SFWMD.

The regional cropland analysis in KB could reveal that trading water from northern Glades

County to southern Orange County is an efficient way to allocate water in order to minimize the

economic loss in the KB. The penalty imposed to northern Glades County is $300 per one MGD

of irrigation water reduction, while the penalty is $ 2.98 million for the same amount of the

water reduction in southern Orange County.

Trading water from Palm Beach County to either Broward County or Miami-Dade County is the

most efficient way to allocate water in the LEC. The penalty for reduction of water in Palm Beach

is only $200 per one MGD. On the other hand, the penalties imposed to Broward County and

Miami-Dade County are $1.4 million and $10,000 for the same amount of water reduction,

respectively.

3

1. Introduction

Irrigation water is an important resource used for agricultural production. The Florida Department of

Environmental Protection announced that traditional sources of fresh groundwater would have difficulty

meeting all of the additional demands by the year of 2030 (FLDEP, 2013 and SFWMD, 2012). The state of

Florida produces approximately 67% of the U.S. oranges and 40% of the world’s orange juice (FDACS,

2014). Sugarcane production in Florida is ranked number one in the nation (USDA, 2012). Shortage of

water will impose significant damage to the rural and agriculture economy in Florida, which leads to

higher prices and costs for consumers to purchase citrus or other agriculture products produced in

Florida.

This study examines the measurement of economic loss (penalty) for the South Florida cropland when

more or less irrigation water is used. Our study focuses on the South Florida Water Management District

(SFWMD), which is one of the five water management districts in Florida directed by the Florida Water

Resources Act to develop a regional water supply plan (FLDEP, 2013). Our research focuses on cropland

in the district, since 78% of the total value of farm products sold in the SFWMD is comprised of cropland

products. The majority of Florida citrus and sugarcane are produced in this area, and agricultural

irrigation was the largest water use sector in 2010, followed by public water supply (FLDEP, 2013).

Changes of irrigation water use for agriculture production affect the economy in the district (Diamond

and Harrington, 2012). This research presents the values of irrigation water and the trends of changes in

values of irrigation from the year of 2000 to 2010. In addition, efficient allocations of irrigation water

across regions in the SFWMD are further investigated in order to reduce the penalty to the agricultural

sector.

2. Data

The data were collected for the years of 2000, 2005 and 2010 in the area of the SFWMD, which includes

15 counties (see Fig 1)2. Since the boundary of the SFWMD is not equal to the county boundaries, the

percentage of the land share in the SFWMD based on each county is calculated3. Based on the

percentage, variables for the penalty function are estimated, which are the value of farm cropland

products sold (CV4) in million dollars, employment in cropland (EMPC5), surface water usage in cropland

2 Monroe County is not included in this study since the data for the county is unavailable. Lake Okeechobee is also

not included in this study area since there is no cropland in the lake. 3 The percentage of land is estimated from the 2010 State & County Facts, US Census Bureau

(http://www.census.gov/en.html) and the Acres of Counties within the SWMD Regional Planning Area, 2013, SFWMD (http://www.sfwmd.gov). 4 CV is compiled from the BEBR Florida Statistical Abstract 1997, 2002, 2007, and 2012 issued by University of

Florida, (http://www.bebr.ufl.edu/data). CV is adjusted by PPI cropland product in the year of 2010 (PPI 2010=100). PPI cropland product (PPI C) is estimated from PPI agricultural product (http://www.bls.gov/ppi/ppiover.htm). 5 EMPC are FR obtained from the BEBR Florida Statistical Abstract 1997, 2002, 2007, and 2012 issued by University

of Florida, (http://www.bebr.ufl.edu/data).

4

(SWC) in million gallons per day (MGD), ground water usage in cropland in MGD (GWC6), the ratio of

irrigated cropland out of the cultivated cropland (RICL7), the ratio of fertilized cropland out of the

cultivated cropland (FR8), and year (YEAR), for each country in the SFWMD. The CV is adjusted according

to the inflation rate based on the producer price index cropland in 2010 (PPI 2010=100). The summary

of the total samples is shown in Table 1.

Table 1: The Summary of the Total Variables in the SFWMD Regions

YEAR CV EMPC SWC GWC Ratio SW9 RICL FR

2000 $4,405.70 27,176 1,660 718 0.70 0.84 0.94

2005 $4,470.60 25,180 1,290 532 0.71 0.83 0.88

2010 $3,234.20 20,698 957 490 0.66 0.79 0.73

Figure 1: The Map of the SFWMD and the Associated Area Number10

6 SWC and GWC are compiled by the USGS Florida Water Science Center, Orlando FL.

7 RICL is compiled from the USDA Census of Agriculture (1997, 2002, 2007, and 2012).

8 RF is estimated from USDA Agricultural Census Data (http://www.agcensus.usda.gov/). Adjusted CV in the Table 1

is the crop value adjusted by PPI C 2010, which is CV in the production function.

