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Evapotranspiration in the Okefenokee Swamp watershed: a comparison of temperature-based and water balance methods
Journal of Hydrology, 131 (1992)293-312
293
Elsevier Science Publishers B.V., A m s t e r d a m
[11
Evapotranspiration in the Okefenokee Swamp watershed: a comparison of temperature-based and water balance methods Z h i - Y o n g Yin a a n d G e o r g e A. B r o o k b
"Department of Geography, Georgia State University, Atlanta, GA 30303, USA bDepartment of Geography, University of Georgia, Athens, GA 30602, USA (Received 30 April 1991; accepted 30 May 1991)
ABSTRACT Yin, Z.-Y. and Brook, G.A., 1992. Evapotranspiration in the Okefenokee Swamp watershed: a comparison of temperature-based and water balance methods. J. Hydrol., 131: 293-312. In the Okefenokee Swamp, actual evapotranspiration (AET) should approximate potential evapotranspiration (PET) as there is rarely a moisture deficit. Even during droughts, a high evapotranspiration rate is maintained owing to a large area of wetlands and a shallow groundwater table in the watershed. Therefore, if AET can be estimated in the Okefenokee Swamp watershed, it can be used to evaluate the accuracy of PET estimates for the region. In this study, temperature-based PET estimates were compared with AET obtained by the water balance method for the Okefenokee Swamp watershed. Swamp water level data were used to identify subperiods with identical storage at the beginning and end of the period, so that a steady-state water balance model could be used to estimate AET as the difference between precipitation and outflow runoff. When the PET estimates were regressed upon AET, Thornthwaite PET had the highest R2 value (0.817), followed by Blaney-Criddle PET (0.781), and Holdridge PET proportioned by biotemperature (0.768). The Thornthwaite method also rendered a long-term average very close to that of AET. Seasonal errors in Thornthwaite PET were reduced by using pan evaporation and temperature data to partition annual values into monthly values. Holdridge PET overestimated evapotranspiration from the Okefenokee Swamp watershed. Using standard crop coefficients, the Blaney-Criddle method would have overestimated evapotranspiration in the humid Okefenokee Swamp watershed. However, by substituting a very low crop coefficient (K = 1.5), the Blaney-Criddle method gave results for the Okefenokee region similar to those obtained by the Thornthwaite method with the lowest error among all the methods examined. Pan evaporation correlated well with AET (R 2 = 0.628) once an appropriate pan coefficient (0.71) had been determined.
INTRODUCTION
Evapotranspiration can be estimated by a variety of methods, such as water balance, mass-transfer, energy balance, the Penman-Monteith combined method, and eddy correlation (Rosenberg et al., 1983). However, most of these methods have limitations. For example, because watershed storage is
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Z.-Y. Y1N AND G.A. BROOK
difficult to estimate, the water balance method is often based on the assumption of no storage change during the period under investigation. The Penman-Monteith method requires knowledge of vegetation behavior under different meteorologic conditions. Solar radiation and humidity data are also needed and these are not always available. Energy balance and eddy correlation methods require sophisticated and expensive instruments. With the exception of the water balance approach, the above methods are relatively difficult to adapt to watershed studies because they are microscale and short time span oriented. The water balance method is not accurate unless multiyear periods are considered. Otherwise, significant storage changes may introduce sizeable errors. Therefore, the dynamic characteristics of the hydrologic regime are often ignored by the water balance approach. To avoid the above difficulties, a modeling approach is widely used in watershed hydrology studies. Actual evapotranspiration (AET) in a watershed is estimated as potential evapotranspiration (PET) multiplied by a coefficient which is determined by antecedent soil moisture conditions (Saxton and McGuinness, 1982). When there is sufficient moisture for vegetation water use, AET equals PET. PET is often estimated using readily available climatological data, such as air temperature and pan evaporation. As PET determines the maximum possible value of AET, it is a very important parameter in watershed modeling. However, it is difficult to verify PET estimates owing to the hypothetical nature of PET (Thornthwaite, 1948). The hydrologic characteristics of the Okefenokee Swamp watershed provide a way to evaluate PET estimates. The Okefenokee Swamp occupies more than 40% of the watershed area. The uplands are characterized by shallow groundwater tables. There are numerous small depressions filled with water scattered over the uplands. Only rarely does moisture stress affect evapotranspiration in this region. Even during droughts, a high evapotranspiration rate in the watershed is maintained because of the swamp, the numerous ponds and shallow groundwater reservoir in the uplands. The purpose of this study, therefore, is to compare temperature-based PET estimates with results from a steady-state water balance model for the Okefenokee watershed. The Thornthwaite (1948), Holdridge (1962), Blaney and Criddle (1950), the pan evaporation methods for estimating PET will be assessed. STUDY AREA AND DATA The Okefenokee Swamp watershed, with an area of 3925 km 2, is located on the lower Atlantic Coastal Plain of southeastern Georgia and northeastern Florida (Fig. 1). The Okefenokee Swamp is one of the largest wetland
EVAPOTRANSPIRATION
1N THE
OKEFENOKEE
SWAMP
295
WATERSHED
Tifton
Patterson Pearson Waycross Nahunta
Watershe Boundar
• Valdos~
Folkston 3SW 'otks/an 9 s w . . . . '~
.....
Hillard
. . . . . . . . . .
r
0
10
20
30
40
I
I
I
I
i
50 KM I
J
• Glen St. Mary • Lake City
ic n
MapLocation ~
Legend: • Weather Station • Discharge Gage
•
Water Level Gage
•
Gainesville
Fig. 1. Weather stations and stream discharge and water level gauges in the Okefenokee Swamp watershed and adjacent areas.
complexes in the United States and a National Wildlife Refuge. The northwest portion of the watershed is composed of the Terrace Uplands which are dissected marine terraces. Trail Ridge, a narrow ridge-like feature, forms the eastern boundary of the swamp. Three streams, the Suwannee River, the
296
Z.-Y. YIN AND G.A. BROOK
St. Mary's River North Prong, and Cypress Creek drain the swamp. The largest of the three is the Suwanee River, which drains the entire Terrace Uplands and most of the Okefenokee Swamp area. Cypress Creek joins the Suwannee River south of the watershed. Mean monthly temperature data were required to calculate monthly Thornthwaite, Holdridge, and Blaney-Criddle PET values. Monthly pan evaporation data were used as an alternative approach to estimate PET. Monthly precipitation and surface runoff were needed in water balance calculations and monthly water level data for the Okefenokee Swamp as indicators of watershed storage. The study period was from 1937 to 1986. Climatic data were obtained from 'Climatological Data for Georgia' (National Oceanic and Atmospheric Administration (NOAA), 1937-1986). Stream discharge data were provided by the United States Geological Survey, and the water level data by the Okefenokee National Wildlife Refuge. Regional average temperatures for the Okefenokee watershed were calculated using data for six weather stations in the area, Fargo, Folkston 9SW (Camp Cornelia), Homerville, Nahunta, Valdosta, and Waycross (Fig. 1). Simple arithmetic averages of temperatures at these stations were used as regional estimates. The longest pan evaporation record in the area is for Tifton, Georgia, about 120 km to the northwest of the Okefenokee Swamp. The data go back to April 1937, but there are many missing values. The only other station with pan evaporation data in Georgia relatively close to the study area is Savannah, about 160km to the northeast of the Okefenokee Swamp. The record for Savannah is shorter than that for Tifton and there are also many missing values. As most of the missing values for Tifton and Savannah are in the winter months, probably due to freezing of the water in the pans, the data for Savannah could not be used to estimate missing values in the Tifton record. Missing values were, therefore, determined using regression relationships between monthly pan evaporation at Tifton and pan evaporation at Lake City and Gainesville in Florida. Three situations were considered: (1) data were available for both Lake City and Gainesville; (2) data were available for only one of the two Florida stations; (3) no data were available for either station. Under (1) and (2), the missing values were determined using regression relationships shown in Table 1, which were developed with data for the period 1965-1986 when all three stations were in operation. Relationships between pan evaporation at these three stations were very good. When data for only one of the two Florida stations were used, the explained variance in pan evaporation at Tifton was about 88%. When data for both stations were available, the explained variance in pan evaporation at Tifton increased to 91%. Case (3) mostly occurred before the two Florida stations began to monitor pan evaporation. Under this situation, missing values of monthly pan
EVAPOTRANSPIRATIONIN THE OKEFENOKEESWAMPWAIERSHED
297
TABLE 1 Regression relationships to predict pan evaporation at Tifton from pan evaporation at other stations, 1965-1986. Dependent variable: pan evaporation at Tifton Variable
Coefficient
R2
Constant Gainesville Lake City
- 19.278 0.506 0.530
0.911
Constant Gainesville
- 12.850 1.017
0.883
Constant Lake City
- 15.882 0.997
0.885
evaporation at Tifton were estimated by a regression relationship between pan evaporation and maximum monthly temperature in the Okefenokee area (Table 2). Data from 1937 to 1986 were used to develop this relationship. The explained variance in pan evaporation at Tifton by this model was not as high as by the relationships between pan evaporation at the three stations. However, the reduced accuracy of the estimated pan evaporation values is unlikely to affect the study of long-term temporal variations because only a few missing values were determined in this way. There are marked spatial variations in precipitation in southeastern Georgia and northeastern Florida particularly during the summer months when isolated thunderstorms are the major type of rainfall. Therefore, data for 12 weather stations were used in calculating regional precipitation: Fargo, Folkston 3SW, Folkston 9SW, Glen St. Mary, Hillard, Homerville, Jasper, Nahunta, Patterson, Pearson, Valdosta, and Waycross (Fig. 1). As the terrain of the study area is flat without greater topographic relief, a simple arithmetic mean of station values was used as an estimate of regional precipitation. There are United States Geological Survey stream gaging stations on the Suwannee River at Fargo and on the St. Mary's River at Moniac and TABLE 2 Regression relationships to predict pan evaporation at Tifton from maximum monthly temperature in the Okefenokee Swamp area, 1937-1986. Dependent variable: In (PANEP) Variable