9 Ratio SW is the rate of the surface water use out of the total irrigation water (SWC + GWC) in cropland.

10 The original map is from the Regional County Acres, SFWMD, Aug. 21, 2013.

5

3. Methodology

3.1 Production

Numerous studies have examined the economic values of irrigation water. Young (2005) performed

water valuation using the theory of product exhaustion, economic rents, and a residual analysis. These

techniques were utilized to measure values of irrigation. The concept is based on producer welfare, in

which one questions if a producer is better off from changes in the quantity of inputs or outputs (Just et

al., 1982). Ward et al. (2006) used the production function termed the benefit function in their study to

estimate the value of irrigated water in Rio Grande Basin, Colorado, New Mexico, and Texas. Our study

utilizes a similar model including additional input variables and a Cobb-Douglas production function11.

Our production function is:

CVi,t = a EMPCi,tc SWCi,t

d GWCi,te RICLi,t

f FRi,tgYEARi,t

h. (1)

The index i and t refer to location (region/area) and time (2000, 2005 or 2010), respectively. The model

includes six inputs: employment, surface water, ground water, share of irrigated land, share of fertilized

land, and year. Coefficients a, c, d, e, f, g and h are constants.

The result of the Cobb-Douglas production function estimated from our data is:

CVi,t = a i,t EMPCi,t0.550 SWCi,t

0.078 GWCi,t0.136 RICLi,t

0.692 FRi,t1.440 YEARi,t

0.290. (2)

All variables are considered significant at the 0.05, or 95 percent, level of significance.

The marginal benefit (MB) of water, which is the producer’s Value Marginal Product (VMP) can be

estimated by the derivation of the production function with respect to water. VMP of water indicates

the effect of producer’s benefit for a unit change of water, which is equivalent to willingness to pay for

changes in the quantity of water (Johansson, 1993; Freeman 2003; Young, 2005). The VMP of surface

water (VMPS) is:

VMPS i,t =∂ CVi,t /∂ SWCi,t. (3)

We assume that the level of surface water use changes from SWCo (the current level) to SWCn (the new

or future level). If all other variables are held constant, then the production (value of crop sold) level

would change from CVo to CVn. The difference of the production level (d CV) is:

d CV i,t = CVni,t - CVoi,t. (4)

11

The Cobb-Douglas production function is used to represent the technological relationship between the amount of two or more inputs and the amount of output that can be produced by those inputs (Nicholson, 1998). In Eq.(1), if b+c+d+e+f+g+h=1, the production function exhibits constant returns to scale. If b+c+d+e+f+g>1, the function exhibits increasing returns to scale. If b+c+d+e+f+g>1, it indicates decreasing returns to scale. The production function in our model (Eq. (2)) shows increasing returns to scale.

6

3.2 Cost

We assume that the level of irrigation water in cropland is determined by farmers. When farmers decide

upon the irrigation water level, we assume that their objective is to maximize their profits by adjusting

their level, or amount, of water use. Thus, water can be optimally used and efficiently allocated in

cropland when farmers choose the amount of irrigation. Under this condition, producer’s profit is

maximized, which interprets that the marginal benefit (MB) of the use of irrigation water is equal to the

marginal cost (MC) of supply of irrigation water (Young, 2005 and Dudu and Chumi, 2008). The marginal

benefit of water is equal to VMP of water from Eq. (3). Hence, the marginal cost of surface water

becomes:

MC i,t = VMPS i,t . (5)

If the surface water levels are changed from the current level (SWCo) to the new level (SWCn), then the

cost difference (d COST) associated by the change in water use (SWn-SWo) can be calculated by the

following:

d COST i,t =( MC i,t) (SWCn i,t -SWCo i,t). (6)

3.3 Economic Loss (Penalty)

Producer’s profit is the difference of the income and the cost, which is:

Profit = CV – COST. (7)

Economic loss can be calculated by the change in producer’s profit when the level of water usage is

changed. Thus, the penalty or economic loss is estimated by the change in profit due to the change in

surface water use12.

PENALTY i,t = d CV i,t – d COST i,t. (8)

From Eqs. (4) and (6),

PENALTY i,t = (CVni,t - CVoi,t) – (MC i,t) (SWCn i,t -SWCo i,t) (9)

From Eqs. (2), (3), and (5), the penalty function in this study can be rewritten by:

12

Presented is an analysis pertaining to solely the SWC vector. This can be done for GWC as well or even better, to the two vectors combined. Eqs. (10) and (11) have a similar structure as the penalty function of Ward et al. (2006) presented.