Coefficient
R2
Constant TMAX
2.83961 0.07011
0.768
298
Z.-Y. YIN AND G.A. BROOK
Macclenny. Cypress Creek, which joins the Suwannee River downstream of Fargo, is not gauged. To obtain total watershed runoff Cypress Creek discharges were estimated using instantaneous discharges of this stream measured by Hyatt from February 1981 to July 1982 (Hyatt, 1984). The monthly average discharge of Cypress Creek was then determined using the multiple regression relationship: CYP
=
0.101 + 0.058 F A R + 0.064 MAC,
R 2 = 0.807,
where CYP is the discharge of Cypress Creek, F A R is the discharge of the Suwannee River at Fargo, and MAC is the discharge of the St. Mary's River at Macclenny. The discharge at Moniac has been monitored continuously from 1950. The discharge before this period was estimated using the longer record for Macclenny by the regression model: MON
-- 0.0629 + 0.217 MAC,
R 2 = 0.861,
where M O N is the discharge at Moniac and MAC is the discharge at Macclenny. This model was developed with data for the periods 19281935 (discontinuous record) and 1950-1959. Complete monthly discharge records from 1937-1986 were then obtained for the St. Mary's River at Moniac and Cypress Creek using the above regression models. Monthly average discharge from the Okefenokee Swamp watershed via the three streams was converted to monthly surface runoff in millimeters from the watershed. The Okefenokee National Wildlife Refuge monitors water levels in the Okefenokee Swamp at several locations. A fairly complete record is available for the Suwannee Canal Recreation Area (SCRA) from 1950 to 1986 (Fig. 1). A very good relationship exists between the swamp water level, discharge of the Suwannee River at Fargo, and precipitation. This allowed the water level record at the SCRA to be extended back to 1937 using the model: WL
=
e 3503671Q0"002082PPI0"018863,
R: = 0.931,
where W L is monthly mean swamp water level at the SCRA, Q is monthly mean discharge of the Suwannee River at Fargo, and PPI is the previous precipitation index, a weighted 11 month running mean of precipitation. The PPI is calculated using the following equation: PPI = (1.43 x P, + 1.71 x P, I + 1.65 x P, ~_ + 1.31 x P, 3 + 1.37 x Pr-4 + 1.07 x P~ 5 + 1.49 × Pt-6 + 1.39 x P, 7 + 1.28 x P, s + 1.20 x Pt 9 + 0.96 x P, ~0)/11/1.35
EVAPOTRANSP1RATION IN THE OKEFENOKEE SWAMP WATERSHED
299
where P, is precipitation in the current month, and P, t to P,_ ~0 are precipitation values for the previous 1-10 months. The weights are actually regression coefficients from a multiple regression of precipitation with swamp water level; they averaged 1.35. PET USING TEMPERATURE-BASED
METHODS
Thornthwaite first defined the concept of potential evapotranspiration in 1948 for climatic classification (Thornthwaite, 1948). It has been widely used in watershed studies and modeling since the 1950s. Mean monthly temperature is used to calculate Thornthwaite PET (cm): PET
=
1.6 x L x (n/30) x (10 x T / I ) ~
where: a = 6.75 x 10 -7 × 1 3 - 7.71 X 10 -5 X 1 2 + 1.792 X 10 -2 X I + 0.49239; I is the annual sum of i; i -- (T/5)~514; L is the monthly mean day-length at a given latitude in units of 12 h; n is the number of days in the month; T is the monthly mean temperature. The Holdridge method calculates annual PET as the mean annual 'biotemperature' multiplied by 58.93mm°C -1. Monthly biotemperature is the average monthly temperature with any negative values converted to 0°C. As Holdridge (1962) dealt only with annual PET, in this study annual Holdridge PET was partitioned to monthly values in two ways: (1) using monthly pan evaporation where PET i = A N N P E T x P A N i / A N N P A N ; (2) using monthly biotemperature where PETi = A N N P E T x BIOTi/(E BIOT/). In these equations, PET i is monthly Holdridge PET in month i (mm), A N N P E T is annual Holdridge PET (mm), PANi is pan evaporation at Tifton in month i(mm), A N N P A N is annual pan evaporation at Tifton(mm), BlOTs is monthly biotemperature in month i(°C), and E BIOT/ is the sum of 12 monthly biotemperatures (°C). The Blaney-Criddle method was designed for irrigated crops in the western United States (Blaney and Criddle, 1950). As irrigation eliminates soil moisture stress, results from the Blaney-Criddle equation can be regarded as PET. This method has been widely used for agriculture purposes (Soil Conservation Service, 1970; Dunne and Leopold, 1978). In the Blaney-Criddle equation: PET
=
K x F
F =
annual sum of (1.8 x T +
32) x d
where K is the crop coefficient depending on crop type, T is monthly mean temperature, and d is the fraction of monthly daylight hours to the annual
300
Z.-Y. YIN AND G.A. BROOK
total. The Blaney-Criddle method is similar to the Thornthwaite method, but the published crop coefficients were determined for western United States locations. As this method was originally developed for dry climates where strong advection is present, it was expected that the published K values, varying from 1.5 to 2.8, would result in the overestimation of AET in the Okefenokee area for specified crops or vegetation types. Therefore, F was calculated first. The value of K was then determined using precipitation and runoff data: K
=
(P -
R)/F
where P and R are long-term averages of precipitation and runoff. The difference between precipitation and runoff was treated as an approximation of evapotranspiration. In this way, K was calculated as 1.50, a value at the bottom of the range for crop coefficients (Dunne and Leopold, 1978). Temporal variations in Blaney-Criddle PET rather than absolute values were the focus of this study. Pan evaporation is often used as an index of evapotranspiration. In theory it should be a better estimate than those provided by temperature-based methods because it includes the effects of solar radiation, wind, and atmospheric demand. Lake evaporation can be estimated as pan evaporation multiplied by a constant from 0.6 to 0.8, the pan coefficient, and used as an estimate of PET. The pan coefficient is higher for humid areas and lower for arid areas. In this study, the pan coefficient (C) was estimated to be 0.71 by the equation: C =
(P-
R)/PAN
where PAN, P and R were long-term monthly averages of pan evaporation, precipitation, and runoff. EVAPOTRANSPIRATION ESTIMATED BY A WATERSHED WATER BALANCE APPROACH The s t e a d y - s t a t e watershed m o d e l
A dynamic watershed water balance model can be presented as P + RI + GI =
AET + Ro + Go + dS
where P is precipitation, AET is actual evapotranspiration, RI and Ro are surface inflow and outflow runoff, G~ and Go are groundwater inflow and outflow, and dS is the change in storage for a stated period. Previous studies have shown that groundwater discharge from the swamp varies from 0 to 6%
301
E V A P O T R A N S P I R A T I O N IN T H E O K E F E N O K E E SWAMP W A T E R S H E D
of the total water loss (Rykiel, 1977; Blood, 1982; Hyatt, 1984). A recent study, using United States Geological Survey groundwater simulation models, suggests that groundwater discharge is only 1.3% of the total water loss (Yu, 1986). Therefore, groundwater discharge from the swamp, being an extremely minor component of the water budget, was not considered in this study. It was also assumed that there were no groundwater gains or losses across the surface boundaries of the watershed. In this way, precipitation became the only water input to the watershed. Changes in the water level of the Okefenokee Swamp indicate changes in swamp water storage. In this study, swamp water levels were also shown to be closely associated with groundwater levels in the uplands in the Okefenokee Swamp watershed. Hyatt (1984) installed 28 shallow wells in the uplands and monitored groundwater levels in these wells during an 18 month period in 1981-1982 (Fig. 2). Groundwater levels in these wells correlated well with water levels at the SCRA (Table 3). Most correlation coefficients were higher than 0.6 and significant at the 0.01 confidence level. At only two locations (wells Nos. 55 and 67), were correlation coefficients significant at the 0.05 confidence level. This indicated a strong spatial correlation between swamp water and upland groundwater levels. Considering that most of Hyatt's wells were located in the Terrace Uplands, northwest of the Okefenokee Swamp, while the swamp water level TABLE 3 Correlations between swamp water level at the SCRA and groundwater levels in the uplands of the Okefenokee Swamp watershed, February 1981 to July 1982 (well data from Hyatt, 1984) Well no.
r
Significancea
Well no.
r
Significancea
40 42 43 44 45 47 48 49 50 51 52 53 54 55
0.693 0.841 0.928 0.699 0.672 0.849 0.872 0.727 0.722 0.717 0.638 0.685 0.518 0.379
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.05
56 57 58 59 60 61 62 63 64 65 66 67 68 69
0.909 0.898 0.891 0.881 0.909 0.889 0.795 0.567 0.571 0.869 0.794 0.445 0.643 0.485
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.05 0.01 0.01
a 0.05: at 0.05 confidence level. 0.01: at 0.01 confidence level.
302
z.-Y. YIN AND GA. BROOK
Fig. 2. Locations and numbers of groundwater wells installed in the Okefenokee watershed in 1981 (from Hyatt, 1984).
gauge (SCRA) was at the eastern edge of the watershed, the relationships between swamp water and upland groundwater levels were clearly very significant. The swamp and groundwater level data examined here were daily observations measured on a tri-weekly schedule. Correlations between monthly or annual swamp water and upland groundwater levels should be even better as short-term variations are smoothed. Therefore, monthly swamp water level data should provide a good estimate of storage in the entire Okefenokee Swamp watershed. Using swamp water level as an index of watershed storage, it was possible to define periods with minimal storage change, characterized by the same beginning and end water levels. Thus, the assumption of a steady-state watershed model became valid, that is P = AET + R o. An estimate of watershed AET can then be obtained using AET = P - Ro.
EVAPOTRANSPIRATION IN THE OKEFENOKEE SWAMP WATERSHED
303
Water budgets for subperiods The long-term average monthly water level at the SCRA (36.551 m) was used to divide the 1937-1986 period into subperiods with identical storage at the beginning and end of the period. The start (and also, therefore, the end) of a subperiod was defined by a change in the monthly water level from below to above the long-term average (36.551 m) or the reverse. For example, if the water level at the SCRA in January was lower than 36.551 m and the water level in February higher, a new subperiod began in February. Any period shorter than three months was combined with the next subperiod to reduce errors. Fifty-six subperiods were defined in this way. For each subperiod, monthly averages of the following variables were calculated: precipitation, outflow runoff, AET as the difference between precipitation and outflow runoff, pan evaporation multiplied by 0.71, Thornthwaite PET, Holdridge PET partitioned by pan evaporation and by biotemperature, and Blaney-Criddle PET (Table 4). The average subperiod lasted for 10.6 months, so that water balance estimates were close to annual water budgets for the watershed. However, two subperiods lasted for 40 months; in one, water levels remained below the average because of an extended drought, while in the other water levels remained above the average due to unusually wet conditions. COMPARISON OF THE PET ESTIMATES Based on the hydrologic characteristics of the Okefenokee Swamp watershed, it was assumed that AET estimated by the water balance method was very close to PET and could be used to evaluate the accuracy of the PET estimates. General characteristics of the water budget components are listed in Table 5. Mean monthly precipitation was 108.2 mm, equivalent to 1298 mm year ~. Estimated AET was 86.0 mm month ~, equal to 1032mmyear ~ and 79% of precipitation. Output runoff was 22.2 mm month- t or 266 mm year ~, and 21% of precipitation. Thornthwaite PET had a long-term average closest to that of AET. The AET/PET ratio was 99% for Thornthwaite PET and 89% for Holdridge PET. Thornthwaite PET apparently was the most accurate estimate of AET, The Holdridge method overestimated PET in this area. Previous studies have indicated that evapotranspiration in terrestrial environments of the Okefenokee watershed is close to or lower than 1000 rnm year ~, and that the percentage of evapotranspiration to precipitation varies between 70% and 85% (Blood, 1982; Hyatt, 1984; Sun, 1986; Yu, 1986). The Holdridge method rendered annual PET estimates between 1157 and l164mm, equivalent to about 90% of precipitation, and 125-132mm
304
Z.-Y. Y1N AND G.A. BROOK
TABLE 4 Monthly averages of water budget components (mm) for subperiods with identical storage at the beginning and end of the period OBS Period 7 19 31 46 59 64 75 86 92 97 108 118 122 134 146 150 155 159 164 171 178 190 201 223 245 252 259 279 299 308 317 341 364 377 396 406 410 419 435 446 457 468
8/37- 1/38 2/38- 7/39 8/39- 1/40 2/40-11/41 12/41- 4/42 5/42-9/42 10/42- 3/44 4/44-7/44 8/44- 2/45 3/45- 6/45 7/56-11/46 12/46- 2/47 3/47- 7/47 8/47- 4/49 5/49-7/49 8/49-11/49 12/49- 4/50 5/50- 8/50 9/50- 1/51 2/51-10/51 11/51- 4/52 5/52- 9/53 10/53- 2/54 3/54- 6/57 7/57-10/57 11/57- 7/58 8/58- 1/59 2/59-10/61 11/61- 5/62 6/62- 4/63 5/63-12/63 1/64- 4/67 5/67- 9/67 10/67- 7/69 8/69-11/70 12/70-3/71 4/71- 6/71 7/71-10/72 11/72- 2/74 3/74- 7/74 8/74- 1/76 2/76- 5/76
N
P
Ro
AET
THORN
PAN71
HPAN
HBIOT
BLANEY
6 18 6 22 5 5 18 4 7 4 17 3 5 21 3 4 5 4 5 9 6 17 5 40 4 9 6 33 7 11 8 40 5 22 16 4 3 16 16 5 18 4
107.3 102.0 94.1 95.0 128.2 137.8 83.6 138.2 106.9 85.4 134.5 57.4 133.2 141.1 134.6 137.4 59.3 135.0 105.4 101.3 89.0 !18.7 66.1 87.7 138.2 116.3 75.1 121.4 81.9 107.9 107.5 127.0 132.6 87.1 119.4 79.7 101.8 118.4 121.5 118.6 109.9 101.0
32.1 7.5 14.9 7.4 66.8 7.3 2.9 28.0 39.4 7.3 48.1 9.8 36.9 63.3 7.5 43.3 7.6 9.1 27.7 9.9 39.0 9.0 38.3 3.8 16.7 30.8 5.7 33.3 16.2 17.2 4.1 47.0 12.5 8.1 37.7 14.2 13.7 34.6 42.3 10.9 30.6 15.8
75.2 94.5 79.2 87.6 61.4 130.5 80.6 110.3 67.5 78.2 86.5 47.6 96.3 77.8 127.1 94.0 51.7 125.9 77.7 91.4 50.1 109.7 27.9 83.8 121.6 85.5 69.4 88.0 65.8 90.7 103.4 80.0 120.1 79.0 81.6 65.5 88.0 83.8 79.2 107.7 79.2 85.2
69.9 95.0 72.0 92.0 32.5 151.2 72.0 136.6 65.2 112.8 96.8 26.5 112.1 81.1 146.6 102.0 40.3 157.3 52.7 109.7 37.4 108.0 36.3 88.7 129.4 72.7 73.0 88.9 50.5 79.4 103.8 79.0 132.8 76.8 86.5 26.2 107.9 97.0 73.3 108.3 80.3 67.8
68.9 95.0 66.3 90.1 66.7 115.4 79.4 120.0 66.6 113.2 77.9 40.2 104.3 75.7 110.2 75.1 65.4 121.8 53.9 101.2 61.7 91.9 46.5 85.1 85.3 74.2 65.0 89.1 79.3 84.7 102.6 84.0 126.7 89.6 82.9 51.1 115.9 91.9 73.8 108.4 78.6 90.7
74.5 106.1 79.2 99.9 74.5 128.5 85.6 138.1 77.9 140.1 99.1 51.2 132.1 92.9 136.2 92.8 78.4 145.3 63.6 112.5 70.9 111.1 55.0 100.4 116.9 89.0 76.8 98.6 81.0 85.9 102.8 91.8 125.8 90.7 90.8 59.5 136.9 102.7 84.5 124.4 92.3 98.2
89.2 102.8 86.4 98.4 68.1 128.3 90.5 120.8 86.7 113.1 103.7 64.8 109.1 96.9 124.9 109.2 77.7 129.8 78.4 109.1 75.5 107.5 73.2 98.6 119.9 84.4 90.4 97.3 77.8 90.2 103.6 91.8 120.5 88.2 95.2 61.2 108.2 104.4 91.1 108.7 94.2 88.9
77.2 90.0 76.0 87.7 65.1 110.6 79.7 108.5 74.6 100.1 89.2 59.2 100.3 83.4 112.9 88.8 69.5 114.3 69.2 95.1 67.9 93.7 63.9 87.1 101.4 80.0 77.6 86.9 71~5 82,1 92,0 82.8 106.6 81.6 84.5 60.3 100.3 90.2 79.9 99.9 82.7 81.1
305
EVAPOTRANSPIRATION IN THE OKEFENOKEE SWAMP WATERSHED
TABLE 4 (continued)
OBS Period 476 483 490 500 514 526 535 545 553 559 567 576 585 593
N
P
Ro
AET
6/76- 4/77 11 118.6 45.6 73.1 5/77- 8/77 4 126.4 4.4 122.1 9/77- 6/78 10 99.3 28.1 71.3 7/78- 4/79 10 85.8 3.7 8 2 . 1 5/79- 9/80 17 120.9 27.7 93.2 10/80- 4/81 7 75.5 11.0 64.5 5/81- 3/82 11 96.5 3.6 92.9 4 / 8 2 - 1 / 8 3 10 l l l . l 8.8 102.3 2/83- 8/83 7 142.8 48.5 94.3 9/83-12/83 4 104.9 8.5 96.4 1/84-11/84 11 120.4 47.7 72.7 12/84- 7/85 8 81.7 4.4 77.3 8/85-5•86 10 102.7 38.5 64.2 6/86-11/86 6 125.5 3.6 121.9
THORN
PAN71
HPAN
HBIOT
BLANEY
74.3 151.3 66.1 75.0 102.2 37.8 85.4 94.8 102.0 59.8 87.0 80.0 71.5 133.1
83.6 138.5 77.9 85.5 97.8 67.7 87.3 87.6 108.3 66.4 95.8 94.3 88.6 108.0
87.9 137.7 77.7 87.7 104.3 69.0 90.0 100.2 112.1 68.7 99.5 100.7 91.5 108.5
85.7 127.0 82.9 89.7 103.8 67.5 95.0 101.1 102.2 84.2 96.4 91.6 91.2 122.5
80.0 112.9 76.8 80.0 92.0 65.0 84.6 89.1 94.0 72.7 86.3 84.6 79.5 101.3
OBS is number of months from January 1937 to the midpoint of a subperiod, Period is the starting and ending months of a subperiod, N is the length of a subperiod (months), P is the watershed precipitation (mm), Ro is the output runoff(mm), AET is the actual evapotranspiration by P - Ro (mm), T H O R N is Thornthwaite PET (mm), PAN71 is pan evaporation at Tifton multiplied by 0.71 (mm), HPAN is Holdridge PET proportioned by pan evaporation (mm), HBIOT is Holdridge PET proportioned by biotemperature (mm), BLANEY is BlaneyCriddle PET with K = 1.50 (ram). TABLE 5 General characteristics of Okefenokee watershed water budget components, 1937-1986 Component
P R0 AET Pan71 Thornthwaite Holdridge Pan BlOT Blaney
Mean (ram)
Standard deviation (ram)
Coefficient of variation (%)
/P
Ratio
Ratio AET/
108.2 22.2 86.0 86.7 86.6
21.8 16.9 21.0 20.3 31.7
20.2 76.4 24.4 23.4 36.7
0.21 0.79 0.80 0.80
0.99 0.99
97.0 96.4 85.8
22.6 16.3 13.5
23.3 16.9 15.7
0.90 0.89 0.79
0.89 0.89 1.00
/P is the ratio to precipitation, A E T / i s the ratio of AET to the various PET estimates, BIOT is biotemperature.
306
Z.-Y. YIN A N D G.A, BROOK
TABLE 6 Regression relationships between AET estimated by water balance and PET estimated by the pan evaporation, Thornthwaite, Holdridge, and Blaney-Criddle methods. Dependent variable: AET (mm) PET (mm) Pan71 Thornthwaite Holdridge Pan BIOT Blaney-Criddle
Constant
Coefficient
R2
r.m.s.e.