7

PENALTY i,t = b1 i,t SWCni,t 0.078 – (0.078 b1 i,t) SWCoi,t

(0.078-1) (d SWC i,t) - CVoi,t, (10)

or

PENALTY i,t = b1 i,t SWCni,t 0.078 – b2 i, t SWCoi,t

(0.078-1) (d SWC i,t) - CVoi,t, (11)13

where b1 i,t = a i,t EMPCi, t0.550 GWCi,t

0.136 RICLi,t0.692 FRi,t

1.440 YEARi,t0.290,

b2 i,t = 0.078 b1 i,t, and

d SWC i,t = SWCn i,t -SWCo i,t

4. Regional Analysis

4.1. The Regions in the SFWMD

The SFWMD is currently divided into four regions: 1. Kissimmee Basin (KB); 2. Lower East Cost (LEC); 3.

Lower West Coast (LWC); and 4. Upper East Cost (UEC). Each region contains several areas, which counts

for 21 areas in the entire SFWMD14 (SFWMD, 2013). Each area is numbered (AREA NO, as indicated in

Table 2), and the area numbers are shown on the map in Fig. 1. The average variables for each region

are summarized in Table 3.

Table 2: Regions and Areas in SFWMD

13

This penalty function is utilized in case only surface water use is changed. See Appendix for the penalty function in case the usage of only ground water or the combination of surface and ground water is changed. 14

Areas 11 and 18 in Monroe County are not included in this study. 15

% County Area is the percentage of the area out of the total county area.

REGION NO

AREA NO County

% County Area15

Kissimmee Basin (KB) 1 1 Glades 0.60 1 2 Highlands 0.75 1 3 Okeechobee 0.75 1 4 Orange 0.32 1 5 Osceola 0.73 1 6 Polk 0.24 Lower East Coast (LEC)

2 7 Broward 1.00 2 8 Collier 0.09 2 9 Hendry 0.48 2 10 Miami-Dade 1.00 2 11 Monroe 0.56

8

Table 3: The Average Values of the Economic Variables Used in the Analysis of the SFWMD Regions

4.2 The Value Marginal Product (VMP) of Irrigation Water in the SFWMD Regions

The VMP are calculated with Eq. (3), and are shown in Table 4. The VMP of surface or ground water is

the change in producer’s income (in million dollars) when the water use changes by a million gallons per

day.

REGION NO REGION YEAR CV EMPC SWC GWC Ratio SW RICL RF

1 KB 2000 616.7$ 3,045 51 142 0.26 0.77 0.92

2005 649.2$ 2,724 59 119 0.33 0.77 0.83

2010 445.5$ 2,917 84 90 0.48 0.75 0.70

2 LEC 2000 2,441.4$ 15,837 1,079 234 0.82 0.88 0.97

2005 2,533.3$ 14,321 869 174 0.83 0.86 0.90

2010 1,864.1$ 12,014 534 144 0.79 0.77 0.72

3 LWC 2000 928.6$ 6,937 212 278 0.43 0.90 0.96

2005 885.8$ 6,953 166 197 0.46 0.88 0.88

2010 650.2$ 4,915 244 242 0.50 0.85 0.71

4 UEC 2000 419.0$ 1,357 318 64 0.83 0.80 0.92

2005 402.3$ 1,182 196 42 0.82 0.80 0.90

2010 274.4$ 852 96 14 0.87 0.78 0.81

SFWMD Total 2000 4,405.7$ 27,176 1,660 718 0.70 0.84 0.94

2005 4,470.6$ 25,180 1,290 532 0.71 0.83 0.88

2010 3,234.2$ 20,698 957 490 0.66 0.79 0.73

2 12 Palm Beach 1.00 Lower West Coast (LWC)

3 13 Charlotte 0.35 3 14 Collier 0.91 3 15 Glades 0.40 3 16 Hendry 0.52 3 17 Lee 1.00 3 18 Monroe 0.44 Upper East Coast (UEC)

4 19 Martin 1.00 4 20 Okeechobee 0.13 4 21 St Lucie 1.00

9

Table 4: The Value Marginal Product (VMP) of Surface or Ground Water in the SFWMD Regions (in

$ million/MGD)

SW GW

2000 2005 2010 2000 2005 2010

KB 0.95 0.86 0.42 0.59 0.74 0.67

LEC 0.18 0.23 0.27 1.43 1.99 1.77

UEC 0.10 0.16 0.22 0.89 1.30 2.72

LWC 0.34 0.42 0.21 0.46 0.61 0.37

SFWMD 0.21 0.27 0.26 0.84 1.15 0.90

The VMP findings reveal that the VMP of ground water is higher than surface water for all regions,

except the KB, in years 2000 and 2005. In the LEC region, the VMP of surface water is much lower than

ground water, which can be interpreted that surface water is more easily accessible in the LEC region

than ground water.