17.509 35.597
0.795 0.586
0.628 0.817
14.1 16.0
16.818 - 20.470 - 28.416
0.714 1.108 1.336
0.638 0.768 0.781
18.5 15.0 11.3
r.m.s.e, is root mean square error, BIOT is biotemperature.
higher than AET determined by the water balance approach. Also it was about 79% of pan evaporation (1463 mm), higher than estimates in previous studies of the area (70-75%). This percentage was also at the higher end of the range for lake evaporation, often varying between 60% and 80% of pan evaporation. PET estimates were plotted against AET (Fig. 3). Linear regression analysis was used to establish relationships between PET estimates and AET (Table 6). All PET estimates correlated well with AET with R 2 values varying from 0.628 to 0.817. Thornthwaite PET had the highest R 2 value (0.817), followed by Blaney-Criddle PET (0.781), and Holdridge PET partitioned by biotemperature (0.768). Pan evaporation and Holdridge PET partitioned by pan evaporation had lower R 2 values. However, when differences between AET and the PET estimates were analyzed, Blaney-Criddle PET rendered the lowest root mean square error (r.m.s.e.) value, indicating an overall higher accuracy than the other methods. The Holdridge PET partitioned by pan evaporation resulted in the highest r.s.m.e, value, followed by Thornthwaite PET, Holdridge PET partitioned by biotemperature, and pan evaporation. In Fig. 4, it is clear that temporal variations in all PET estimates closely parallel variations in AET. MODIFIED T H O R N T H W A I T E PET ESTIMATES
Thornthwaite PET has been criticized as greatly underestimating evapotranspiration in semiarid regions (Dagg and Blackie, 1970). It may also overestimate evapotranspiration in winter and underestimate it in summer (Pelton et al., 1960). In humid regions, Thornthwaite PET appears to
EVAPOTRANSPIRATION 1N THE OKEFENOKEE SWAMP WATERSHED
307
160 -
i~o
2
PAN
THORNTHWAITE
150 -
EVAPORATION
+
PET
140
PAN*O 71
+
,
+
130
130 1
120
÷
~llO
++
I10 ÷+
100
90
+
8O
8o
÷ + ** +
70
+ + ++
+,
+ + * ~++ ~++ +
70
,
++ + ÷ +++
÷
6O 5O
40506030 I i
++
40
+*
30
+
+ 20
40
60
80
100
120
140
160
20
40
.
J
60
80
100 AET (mm)
AET (mm)
160
160 -
]50
150
140
140
130
130
120
90 ~0
%÷ J +
160
"
!
140
160
PET
PARTITIONED BY BID
T + ÷++ ++*+ % ~+ *, ++
110
I00 [5 c_
140
120
+
I10 E --
HOLDRIDGE
120
+
-~
ioo
E
9O
a.
80
70
7o
60
6O
t +
÷,
5o~ HOLDRIDGE
PET
40 ~
PARTITIONED BY PAN EP
20~ 20
,
, 40
~
, 60
,
~ 80
. . . . . 100
30,
, , 140 160
120
AET (mm)
i 20
40
60
80
100
120
AET (mm)
]
]60
BLANEY-
CRIDDLE
140 i
PET
K=150
120
+
d
+÷ ~ "+÷
+
+
20
i 20
i 40
i
i 60
r
i 80
r
i I00
i
i 120
i
i 140
, 160
AET (mm)
Fig. 3. Relationships between AET estimated by water balance and PET estimated by pan evaporation, Thornthwaite, Holdridge, and Blaney-Criddle methods, 1937 1986.
308
Z.-Y. Y I N A N D G . A . B R O O K
PAN EVPORATION
THORNTHWAITEPET
PAN*O 71 160 150 140 130 "~ 120 110
~ ,~
--
AET
*
160 150 140 130 120 110
PET
*i
--
90
908070605040 3020 1930
80 ?O
50
70
70
50
HOLDRIDGE PET
FtOLDRIDGE PET
PARTITIONED BY PAN EP
pARTITIONED BY BlOaT
100 T 150 ] 140 130 j 120 J
--
?
16o Y AET
150 ~
~ PET
70 60 59
?° t
~
PET
7
80 i !
It' 50
1930
90
70
I'
^
4o 30 G 20 ~ 1930
I , 70
50
, 90
YFAR
YEAR BLANEY CRIDDLE PET K = 1.50 AET
~
PET
1O0
•
90 80
~
AET
9o~
ao]
160 150 140 130 ~" 120 £ 110
--
140
99 ~
60 5O 40 30 ~
90
yEAR
YEAR
~
~ PET ~
100
lO0
50. 40 30 2( 1930
~
AET
i
A
70
60 5(1 4O 30 1930
50
70
90
YEAR
Fig. 4. Temporal changes in AET estimated by water balance and PET estimated by pan evaporation, Thornthwaite, Holdridge, and Blaney-Criddle methods, 1937-1986.
overestimate evapotranspiration in summer and underestimate it in winter, although annual values are close to PET estimated by other more sophisticated methods, such as that of Penman (Shih et al., 1983). As Fig. 4 shows, for the Okefenokee Swamp watershed Thornthwaite PET was often higher than the AET when AET was high, and lower than AET when it was low, implying overestimation in summer and underestimation in winter. These seasonal
EVAPOTRANSPIRATION 1N THE OKEFENOKEE SWAMP WATERSHED
309
errors increased variations in Thornthwaite PET relative to AET and caused a relatively high r.m.s.e, value. To reduce seasonal errors in Thornthwaite PET, annual Thornthwaite PET was partitioned into monthly values using the seasonality of pan evaporation and biotemperature according to the following relationships: PETi =
A N N P E T x PANi/ANNPAN
PETi -- A N N P E T x BIOTi/(EBIOTi) where PET i is monthly Thornthwaite PET in month i(mm), ANNPET is annual Thornthwaite PET (mm), PANi is pan evaporation at Tifton in month i(mm), A N N P A N is annual pan evaporation at Tifton(mm), BIOTi is monthly biotemperature in month i(°C), and Y~BIOT~ is the sum of 12 monthly biotemperatures (°C). The modified Thornthwaite PET estimates had almost the same long-term means as the original Thornthwaite values (Table 7) and also paralleled the temporal variations in AET. However, the range of values was reduced (Fig. 5). At times when the original Thornthwaite method overestimated PET at high AET values and underestimated PET at low AET values, the modified PET estimates were closer to the AET values. Although correlations between AET and the modified Thornthwaite PET estimates were not as good as with the original Thornthwaite PET, largely due to reduced fluctuations in the modified PET data, lower r.m.s.e, values were achieved, especially in the case of the Thornthwaite PET partitioned by biotemperature, suggesting higher accuracy (Table 7). CONCLUSIONS
Steady-state water balance models can be used in studies of temporal variations in watershed hydrology if periods with no or minimal storage change can be identified. In watersheds with large lakes or wetlands, as in the case of the Okefenokee Swamp watershed, water levels can be used as an effective index of watershed storage. The assumption of a steady-state condition greatly simplifies the modeling procedure while the dynamic features of the hydrologic system can still be investigated. This approach widens the scope of the water balance method in watershed hydrologic studies. It also offers a means of evaluating the accuracy of estimates of hydrologic components by other methods. The results of this study suggest that temperature-based methods can give reasonably accurate estimates of PET. The PET estimated by the pan evaporation, Thornthwaite, Holdridge, and Blaney-Criddle methods closely
310
Z-Y.
THORNTHWAITE
YIN AND
G.A.
BROOK
PET
PARTITIONED BY PAN EP 160 150
B -
~
140 130 120 llO
ioo~ 9o
,~
gO 70
~
60 50 4O 30 2D 1930
50
70
90
YEAR •
THORNTHWAITE
--
AET
TItORNTHWAITE
~ THORNTHWAITE PAN
PET
PARTITIONED BY RIO T lBO T 150 140
|
13o 110 ] 100 ]
,,a
80
<
60 50 40J 30 ~ 2O I 1930
-, • 5'0
70
90
YEAR •
THORNTHWAITE
AET
~ THOBNTHWAITE B10T
Fig. 5. Temporal changes in AET estimated by water balance and PET estimated by the modified Thornthwaite PET estimates, 1937-1986.
TABLE 7 Descriptive statistics of modified Thornthwaite PET estimates and regression relationships with AET estimated by water balance, 1937-1986 Modified Thornthwaite
Mean (mm)
Standard deviation (mm)
Coefficient of variation
Ratio
/P
Ratio AET/
Dependent variable: A E T (mm) Constant
Coefficient
R2
r.m.s.e.
17.535 - 18.291
0.792 1.218
0.626 0.746
14.0 11.3
(%) Pan BlOT
86.5 86.0
20.2 14.7
23.3 17.1
0.80 0.79
0.99 1.00
r.m.s.e, is root mean square error, BIOT is biotemperature.
EVAPOTRANSPIRATION IN THE OKEFENOKEE SWAMP WATERSHED
311
paralleled AET estimated by the water balance approach during the study period. Although developed for humid tropical and subtropical regions, the Holdridge method overestimated evapotranspiration in the Okefenokee Swamp watershed. If Holdridge PET estimates are used in a watershed water balance model for this area, runoff would be underestimated. Of the methods examined, Thornthwaite PET had the highest R 2 value of 0.817 when correlated with the AET and a long-term average only 0.8% higher than that of the AET. Although the Thornthwaite method may overestimate PET in winter and underestimate it in summer, seasonal errors can be reduced by partitioning annual PET into monthly values according to monthly variations in pan evaporation or temperature. The Blaney-Criddle method was originally designed for irrigated crops under a dry and advective environment. Therefore, it tends to overestimate evapotranspiration in humid areas such as the Okefenokee Swamp watershed. In this study, a crop coefficient of 1.50 rendered good PET estimates for the Okefenokee Swamp watershed with the lowest error among the methods examined. Results from this study indicate that the Blaney-Criddle method can be used in humid regions if crop coefficients are determined for this environment. Pan evaporation had the lowest R 2 value when correlated with AET, but its error was relatively low. A pan coefficient of 0.71 was estimated for the Okefenokee area. Tifton, where pan evaporation is measured, is 120 km from the study area. Therefore, it may not represent actual conditions in the Okefenokee Swamp watershed. This may explain the wide scatter of points in the plot between AET and pan evaporation, and the low R 2 value between these two variables. As pan evaporation is not measured at all weather stations, data availability will restrict the application of pan evaporation in local studies.