4.3 Penalties of SWMGD Regions

To compare the penalty across regions, the penalty resulting from the change in the same amount of

water should be analyzed across the regions. Figure 2 shows the penalty (in $ million) incurred if the

surface or ground water is used from an additional -10 to +10 MGD across the regions during the years

of 2000, 2005 and 2010.

Figure 3 reveals that KB would have a significant damage to crop farming if surface water level changes,

compared to the other regions. While the degree of damage in KB is diminishing over the decade, KB still

has the largest economic impact if the region has a change in surface water. Another notable trend is

the penalty in the UEC is rising at a faster rate than in the other regions, which seems to minimize the

penalty gap in the four regions of the SWMGD.

Regarding the change in the amounts of ground water, the economic loss in the UEC rose significantly

over the last ten years. Our research results indicate that if the UEC switches to using more ground

water than surface water, the region would experience a significant economic loss.

10

Figure 2: Surface and Ground Water Penalties for the SFWMD Region

Note: The water penalties depict if surface or ground water is used from an additional -10 to 10 MGD

across the regions in 2000, 2005, and 2010. The horizontal axis shows the change in surface (see figures

on the left) or ground water (see the figures on the right), in MGD. The vertical axis shows the penalty in

million dollars, and the scale ranges from 0 to 0.8 million dollars for changes in surface water and from 0

to 2 million dollars for changes in ground water use16.

16

Since the penalties caused by changes in ground water use are relatively greater than the ones caused by changes in surface water use, the scale ranges are different when comparing the left and right figures.

11

4.5 Penalties across the Areas of the LEC

The LEC is the intense crop farming region in the SWFMD. The region generates approximately 58% of

the total value of crop sold, and uses nearly 56 percent and 30 percent of surface and ground water,

respectively, in the SFWMD in 2010. Since the LEC is an important crop farming region in the SFWMD,

the penalty values were examined across the areas in the LEC.

4.5.1 Penalties incurred by the Changing in Surface Water Use in the LEC

For the cross area analysis, the penalties caused by the change in absolute amount of the surface or

ground water are compared in Fig. 3. Regarding the penalty due to the change in the surface water, the

figures present the penalty in eastern Collier County (LEC 7), which are extremely high during the years

of 2000 and 2005, but the penalty in Broward County (LEC 8) rose sharply in 2010. The penalties in

eastern Hendry County (LEC 9) and Palm Beach County (LEC 12) show nearly zero, over the last decade.

In Miami-Dade County (LEC 10), the penalty is rising notably from the years of 2000 to 2010. This

analysis can be interpreted that the economic losses due to the surface water changes are significantly

larger in Broward (LEC 7), eastern Collier (LEC 8), and Palm Beach Counties (LEC 12) compared to the

eastern Hendry (LEC 9) and Palm Beach Counties (LEC 12). Thus, if we assume that the ground water use

is constant in the LEC, and if a million gallons of water per day would represent a shortage in the LEC,

then the water should be traded from eastern Hendry (LEC 9) or Palm Beach Counties (LEC 12) to

Broward (LEC 7), eastern Collier (LEC 8), or Miami-Dade Counties (LEC 12).

Figure 3: The Penalties in the Areas of the LEC Region in Years 2000, 2005 and 2010

Note: The figures depict the penalty (in $ million) if surface and ground water is used an additional -2.0

to +2.0 MGD across the areas in the LEC. The horizontal axis shows the change in surface (see the figures

on the left) or ground water (see the figures on the right) in MGD. The vertical axis shows the penalty in

million dollars, and the scale ranges from 0 to 1.8 million dollars for changes in surface water use and

from 0 to 1 million dollars for changes in ground water use.

12

4.5.2 Penalties Incurred by the Changing in Ground Water Use in the LEC

Regarding the penalty due to the change in amounts of ground water, Broward County (LEC 12) presents

the highest penalty in the LEC. The penalty in Palm Beach County (LEC 12) rises rapidly over time. The

penalty in eastern Hendry County (LEC 9), on the other hand, is very low. From these analyses, eastern

Hendry County (LEC 9) would have the lowest economic loss when the amount of surface or ground

water use is increasing or decreasing; however, Broward County (LEC 7) would have the largest

economic loss when the amount of either surface or ground water use is changed.

4.6 Water Trade-off Analyses across the Areas of the KB and LEC Regions

We assume that the surface and ground water are perfect substitutes, and both the surface and ground

water are available. If each area needs an additional one MGD of water for cropland, it should choose

either surface or ground water associated with the lower penalty, or economic loss. Table 5 presents the

penalty resulting in using an additional +1 or -1 MGD of surface or ground water, showing the penalty

ranking, in the case of surface and ground being substitutable in the KB and LEC regions, in year 2010.

The first two columns in Table 6 show the penalties associated with the change in the amounts of

surface water only. The next two columns show the penalties caused by the change in the amounts of

13

ground water only. These penalties can be interpreted as representing the values of surface water or

ground water. In the KB, southern Orange County (KB 4) and eastern Polk County (KB 6) have

outstandingly high penalties. Since these areas use less than 1 MGD of surface water, the estimation of

the penalties is practically unavailable. Thus it is assumed that nearly all income is lost in those areas. In

the LEC, Broward County (LEC 7) is in a similar situation.

If the water level changes by +1 or -1 MGD, then each county chooses the surface or ground water

associated with lower penalty. The fifth and sixth columns show lower penalties due to the change in

either surface or ground water level. The next column indicates which irrigation water is preferred:

surface water (SW) or ground water (GW). If surface water is associated with a lower penalty, then it is

shown in blue in the column. The last column shows the ranking from the lowest to the highest penalty

within the KB or LEC.

Table 5: Water Penalties Associated with Altering Surface or Ground water by +1 or -1 MGD, and

Corresponding Rankings, in the KB and LEC Regions (in $ million)

When SW changes When GW changes When either SW or GW changes

d SW=-1 mgd

d GW=+1 mgd

d GW=-1 mgd

d GW=+1 mgd

d irrigation water=-1

mgd

d irrigation water=+1

mgd Lower

penalty

Rank (Lowest

to highest

penalty)

KB

KB 1 0.0003 0.0003 0.0046 0.0043 0.0003 0.0003 SW 1

KB 2 0.2897 0.2224 0.0130 0.0125 0.0130 0.0125 GW 4

KB 3 0.0183 0.0157 0.0052 0.0049 0.0052 0.0049 GW 2

KB 4 78.5176 24.6555 4.0357 1.5290 4.0357 1.5290 GW 6

KB 5 0.7204 0.3467 0.0096 0.0089 0.0096 0.0089 GW 3

KB 6 83.1451 22.2409 2.9821 1.3050 2.9821 1.3050 GW 5

LEC

LEC 7 46.7969 11.4394 1.3913 0.6508 1.3913 0.6508 GW 5

LEC 8 0.7669 0.2751 0.0083 0.0075 0.0083 0.0075 GW 3

LEC 9 0.0004 0.0004 0.0060 0.0058 0.0004 0.0004 SW 2

LEC 10 0.5730 0.4716 0.0105 0.0103 0.0105 0.0103 GW 4

LEC 12 0.0002 0.0002 0.1430 0.1343 0.0002 0.0002 SW 1

Table 5 shows lower penalties for using ground water than in using surface water in all areas, with the

exception of northern Glades County (KB 1). The lowest penalty is in northern Glades County (KB 1).

We assume that only surface water can be traded between the areas. If 1 MGD of water is experiencing

a shortage in the KB, and if the water is traded from southern Glades County (KB 1) to southern Orange

County (KB 4), then it minimizes the economic loss in the KB. The ranking prioritizes the areas that

14

should export water. The areas with the lower ranked number, with a lower value of surface water,

should export water to the area with the high ranked number, which has a higher value of irrigation

water. For example, if water is distributed from Palm Beach County (LEC 12) or eastern Hendry County

(LEC 9), and allocated to Miami-Dade (LEC 10) or Broward Counties (LEC 7), then the LEC could end up

with a lower penalty, which would result in minimizing the economic loss in the entire LEC.

Figure 4: The Production Function and Cost

Function Depending on Surface and Ground

Water in the LEC, in year 2010

Figure 5: Penalty Depending on Surface and

Ground Water in the LEC, in year 2010

Similar to the analyses in Figure 3, the effects of changes in combined surface and ground water use can

be shown17. Figure 4 shows the production function adjusted by two inputs (surface and ground water)

and the cost function, assuming ceteris paribus; all other variables except water are remaining

unchanged. The red dot symbolizes the present maximum profit point for the LEC. Figure 5 depicts the

difference between the production function and the cost function, or the penalty (scale limited, or

truncated, to $120 million). Figure 6 shows the combinations of surface and ground water use (from

Figure 5), representing the lowest cost of water used in cropland farming, in the red shaded area.

Further analysis is needed for other regions to determine the optimal water allocation, which is

minimizing the penalty, in the SFWMD.

17

See Appendix for the penalty function utilized in case the combined surface and ground water is changed.