REFERENCES Blaney, H.F. and Criddle, W.D., 1950. Determining Water Requirements in Irrigated Area from Climatological Irrigation Data. US Department of Agriculture, Soil Conservation Service Tech. Pap. No. 96, 48 pp. Blood, E.R., 1982. Surface Water Hydrology and Biogeochemistry of the Okefenokee Swamp, Watershed. Okefenokee Ecosystem Investigations, Department of Zoology and Institute of Ecology, University of Georgia, Athens, Tech. Rep. No. 7, 194 pp. Dagg, M. and Blackie, J.R., 1970. Estimates of evaporation in East Africa in relation to climatological classification. Geogr. J., 136: 227-234. Dunne, T. and Leopold, L. B., 1978. Water in Environmental Planning. W.H. Freeman and Co., New York, 818 pp. Holdridge, L.R., 1962. The determination of atmospheric water movements. Ecology, 43: 1-9.
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Hyatt, R.A., 1984. Hydrology and Geochemistry of the Okefenokee Swamp Basin. Okefenokee Ecosystem Investigations. Department of Zoology and Institute of Ecology, University of Georgia, Athens, Technical Rep. No. 17, 361 pp. National Oceanic and Atmospheric Administration (NOAA), 1937-1986. Climatological Data for Georgia, Vols. 41-90 (including publications of the same title published by the US Weather Bureau), Ashville, NC. Pelton, W.L., King, K.M. and Tanner, C.B., 1960. An evaluation of the Thornthwaite method for determining potential evapotranspiration. Agron. J., 52: 387-395. Rosenberg, N.J., Blad, B.L. and Verma, S.B., 1983. Microclimate: The Biological Environment. Wiley, New York, 495 pp. Rykiel, Jr., E.J., 1977. The Okefenokee watershed: water balance and nutrient budgets. Ph.D. Dissertation, University of Georgia, Athens, 246 pp. Saxton, K.E. and McGuinness, J.L., 1982. Evapotranspiration. In: C.T. Haan, H.P. Johnson and D.L. Brakensiek (Eds.), Hydrologic Modeling of Small Watersheds. ASAE, St. Joseph, Michigan, pp. 229-273. Shih, S.F., Allen, L.H., Hammond, L.C., Jones, J.W., Rogers, J.S. and Smajstrla, A.G., 1983. Basinwide water requirement estimation in southern Florida. Trans. ASAE, 26: 760-766. Soil Conservation Service, 1970. Irrigation Water Requirements. US Department of Agriculture, Technical Release No. 21. Sun, C.-H., 1986. COASTAL--A Distributed Hydrologic Simulation Model for Lower Coastal Plain Watersheds in Georgia. Okefenokee Ecosystem Investigations. Department of Zoology and Institute of Ecology, University of Georgia, Athens, Tech. Rep. No. 19, 217 pp. Thornthwaite, C.W., 1948. An approach toward a rational classification of climate. Geogr. Rev., 38: 55-94. Yu, K.B., 1986. The Hydrology of the Okefenokee Swamp Watershed with Emphasis on Groundwater Flow. Okefenokee Ecosystem Investigations. Department of Zoology and Institute of Ecology, University of Georgia, Athens, Tech. Rep. No. 20, 226 pp.
293
Elsevier Science Publishers B.V., A m s t e r d a m
[11
Evapotranspiration in the Okefenokee Swamp watershed: a comparison of temperature-based and water balance methods Z h i - Y o n g Yin a a n d G e o r g e A. B r o o k b
"Department of Geography, Georgia State University, Atlanta, GA 30303, USA bDepartment of Geography, University of Georgia, Athens, GA 30602, USA (Received 30 April 1991; accepted 30 May 1991)
ABSTRACT Yin, Z.-Y. and Brook, G.A., 1992. Evapotranspiration in the Okefenokee Swamp watershed: a comparison of temperature-based and water balance methods. J. Hydrol., 131: 293-312. In the Okefenokee Swamp, actual evapotranspiration (AET) should approximate potential evapotranspiration (PET) as there is rarely a moisture deficit. Even during droughts, a high evapotranspiration rate is maintained owing to a large area of wetlands and a shallow groundwater table in the watershed. Therefore, if AET can be estimated in the Okefenokee Swamp watershed, it can be used to evaluate the accuracy of PET estimates for the region. In this study, temperature-based PET estimates were compared with AET obtained by the water balance method for the Okefenokee Swamp watershed. Swamp water level data were used to identify subperiods with identical storage at the beginning and end of the period, so that a steady-state water balance model could be used to estimate AET as the difference between precipitation and outflow runoff. When the PET estimates were regressed upon AET, Thornthwaite PET had the highest R2 value (0.817), followed by Blaney-Criddle PET (0.781), and Holdridge PET proportioned by biotemperature (0.768). The Thornthwaite method also rendered a long-term average very close to that of AET. Seasonal errors in Thornthwaite PET were reduced by using pan evaporation and temperature data to partition annual values into monthly values. Holdridge PET overestimated evapotranspiration from the Okefenokee Swamp watershed. Using standard crop coefficients, the Blaney-Criddle method would have overestimated evapotranspiration in the humid Okefenokee Swamp watershed. However, by substituting a very low crop coefficient (K = 1.5), the Blaney-Criddle method gave results for the Okefenokee region similar to those obtained by the Thornthwaite method with the lowest error among all the methods examined. Pan evaporation correlated well with AET (R 2 = 0.628) once an appropriate pan coefficient (0.71) had been determined.
INTRODUCTION
Evapotranspiration can be estimated by a variety of methods, such as water balance, mass-transfer, energy balance, the Penman-Monteith combined method, and eddy correlation (Rosenberg et al., 1983). However, most of these methods have limitations. For example, because watershed storage is
0022-1694/92/$05.00
© 1992 - - Elsevier Science Publishers B.V. All rights reserved
294
Z.-Y. Y1N AND G.A. BROOK
difficult to estimate, the water balance method is often based on the assumption of no storage change during the period under investigation. The Penman-Monteith method requires knowledge of vegetation behavior under different meteorologic conditions. Solar radiation and humidity data are also needed and these are not always available. Energy balance and eddy correlation methods require sophisticated and expensive instruments. With the exception of the water balance approach, the above methods are relatively difficult to adapt to watershed studies because they are microscale and short time span oriented. The water balance method is not accurate unless multiyear periods are considered. Otherwise, significant storage changes may introduce sizeable errors. Therefore, the dynamic characteristics of the hydrologic regime are often ignored by the water balance approach. To avoid the above difficulties, a modeling approach is widely used in watershed hydrology studies. Actual evapotranspiration (AET) in a watershed is estimated as potential evapotranspiration (PET) multiplied by a coefficient which is determined by antecedent soil moisture conditions (Saxton and McGuinness, 1982). When there is sufficient moisture for vegetation water use, AET equals PET. PET is often estimated using readily available climatological data, such as air temperature and pan evaporation. As PET determines the maximum possible value of AET, it is a very important parameter in watershed modeling. However, it is difficult to verify PET estimates owing to the hypothetical nature of PET (Thornthwaite, 1948). The hydrologic characteristics of the Okefenokee Swamp watershed provide a way to evaluate PET estimates. The Okefenokee Swamp occupies more than 40% of the watershed area. The uplands are characterized by shallow groundwater tables. There are numerous small depressions filled with water scattered over the uplands. Only rarely does moisture stress affect evapotranspiration in this region. Even during droughts, a high evapotranspiration rate in the watershed is maintained because of the swamp, the numerous ponds and shallow groundwater reservoir in the uplands. The purpose of this study, therefore, is to compare temperature-based PET estimates with results from a steady-state water balance model for the Okefenokee watershed. The Thornthwaite (1948), Holdridge (1962), Blaney and Criddle (1950), the pan evaporation methods for estimating PET will be assessed. STUDY AREA AND DATA The Okefenokee Swamp watershed, with an area of 3925 km 2, is located on the lower Atlantic Coastal Plain of southeastern Georgia and northeastern Florida (Fig. 1). The Okefenokee Swamp is one of the largest wetland
EVAPOTRANSPIRATION
1N THE
OKEFENOKEE
SWAMP
295
WATERSHED
Tifton
Patterson Pearson Waycross Nahunta
Watershe Boundar
• Valdos~
Folkston 3SW 'otks/an 9 s w . . . . '~
.....
Hillard
. . . . . . . . . .
r
0
10
20
30
40
I
I
I
I
i
50 KM I
J
• Glen St. Mary • Lake City
ic n
MapLocation ~
Legend: • Weather Station • Discharge Gage
•
Water Level Gage
•
Gainesville
Fig. 1. Weather stations and stream discharge and water level gauges in the Okefenokee Swamp watershed and adjacent areas.