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GWCn LWC

2E-06 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 100 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95 2

SWCn 0 16 33 49 65 82 98 115 131 147 164 180 196 213 229 245 262 278 294 311 327 344 360 376 393 409 425 442 458 474 491 507 523 540 556 573 589 605 622 638 654

1.08E-06 0 510 515 519 524 528 533 537 542 546 550 555 559 564 568 573 577 581 586 590 595 599 604 608 613 617 621 626 630 635 639 644 648 652 657 661 666 670 675 679 683 688

0.05 23 513 176 146 130 118 110 103 99 95 92 90 88 87 86 85 85 85 86 86 87 88 89 90 91 92 94 96 97 99 101 103 105 107 109 111 113 116 118 120 123 125

0.1 46 516 159 128 110 98 89 82 76 72 69 66 64 63 61 61 60 60 60 60 61 62 62 63 64 66 67 68 70 72 73 75 77 79 81 83 85 87 89 92 94 96

0.15 69 518 150 118 99 86 77 69 64 59 56 53 51 49 47 47 46 46 46 46 46 47 47 48 49 50 51 53 54 56 57 59 61 63 65 67 69 71 73 75 77 80

0.2 92 521 144 111 92 78 69 61 55 50 47 44 41 39 38 37 36 36 36 36 36 36 37 38 39 40 41 42 43 45 46 48 50 52 53 55 57 59 62 64 66 68

0.25 116 523 140 106 86 73 63 55 49 44 40 37 35 33 31 30 29 28 28 28 28 29 29 30 31 32 33 34 35 37 38 40 42 43 45 47 49 51 53 55 57 60

0.3 139 526 137 103 82 69 58 50 44 39 35 32 29 27 26 24 23 23 23 22 23 23 23 24 25 26 27 28 29 31 32 34 35 37 39 41 42 44 46 49 51 53

0.35 162 528 135 100 79 65 55 47 40 35 31 28 25 23 21 20 19 18 18 18 18 18 19 19 20 21 22 23 24 26 27 29 30 32 34 35 37 39 41 43 45 48

0.4 185 531 133 98 77 63 52 44 38 32 28 25 22 20 18 17 16 15 14 14 14 14 15 15 16 17 18 19 20 22 23 24 26 28 29 31 33 35 37 39 41 43

0.45 208 533 132 96 75 61 50 42 35 30 26 22 19 17 15 14 13 12 12 11 11 11 12 12 13 14 15 16 17 18 20 21 23 24 26 28 30 31 33 35 37 40

0.5 231 536 131 95 74 59 48 40 33 28 24 20 17 15 13 12 10 10 9 9 9 9 9 10 10 11 12 13 14 15 17 18 20 21 23 25 27 28 30 32 34 37

0.55 254 539 131 94 73 58 47 39 32 27 22 18 16 13 11 10 9 8 7 7 7 7 7 8 8 9 10 11 12 13 14 16 17 19 21 22 24 26 28 30 32 34

0.6 277 541 130 94 72 57 46 38 31 25 21 17 14 12 10 8 7 6 6 5 5 5 5 6 6 7 8 9 10 11 13 14 15 17 19 20 22 24 26 28 30 32

0.65 301 544 130 93 72 57 46 37 30 24 20 16 13 11 9 7 6 5 4 4 4 4 4 4 5 6 6 7 9 10 11 12 14 15 17 19 20 22 24 26 28 30

0.7 324 546 131 93 71 56 45 36 29 24 19 15 12 10 8 6 5 4 3 3 3 3 3 3 4 4 5 6 7 8 10 11 12 14 16 17 19 21 23 25 27 29

0.75 347 549 131 93 71 56 45 36 29 23 19 15 12 9 7 5 4 3 2 2 2 2 2 2 3 3 4 5 6 7 9 10 11 13 14 16 18 20 22 23 25 27

0.8 370 551 131 94 71 56 45 36 29 23 18 14 11 9 7 5 3 2 2 1 1 1 1 2 2 3 4 4 5 7 8 9 11 12 14 15 17 19 21 22 24 26

0.85 393 554 132 94 72 56 45 36 29 23 18 14 11 8 6 4 3 2 1 1 1 1 1 1 2 2 3 4 5 6 7 8 10 11 13 14 16 18 20 22 24 26

0.9 416 556 132 94 72 56 45 36 29 23 18 14 11 8 6 4 3 2 1 1 0 0 0 1 1 2 2 3 4 5 7 8 9 11 12 14 16 17 19 21 23 25

0.95 439 559 133 95 72 57 45 36 29 23 18 14 11 8 6 4 3 2 1 0 0 0 0 0 1 1 2 3 4 5 6 8 9 10 12 14 15 17 19 21 23 25

100 462 561 134 95 73 57 46 36 29 23 18 14 11 8 6 4 3 2 1 0 0 - 0 0 1 1 2 3 4 5 6 7 9 10 12 13 15 17 18 20 22 24

1.05 485 564 135 96 74 58 46 37 29 24 19 15 11 9 6 4 3 2 1 1 0 0 0 0 1 1 2 3 4 5 6 7 9 10 12 13 15 17 18 20 22 24

1.1 509 567 136 97 74 58 47 37 30 24 19 15 12 9 7 5 3 2 1 1 0 0 0 1 1 1 2 3 4 5 6 7 9 10 12 13 15 16 18 20 22 24

1.15 532 569 137 98 75 59 47 38 31 25 20 15 12 9 7 5 4 2 2 1 1 0 1 1 1 2 2 3 4 5 6 7 9 10 12 13 15 17 18 20 22 24

1.2 555 572 138 99 76 60 48 39 31 25 20 16 13 10 7 6 4 3 2 1 1 1 1 1 1 2 3 3 4 5 6 8 9 10 12 13 15 17 18 20 22 24

1.25 578 574 139 100 77 61 49 39 32 26 21 17 13 10 8 6 5 3 2 2 1 1 1 1 2 2 3 4 5 6 7 8 9 11 12 14 15 17 19 21 22 24

1.3 601 577 140 101 78 62 50 40 33 27 22 17 14 11 9 7 5 4 3 2 2 2 2 2 2 3 3 4 5 6 7 8 10 11 13 14 16 17 19 21 23 25

1.35 624 579 141 102 79 63 51 41 34 27 22 18 15 12 9 7 6 5 4 3 3 2 2 3 3 3 4 5 6 7 8 9 10 12 13 14 16 18 19 21 23 25

1.4 647 582 143 103 80 64 52 42 34 28 23 19 15 12 10 8 7 5 4 4 3 3 3 3 3 4 5 5 6 7 8 9 11 12 13 15 17 18 20 22 24 26

1.45 670 584 144 104 81 65 53 43 35 29 24 20 16 13 11 9 7 6 5 4 4 4 4 4 4 5 5 6 7 8 9 10 11 13 14 16 17 19 21 22 24 26

1.5 694 587 145 106 82 66 54 44 36 30 25 21 17 14 12 10 8 7 6 5 5 4 4 5 5 5 6 7 7 8 10 11 12 13 15 16 18 19 21 23 25 27

1.55 717 590 147 107 83 67 55 45 37 31 26 22 18 15 13 11 9 8 7 6 6 5 5 5 6 6 7 7 8 9 10 11 13 14 15 17 18 20 22 24 25 27

1.6 740 592 148 108 85 68 56 46 39 32 27 23 19 16 14 12 10 9 8 7 6 6 6 6 7 7 8 8 9 10 11 12 13 15 16 18 19 21 23 24 26 28

1.65 763 595 150 110 86 69 57 47 40 33 28 24 20 17 15 13 11 10 9 8 7 7 7 7 7 8 8 9 10 11 12 13 14 16 17 18 20 22 23 25 27 29

1.7 786 597 151 111 87 71 58 49 41 34 29 25 21 18 16 14 12 11 10 9 8 8 8 8 8 9 9 10 11 12 13 14 15 16 18 19 21 22 24 26 28 30

1.75 809 600 153 112 89 72 60 50 42 36 30 26 22 19 17 15 13 12 11 10 9 9 9 9 9 10 10 11 12 13 14 15 16 17 19 20 22 23 25 27 29 30

1.8 832 602 154 114 90 73 61 51 43 37 32 27 24 20 18 16 14 13 12 11 10 10 10 10 10 11 11 12 13 14 15 16 17 18 20 21 23 24 26 28 29 31

1.85 855 605 156 115 91 75 62 52 45 38 33 28 25 22 19 17 15 14 13 12 12 11 11 11 11 12 12 13 14 15 16 17 18 19 21 22 24 25 27 29 30 32

1.9 878 607 157 117 93 76 64 54 46 39 34 30 26 23 20 18 16 15 14 13 13 12 12 12 12 13 13 14 15 16 17 18 19 20 22 23 25 26 28 30 31 33

1.95 902 610 159 118 94 78 65 55 47 41 35 31 27 24 22 19 18 16 15 14 14 13 13 13 14 14 14 15 16 17 18 19 20 21 23 24 26 27 29 31 32 34

2 925 612 161 120 96 79 66 57 49 42 37 32 29 25 23 21 19 18 16 16 15 15 15 15 15 15 16 16 17 18 19 20 21 22 24 25 27 28 30 32 33 35

15

Figure 6: Optimal Penalties (i.e., Lowest) in a Two-Input Combination of Surface and Ground Water