complexes in the United States and a National Wildlife Refuge. The northwest portion of the watershed is composed of the Terrace Uplands which are dissected marine terraces. Trail Ridge, a narrow ridge-like feature, forms the eastern boundary of the swamp. Three streams, the Suwannee River, the
296
Z.-Y. YIN AND G.A. BROOK
St. Mary's River North Prong, and Cypress Creek drain the swamp. The largest of the three is the Suwanee River, which drains the entire Terrace Uplands and most of the Okefenokee Swamp area. Cypress Creek joins the Suwannee River south of the watershed. Mean monthly temperature data were required to calculate monthly Thornthwaite, Holdridge, and Blaney-Criddle PET values. Monthly pan evaporation data were used as an alternative approach to estimate PET. Monthly precipitation and surface runoff were needed in water balance calculations and monthly water level data for the Okefenokee Swamp as indicators of watershed storage. The study period was from 1937 to 1986. Climatic data were obtained from 'Climatological Data for Georgia' (National Oceanic and Atmospheric Administration (NOAA), 1937-1986). Stream discharge data were provided by the United States Geological Survey, and the water level data by the Okefenokee National Wildlife Refuge. Regional average temperatures for the Okefenokee watershed were calculated using data for six weather stations in the area, Fargo, Folkston 9SW (Camp Cornelia), Homerville, Nahunta, Valdosta, and Waycross (Fig. 1). Simple arithmetic averages of temperatures at these stations were used as regional estimates. The longest pan evaporation record in the area is for Tifton, Georgia, about 120 km to the northwest of the Okefenokee Swamp. The data go back to April 1937, but there are many missing values. The only other station with pan evaporation data in Georgia relatively close to the study area is Savannah, about 160km to the northeast of the Okefenokee Swamp. The record for Savannah is shorter than that for Tifton and there are also many missing values. As most of the missing values for Tifton and Savannah are in the winter months, probably due to freezing of the water in the pans, the data for Savannah could not be used to estimate missing values in the Tifton record. Missing values were, therefore, determined using regression relationships between monthly pan evaporation at Tifton and pan evaporation at Lake City and Gainesville in Florida. Three situations were considered: (1) data were available for both Lake City and Gainesville; (2) data were available for only one of the two Florida stations; (3) no data were available for either station. Under (1) and (2), the missing values were determined using regression relationships shown in Table 1, which were developed with data for the period 1965-1986 when all three stations were in operation. Relationships between pan evaporation at these three stations were very good. When data for only one of the two Florida stations were used, the explained variance in pan evaporation at Tifton was about 88%. When data for both stations were available, the explained variance in pan evaporation at Tifton increased to 91%. Case (3) mostly occurred before the two Florida stations began to monitor pan evaporation. Under this situation, missing values of monthly pan
EVAPOTRANSPIRATIONIN THE OKEFENOKEESWAMPWAIERSHED
297
TABLE 1 Regression relationships to predict pan evaporation at Tifton from pan evaporation at other stations, 1965-1986. Dependent variable: pan evaporation at Tifton Variable
Coefficient
R2
Constant Gainesville Lake City
- 19.278 0.506 0.530
0.911
Constant Gainesville
- 12.850 1.017
0.883
Constant Lake City
- 15.882 0.997
0.885
evaporation at Tifton were estimated by a regression relationship between pan evaporation and maximum monthly temperature in the Okefenokee area (Table 2). Data from 1937 to 1986 were used to develop this relationship. The explained variance in pan evaporation at Tifton by this model was not as high as by the relationships between pan evaporation at the three stations. However, the reduced accuracy of the estimated pan evaporation values is unlikely to affect the study of long-term temporal variations because only a few missing values were determined in this way. There are marked spatial variations in precipitation in southeastern Georgia and northeastern Florida particularly during the summer months when isolated thunderstorms are the major type of rainfall. Therefore, data for 12 weather stations were used in calculating regional precipitation: Fargo, Folkston 3SW, Folkston 9SW, Glen St. Mary, Hillard, Homerville, Jasper, Nahunta, Patterson, Pearson, Valdosta, and Waycross (Fig. 1). As the terrain of the study area is flat without greater topographic relief, a simple arithmetic mean of station values was used as an estimate of regional precipitation. There are United States Geological Survey stream gaging stations on the Suwannee River at Fargo and on the St. Mary's River at Moniac and TABLE 2 Regression relationships to predict pan evaporation at Tifton from maximum monthly temperature in the Okefenokee Swamp area, 1937-1986. Dependent variable: In (PANEP) Variable
Coefficient
R2
Constant TMAX
2.83961 0.07011
0.768
298
Z.-Y. YIN AND G.A. BROOK
Macclenny. Cypress Creek, which joins the Suwannee River downstream of Fargo, is not gauged. To obtain total watershed runoff Cypress Creek discharges were estimated using instantaneous discharges of this stream measured by Hyatt from February 1981 to July 1982 (Hyatt, 1984). The monthly average discharge of Cypress Creek was then determined using the multiple regression relationship: CYP
=
0.101 + 0.058 F A R + 0.064 MAC,
R 2 = 0.807,
where CYP is the discharge of Cypress Creek, F A R is the discharge of the Suwannee River at Fargo, and MAC is the discharge of the St. Mary's River at Macclenny. The discharge at Moniac has been monitored continuously from 1950. The discharge before this period was estimated using the longer record for Macclenny by the regression model: MON
-- 0.0629 + 0.217 MAC,
R 2 = 0.861,
where M O N is the discharge at Moniac and MAC is the discharge at Macclenny. This model was developed with data for the periods 19281935 (discontinuous record) and 1950-1959. Complete monthly discharge records from 1937-1986 were then obtained for the St. Mary's River at Moniac and Cypress Creek using the above regression models. Monthly average discharge from the Okefenokee Swamp watershed via the three streams was converted to monthly surface runoff in millimeters from the watershed. The Okefenokee National Wildlife Refuge monitors water levels in the Okefenokee Swamp at several locations. A fairly complete record is available for the Suwannee Canal Recreation Area (SCRA) from 1950 to 1986 (Fig. 1). A very good relationship exists between the swamp water level, discharge of the Suwannee River at Fargo, and precipitation. This allowed the water level record at the SCRA to be extended back to 1937 using the model: WL
=
e 3503671Q0"002082PPI0"018863,
R: = 0.931,
where W L is monthly mean swamp water level at the SCRA, Q is monthly mean discharge of the Suwannee River at Fargo, and PPI is the previous precipitation index, a weighted 11 month running mean of precipitation. The PPI is calculated using the following equation: PPI = (1.43 x P, + 1.71 x P, I + 1.65 x P, ~_ + 1.31 x P, 3 + 1.37 x Pr-4 + 1.07 x P~ 5 + 1.49 × Pt-6 + 1.39 x P, 7 + 1.28 x P, s + 1.20 x Pt 9 + 0.96 x P, ~0)/11/1.35
EVAPOTRANSP1RATION IN THE OKEFENOKEE SWAMP WATERSHED
299
where P, is precipitation in the current month, and P, t to P,_ ~0 are precipitation values for the previous 1-10 months. The weights are actually regression coefficients from a multiple regression of precipitation with swamp water level; they averaged 1.35. PET USING TEMPERATURE-BASED
METHODS
Thornthwaite first defined the concept of potential evapotranspiration in 1948 for climatic classification (Thornthwaite, 1948). It has been widely used in watershed studies and modeling since the 1950s. Mean monthly temperature is used to calculate Thornthwaite PET (cm): PET
=
1.6 x L x (n/30) x (10 x T / I ) ~
where: a = 6.75 x 10 -7 × 1 3 - 7.71 X 10 -5 X 1 2 + 1.792 X 10 -2 X I + 0.49239; I is the annual sum of i; i -- (T/5)~514; L is the monthly mean day-length at a given latitude in units of 12 h; n is the number of days in the month; T is the monthly mean temperature. The Holdridge method calculates annual PET as the mean annual 'biotemperature' multiplied by 58.93mm°C -1. Monthly biotemperature is the average monthly temperature with any negative values converted to 0°C. As Holdridge (1962) dealt only with annual PET, in this study annual Holdridge PET was partitioned to monthly values in two ways: (1) using monthly pan evaporation where PET i = A N N P E T x P A N i / A N N P A N ; (2) using monthly biotemperature where PETi = A N N P E T x BIOTi/(E BIOT/). In these equations, PET i is monthly Holdridge PET in month i (mm), A N N P E T is annual Holdridge PET (mm), PANi is pan evaporation at Tifton in month i(mm), A N N P A N is annual pan evaporation at Tifton(mm), BlOTs is monthly biotemperature in month i(°C), and E BIOT/ is the sum of 12 monthly biotemperatures (°C). The Blaney-Criddle method was designed for irrigated crops in the western United States (Blaney and Criddle, 1950). As irrigation eliminates soil moisture stress, results from the Blaney-Criddle equation can be regarded as PET. This method has been widely used for agriculture purposes (Soil Conservation Service, 1970; Dunne and Leopold, 1978). In the Blaney-Criddle equation: PET
=
K x F
F =
annual sum of (1.8 x T +
32) x d
where K is the crop coefficient depending on crop type, T is monthly mean temperature, and d is the fraction of monthly daylight hours to the annual
300
Z.-Y. YIN AND G.A. BROOK
total. The Blaney-Criddle method is similar to the Thornthwaite method, but the published crop coefficients were determined for western United States locations. As this method was originally developed for dry climates where strong advection is present, it was expected that the published K values, varying from 1.5 to 2.8, would result in the overestimation of AET in the Okefenokee area for specified crops or vegetation types. Therefore, F was calculated first. The value of K was then determined using precipitation and runoff data: K
=
(P -
R)/F
where P and R are long-term averages of precipitation and runoff. The difference between precipitation and runoff was treated as an approximation of evapotranspiration. In this way, K was calculated as 1.50, a value at the bottom of the range for crop coefficients (Dunne and Leopold, 1978). Temporal variations in Blaney-Criddle PET rather than absolute values were the focus of this study. Pan evaporation is often used as an index of evapotranspiration. In theory it should be a better estimate than those provided by temperature-based methods because it includes the effects of solar radiation, wind, and atmospheric demand. Lake evaporation can be estimated as pan evaporation multiplied by a constant from 0.6 to 0.8, the pan coefficient, and used as an estimate of PET. The pan coefficient is higher for humid areas and lower for arid areas. In this study, the pan coefficient (C) was estimated to be 0.71 by the equation: C =
(P-
R)/PAN
where PAN, P and R were long-term monthly averages of pan evaporation, precipitation, and runoff. EVAPOTRANSPIRATION ESTIMATED BY A WATERSHED WATER BALANCE APPROACH The s t e a d y - s t a t e watershed m o d e l
A dynamic watershed water balance model can be presented as P + RI + GI =
AET + Ro + Go + dS
where P is precipitation, AET is actual evapotranspiration, RI and Ro are surface inflow and outflow runoff, G~ and Go are groundwater inflow and outflow, and dS is the change in storage for a stated period. Previous studies have shown that groundwater discharge from the swamp varies from 0 to 6%
301
E V A P O T R A N S P I R A T I O N IN T H E O K E F E N O K E E SWAMP W A T E R S H E D
of the total water loss (Rykiel, 1977; Blood, 1982; Hyatt, 1984). A recent study, using United States Geological Survey groundwater simulation models, suggests that groundwater discharge is only 1.3% of the total water loss (Yu, 1986). Therefore, groundwater discharge from the swamp, being an extremely minor component of the water budget, was not considered in this study. It was also assumed that there were no groundwater gains or losses across the surface boundaries of the watershed. In this way, precipitation became the only water input to the watershed. Changes in the water level of the Okefenokee Swamp indicate changes in swamp water storage. In this study, swamp water levels were also shown to be closely associated with groundwater levels in the uplands in the Okefenokee Swamp watershed. Hyatt (1984) installed 28 shallow wells in the uplands and monitored groundwater levels in these wells during an 18 month period in 1981-1982 (Fig. 2). Groundwater levels in these wells correlated well with water levels at the SCRA (Table 3). Most correlation coefficients were higher than 0.6 and significant at the 0.01 confidence level. At only two locations (wells Nos. 55 and 67), were correlation coefficients significant at the 0.05 confidence level. This indicated a strong spatial correlation between swamp water and upland groundwater levels. Considering that most of Hyatt's wells were located in the Terrace Uplands, northwest of the Okefenokee Swamp, while the swamp water level TABLE 3 Correlations between swamp water level at the SCRA and groundwater levels in the uplands of the Okefenokee Swamp watershed, February 1981 to July 1982 (well data from Hyatt, 1984) Well no.
r
Significancea
Well no.
r
Significancea
40 42 43 44 45 47 48 49 50 51 52 53 54 55
0.693 0.841 0.928 0.699 0.672 0.849 0.872 0.727 0.722 0.717 0.638 0.685 0.518 0.379
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.05
56 57 58 59 60 61 62 63 64 65 66 67 68 69
0.909 0.898 0.891 0.881 0.909 0.889 0.795 0.567 0.571 0.869 0.794 0.445 0.643 0.485
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.05 0.01 0.01
a 0.05: at 0.05 confidence level. 0.01: at 0.01 confidence level.