Use in the LEC, in year 2010

5 Summary

Our study finds that penalties caused by changing surface and ground water usage are increasing in the

LEC and UEC from the year of 2000 to 2010. The LEC is the most important crop farming region in the

SFWMD. The rising rate of penalties relative to the change in irrigation water levels would negatively

impact the economy in South Florida. The recent data shows that the amount of irrigation water is

declining in the region, which correlates to the crop value sold in the region. Although an economic loss

to agriculture sector is already being experienced in the region, our study provides some strategies to

minimize the economic loss associated with a reduction in irrigation water use in the region. Through an

analyses of the penalties associated with water use across the region, the highest penalty due to a

reduction in irrigation water use is evidenced in the KB. The study has found that water can be traded to

the KB from other regions in order to sustain economic profits to agriculture, for the entire SFWMD. The

regional analysis in the KB demonstrates that exporting, or trading water from northern Glades County

to southern Orange County is an efficient way to allocate water in order to minimize the economic loss.

The same observation could be made in that water can be exported or traded from Palm Beach County

to Broward or Miami-Dade Counties in the LEC in order to minimize economic loss to the agriculture

sector.

This study analyzed the water penalties associated with varying irrigation water usage in the South

Florida region for the years of 2000, 2005, and 2010. Our estimations of the penalties did not include

pumping costs or geographical considerations. Further research in production costs as well as

forecasting the trend of the penalties across the SWFMD regions is needed to determine the optimal

usage and allocation of water for the South Florida agriculture sector.

16

Acknowledgements:

Richard Marella at USGS Florida Water Science Center and Jose Otero at SFWMD were helpful in

providing data. This work was supported by grants from the National Science Foundation (#1204762)

and the Agriculture and Food Research Initiative of the USDA National Institute of Food and Agriculture

(NIFA) (#2012-67003-19862).

References:

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Affecting Water Use in South Florida. Prepared for The Everglades Foundation.

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California Water Management. Journal of Water Resources Planning and Management Vol. 129 (3), 155-

164.

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18

Appendix:

• The penalty function (partial derivative) to SWC is calculated as:

Penaltyi,t = b1i,t*SWCni,t0.0784 – (b1i,t *0.0784)*SWCoi,t

0.0784-1 *(SWCni,t - SWCoi,t) – CVi,t

or

Penaltyi,t = b1i,t*SWCni,t0.0784 – b2i,t*SWCoi,t

0.0784-1 *(dSWCi,t) – CVi,t

In which: SWCn = SWC new level of use SWCo = SWC old level of use CV = Value of Crop Sold ($million/year) adjusted by PPI cropland product, with PPI 2010=100 b1i,t = αi,t * EMPLi,t

0.5499 * GWCi,t 0.1365 * RICLi,t

0.6921 * RFi,t1.4397 * Yeart

0.2900 in which: αi = individual county adjusted “total factor productivity” EMPL = Employment in Cropland SWC = Use of Surface Water Irrigation (MGD) in Cropland RICL = Rate of land share of irrigated cropland out of cultivated cropland RF = Rate of Fertilized land out of cultivated cropland Year = Year numbering: 2000=1, 2005=2, and 2010 = 4 (geometric series)

• The penalty function (partial derivative) to GWC is calculated as:

Penaltyi,t = b1i,t*GWCni,t0.1365 – (b1i,t *0.1365)*GWCoi,t

0.1365-1 *(GWCni,t - GWCoi,t) – CVi,t

or

Penaltyi,t = b1i,t*GWCni,t0.1365 – b3i,t*GWCoit

0.1365-1 *(dGWCi,t) – CVi,t

In which: b1i,t = αi,t * EMPLi,t

0.5499 * SWCi,t 0.0784 * RICLi,t

0.6921 * RFi,t1.4397 * Yeart

0.2900

• Similarly the penalty function to both SWC and GWC can be derived as:

Penaltyi,t = (b1i,t * 0.0784 * SWCoi,t0.0784-1 * GWCoi,t

0.1365) * (SWCni,t - SWCoi,t) +

(b1i,t * SWCoi,t0.0784 * 0.1365 * GWCoi,t

0.1365-1) * (GWCni,t - GWCoi,t) +

(CVoi,t – b1i,t * SWCni,t0.0784 * GWCni,t

0.1365)

In which: b1i,t = αi,t * EMPLi,t

0.5499 * RICLi,t0.6921 * RFi,t

1.4397 * Yeart0.2900

or

Penaltyi,t = b4i,t*SWCoi,t0.0764-1 * d SWCi,t + b5i,t*GWCoi,t

0.1365-1 * d GWCi,t –

b1i,t*(SWCni,t0.0764 * SWGni,t

0.1365 – SWCoi,t0.0764 * SWGoi,t

0.1365)