302
z.-Y. YIN AND GA. BROOK
Fig. 2. Locations and numbers of groundwater wells installed in the Okefenokee watershed in 1981 (from Hyatt, 1984).
gauge (SCRA) was at the eastern edge of the watershed, the relationships between swamp water and upland groundwater levels were clearly very significant. The swamp and groundwater level data examined here were daily observations measured on a tri-weekly schedule. Correlations between monthly or annual swamp water and upland groundwater levels should be even better as short-term variations are smoothed. Therefore, monthly swamp water level data should provide a good estimate of storage in the entire Okefenokee Swamp watershed. Using swamp water level as an index of watershed storage, it was possible to define periods with minimal storage change, characterized by the same beginning and end water levels. Thus, the assumption of a steady-state watershed model became valid, that is P = AET + R o. An estimate of watershed AET can then be obtained using AET = P - Ro.
EVAPOTRANSPIRATION IN THE OKEFENOKEE SWAMP WATERSHED
303
Water budgets for subperiods The long-term average monthly water level at the SCRA (36.551 m) was used to divide the 1937-1986 period into subperiods with identical storage at the beginning and end of the period. The start (and also, therefore, the end) of a subperiod was defined by a change in the monthly water level from below to above the long-term average (36.551 m) or the reverse. For example, if the water level at the SCRA in January was lower than 36.551 m and the water level in February higher, a new subperiod began in February. Any period shorter than three months was combined with the next subperiod to reduce errors. Fifty-six subperiods were defined in this way. For each subperiod, monthly averages of the following variables were calculated: precipitation, outflow runoff, AET as the difference between precipitation and outflow runoff, pan evaporation multiplied by 0.71, Thornthwaite PET, Holdridge PET partitioned by pan evaporation and by biotemperature, and Blaney-Criddle PET (Table 4). The average subperiod lasted for 10.6 months, so that water balance estimates were close to annual water budgets for the watershed. However, two subperiods lasted for 40 months; in one, water levels remained below the average because of an extended drought, while in the other water levels remained above the average due to unusually wet conditions. COMPARISON OF THE PET ESTIMATES Based on the hydrologic characteristics of the Okefenokee Swamp watershed, it was assumed that AET estimated by the water balance method was very close to PET and could be used to evaluate the accuracy of the PET estimates. General characteristics of the water budget components are listed in Table 5. Mean monthly precipitation was 108.2 mm, equivalent to 1298 mm year ~. Estimated AET was 86.0 mm month ~, equal to 1032mmyear ~ and 79% of precipitation. Output runoff was 22.2 mm month- t or 266 mm year ~, and 21% of precipitation. Thornthwaite PET had a long-term average closest to that of AET. The AET/PET ratio was 99% for Thornthwaite PET and 89% for Holdridge PET. Thornthwaite PET apparently was the most accurate estimate of AET, The Holdridge method overestimated PET in this area. Previous studies have indicated that evapotranspiration in terrestrial environments of the Okefenokee watershed is close to or lower than 1000 rnm year ~, and that the percentage of evapotranspiration to precipitation varies between 70% and 85% (Blood, 1982; Hyatt, 1984; Sun, 1986; Yu, 1986). The Holdridge method rendered annual PET estimates between 1157 and l164mm, equivalent to about 90% of precipitation, and 125-132mm
304
Z.-Y. Y1N AND G.A. BROOK
TABLE 4 Monthly averages of water budget components (mm) for subperiods with identical storage at the beginning and end of the period OBS Period 7 19 31 46 59 64 75 86 92 97 108 118 122 134 146 150 155 159 164 171 178 190 201 223 245 252 259 279 299 308 317 341 364 377 396 406 410 419 435 446 457 468
8/37- 1/38 2/38- 7/39 8/39- 1/40 2/40-11/41 12/41- 4/42 5/42-9/42 10/42- 3/44 4/44-7/44 8/44- 2/45 3/45- 6/45 7/56-11/46 12/46- 2/47 3/47- 7/47 8/47- 4/49 5/49-7/49 8/49-11/49 12/49- 4/50 5/50- 8/50 9/50- 1/51 2/51-10/51 11/51- 4/52 5/52- 9/53 10/53- 2/54 3/54- 6/57 7/57-10/57 11/57- 7/58 8/58- 1/59 2/59-10/61 11/61- 5/62 6/62- 4/63 5/63-12/63 1/64- 4/67 5/67- 9/67 10/67- 7/69 8/69-11/70 12/70-3/71 4/71- 6/71 7/71-10/72 11/72- 2/74 3/74- 7/74 8/74- 1/76 2/76- 5/76
N
P
Ro
AET
THORN
PAN71
HPAN
HBIOT
BLANEY
6 18 6 22 5 5 18 4 7 4 17 3 5 21 3 4 5 4 5 9 6 17 5 40 4 9 6 33 7 11 8 40 5 22 16 4 3 16 16 5 18 4
107.3 102.0 94.1 95.0 128.2 137.8 83.6 138.2 106.9 85.4 134.5 57.4 133.2 141.1 134.6 137.4 59.3 135.0 105.4 101.3 89.0 !18.7 66.1 87.7 138.2 116.3 75.1 121.4 81.9 107.9 107.5 127.0 132.6 87.1 119.4 79.7 101.8 118.4 121.5 118.6 109.9 101.0
32.1 7.5 14.9 7.4 66.8 7.3 2.9 28.0 39.4 7.3 48.1 9.8 36.9 63.3 7.5 43.3 7.6 9.1 27.7 9.9 39.0 9.0 38.3 3.8 16.7 30.8 5.7 33.3 16.2 17.2 4.1 47.0 12.5 8.1 37.7 14.2 13.7 34.6 42.3 10.9 30.6 15.8
75.2 94.5 79.2 87.6 61.4 130.5 80.6 110.3 67.5 78.2 86.5 47.6 96.3 77.8 127.1 94.0 51.7 125.9 77.7 91.4 50.1 109.7 27.9 83.8 121.6 85.5 69.4 88.0 65.8 90.7 103.4 80.0 120.1 79.0 81.6 65.5 88.0 83.8 79.2 107.7 79.2 85.2
69.9 95.0 72.0 92.0 32.5 151.2 72.0 136.6 65.2 112.8 96.8 26.5 112.1 81.1 146.6 102.0 40.3 157.3 52.7 109.7 37.4 108.0 36.3 88.7 129.4 72.7 73.0 88.9 50.5 79.4 103.8 79.0 132.8 76.8 86.5 26.2 107.9 97.0 73.3 108.3 80.3 67.8
68.9 95.0 66.3 90.1 66.7 115.4 79.4 120.0 66.6 113.2 77.9 40.2 104.3 75.7 110.2 75.1 65.4 121.8 53.9 101.2 61.7 91.9 46.5 85.1 85.3 74.2 65.0 89.1 79.3 84.7 102.6 84.0 126.7 89.6 82.9 51.1 115.9 91.9 73.8 108.4 78.6 90.7
74.5 106.1 79.2 99.9 74.5 128.5 85.6 138.1 77.9 140.1 99.1 51.2 132.1 92.9 136.2 92.8 78.4 145.3 63.6 112.5 70.9 111.1 55.0 100.4 116.9 89.0 76.8 98.6 81.0 85.9 102.8 91.8 125.8 90.7 90.8 59.5 136.9 102.7 84.5 124.4 92.3 98.2
89.2 102.8 86.4 98.4 68.1 128.3 90.5 120.8 86.7 113.1 103.7 64.8 109.1 96.9 124.9 109.2 77.7 129.8 78.4 109.1 75.5 107.5 73.2 98.6 119.9 84.4 90.4 97.3 77.8 90.2 103.6 91.8 120.5 88.2 95.2 61.2 108.2 104.4 91.1 108.7 94.2 88.9
77.2 90.0 76.0 87.7 65.1 110.6 79.7 108.5 74.6 100.1 89.2 59.2 100.3 83.4 112.9 88.8 69.5 114.3 69.2 95.1 67.9 93.7 63.9 87.1 101.4 80.0 77.6 86.9 71~5 82,1 92,0 82.8 106.6 81.6 84.5 60.3 100.3 90.2 79.9 99.9 82.7 81.1
305
EVAPOTRANSPIRATION IN THE OKEFENOKEE SWAMP WATERSHED
TABLE 4 (continued)
OBS Period 476 483 490 500 514 526 535 545 553 559 567 576 585 593
N
P
Ro
AET
6/76- 4/77 11 118.6 45.6 73.1 5/77- 8/77 4 126.4 4.4 122.1 9/77- 6/78 10 99.3 28.1 71.3 7/78- 4/79 10 85.8 3.7 8 2 . 1 5/79- 9/80 17 120.9 27.7 93.2 10/80- 4/81 7 75.5 11.0 64.5 5/81- 3/82 11 96.5 3.6 92.9 4 / 8 2 - 1 / 8 3 10 l l l . l 8.8 102.3 2/83- 8/83 7 142.8 48.5 94.3 9/83-12/83 4 104.9 8.5 96.4 1/84-11/84 11 120.4 47.7 72.7 12/84- 7/85 8 81.7 4.4 77.3 8/85-5•86 10 102.7 38.5 64.2 6/86-11/86 6 125.5 3.6 121.9
THORN
PAN71
HPAN
HBIOT
BLANEY
74.3 151.3 66.1 75.0 102.2 37.8 85.4 94.8 102.0 59.8 87.0 80.0 71.5 133.1
83.6 138.5 77.9 85.5 97.8 67.7 87.3 87.6 108.3 66.4 95.8 94.3 88.6 108.0
87.9 137.7 77.7 87.7 104.3 69.0 90.0 100.2 112.1 68.7 99.5 100.7 91.5 108.5
85.7 127.0 82.9 89.7 103.8 67.5 95.0 101.1 102.2 84.2 96.4 91.6 91.2 122.5
80.0 112.9 76.8 80.0 92.0 65.0 84.6 89.1 94.0 72.7 86.3 84.6 79.5 101.3
OBS is number of months from January 1937 to the midpoint of a subperiod, Period is the starting and ending months of a subperiod, N is the length of a subperiod (months), P is the watershed precipitation (mm), Ro is the output runoff(mm), AET is the actual evapotranspiration by P - Ro (mm), T H O R N is Thornthwaite PET (mm), PAN71 is pan evaporation at Tifton multiplied by 0.71 (mm), HPAN is Holdridge PET proportioned by pan evaporation (mm), HBIOT is Holdridge PET proportioned by biotemperature (mm), BLANEY is BlaneyCriddle PET with K = 1.50 (ram). TABLE 5 General characteristics of Okefenokee watershed water budget components, 1937-1986 Component
P R0 AET Pan71 Thornthwaite Holdridge Pan BlOT Blaney
Mean (ram)
Standard deviation (ram)
Coefficient of variation (%)
/P
Ratio
Ratio AET/
108.2 22.2 86.0 86.7 86.6
21.8 16.9 21.0 20.3 31.7
20.2 76.4 24.4 23.4 36.7
0.21 0.79 0.80 0.80
0.99 0.99
97.0 96.4 85.8
22.6 16.3 13.5
23.3 16.9 15.7
0.90 0.89 0.79
0.89 0.89 1.00
/P is the ratio to precipitation, A E T / i s the ratio of AET to the various PET estimates, BIOT is biotemperature.
306
Z.-Y. YIN A N D G.A, BROOK
TABLE 6 Regression relationships between AET estimated by water balance and PET estimated by the pan evaporation, Thornthwaite, Holdridge, and Blaney-Criddle methods. Dependent variable: AET (mm) PET (mm) Pan71 Thornthwaite Holdridge Pan BIOT Blaney-Criddle
Constant
Coefficient
R2
r.m.s.e.
17.509 35.597
0.795 0.586
0.628 0.817
14.1 16.0
16.818 - 20.470 - 28.416
0.714 1.108 1.336
0.638 0.768 0.781
18.5 15.0 11.3
r.m.s.e, is root mean square error, BIOT is biotemperature.
higher than AET determined by the water balance approach. Also it was about 79% of pan evaporation (1463 mm), higher than estimates in previous studies of the area (70-75%). This percentage was also at the higher end of the range for lake evaporation, often varying between 60% and 80% of pan evaporation. PET estimates were plotted against AET (Fig. 3). Linear regression analysis was used to establish relationships between PET estimates and AET (Table 6). All PET estimates correlated well with AET with R 2 values varying from 0.628 to 0.817. Thornthwaite PET had the highest R 2 value (0.817), followed by Blaney-Criddle PET (0.781), and Holdridge PET partitioned by biotemperature (0.768). Pan evaporation and Holdridge PET partitioned by pan evaporation had lower R 2 values. However, when differences between AET and the PET estimates were analyzed, Blaney-Criddle PET rendered the lowest root mean square error (r.m.s.e.) value, indicating an overall higher accuracy than the other methods. The Holdridge PET partitioned by pan evaporation resulted in the highest r.s.m.e, value, followed by Thornthwaite PET, Holdridge PET partitioned by biotemperature, and pan evaporation. In Fig. 4, it is clear that temporal variations in all PET estimates closely parallel variations in AET. MODIFIED T H O R N T H W A I T E PET ESTIMATES
Thornthwaite PET has been criticized as greatly underestimating evapotranspiration in semiarid regions (Dagg and Blackie, 1970). It may also overestimate evapotranspiration in winter and underestimate it in summer (Pelton et al., 1960). In humid regions, Thornthwaite PET appears to
EVAPOTRANSPIRATION 1N THE OKEFENOKEE SWAMP WATERSHED
307
160 -
i~o
2
PAN
THORNTHWAITE
150 -
EVAPORATION
+
PET
140
PAN*O 71
+
,
+
130
130 1
120
÷
~llO
++
I10 ÷+
100
90
+
8O
8o
÷ + ** +
70
+ + ++
+,
+ + * ~++ ~++ +
70
,
++ + ÷ +++
÷
6O 5O
40506030 I i
++
40
+*
30
+
+ 20
40
60
80
100
120
140
160
20
40
.
J
60
80
100 AET (mm)
AET (mm)
160
160 -
]50
150
140
140
130
130
120
90 ~0
%÷ J +
160
"
!
140
160
PET
PARTITIONED BY BID
T + ÷++ ++*+ % ~+ *, ++
110
I00 [5 c_
140
120
+
I10 E --
HOLDRIDGE
120
+
-~
ioo
E
9O
a.
80
70
7o
60
6O
t +
÷,
5o~ HOLDRIDGE
PET
40 ~
PARTITIONED BY PAN EP
20~ 20
,
, 40
~
, 60
,
~ 80
. . . . . 100
30,
, , 140 160
120
AET (mm)
i 20
40
60
80
100
120
AET (mm)
]
]60
BLANEY-
CRIDDLE
140 i
PET
K=150
120
+
d
+÷ ~ "+÷
+
+
20
i 20
i 40
i
i 60
r
i 80
r
i I00
i
i 120
i
i 140
, 160
AET (mm)
Fig. 3. Relationships between AET estimated by water balance and PET estimated by pan evaporation, Thornthwaite, Holdridge, and Blaney-Criddle methods, 1937 1986.
308
Z.-Y. Y I N A N D G . A . B R O O K
PAN EVPORATION
THORNTHWAITEPET
PAN*O 71 160 150 140 130 "~ 120 110
~ ,~
--
AET
*
160 150 140 130 120 110
PET
*i
--
90
908070605040 3020 1930
80 ?O
50
70
70
50
HOLDRIDGE PET
FtOLDRIDGE PET
PARTITIONED BY PAN EP
pARTITIONED BY BlOaT
100 T 150 ] 140 130 j 120 J
--
?
16o Y AET
150 ~
~ PET
70 60 59
?° t
~
PET
7
80 i !
It' 50
1930
90
70
I'
^
4o 30 G 20 ~ 1930
I , 70
50
, 90
YFAR
YEAR BLANEY CRIDDLE PET K = 1.50 AET
~
PET
1O0
•
90 80
~
AET
9o~
ao]
160 150 140 130 ~" 120 £ 110
--
140
99 ~
60 5O 40 30 ~
90
yEAR
YEAR
~
~ PET ~
100
lO0
50. 40 30 2( 1930
~
AET
i
A
70
60 5(1 4O 30 1930
50
70
90
YEAR
Fig. 4. Temporal changes in AET estimated by water balance and PET estimated by pan evaporation, Thornthwaite, Holdridge, and Blaney-Criddle methods, 1937-1986.
overestimate evapotranspiration in summer and underestimate it in winter, although annual values are close to PET estimated by other more sophisticated methods, such as that of Penman (Shih et al., 1983). As Fig. 4 shows, for the Okefenokee Swamp watershed Thornthwaite PET was often higher than the AET when AET was high, and lower than AET when it was low, implying overestimation in summer and underestimation in winter. These seasonal
EVAPOTRANSPIRATION 1N THE OKEFENOKEE SWAMP WATERSHED
309
errors increased variations in Thornthwaite PET relative to AET and caused a relatively high r.m.s.e, value. To reduce seasonal errors in Thornthwaite PET, annual Thornthwaite PET was partitioned into monthly values using the seasonality of pan evaporation and biotemperature according to the following relationships: PETi =
A N N P E T x PANi/ANNPAN
PETi -- A N N P E T x BIOTi/(EBIOTi) where PET i is monthly Thornthwaite PET in month i(mm), ANNPET is annual Thornthwaite PET (mm), PANi is pan evaporation at Tifton in month i(mm), A N N P A N is annual pan evaporation at Tifton(mm), BIOTi is monthly biotemperature in month i(°C), and Y~BIOT~ is the sum of 12 monthly biotemperatures (°C). The modified Thornthwaite PET estimates had almost the same long-term means as the original Thornthwaite values (Table 7) and also paralleled the temporal variations in AET. However, the range of values was reduced (Fig. 5). At times when the original Thornthwaite method overestimated PET at high AET values and underestimated PET at low AET values, the modified PET estimates were closer to the AET values. Although correlations between AET and the modified Thornthwaite PET estimates were not as good as with the original Thornthwaite PET, largely due to reduced fluctuations in the modified PET data, lower r.m.s.e, values were achieved, especially in the case of the Thornthwaite PET partitioned by biotemperature, suggesting higher accuracy (Table 7). CONCLUSIONS
Steady-state water balance models can be used in studies of temporal variations in watershed hydrology if periods with no or minimal storage change can be identified. In watersheds with large lakes or wetlands, as in the case of the Okefenokee Swamp watershed, water levels can be used as an effective index of watershed storage. The assumption of a steady-state condition greatly simplifies the modeling procedure while the dynamic features of the hydrologic system can still be investigated. This approach widens the scope of the water balance method in watershed hydrologic studies. It also offers a means of evaluating the accuracy of estimates of hydrologic components by other methods. The results of this study suggest that temperature-based methods can give reasonably accurate estimates of PET. The PET estimated by the pan evaporation, Thornthwaite, Holdridge, and Blaney-Criddle methods closely
310
Z-Y.
THORNTHWAITE
YIN AND
G.A.
BROOK
PET
PARTITIONED BY PAN EP 160 150
B -
~
140 130 120 llO
ioo~ 9o
,~
gO 70
~
60 50 4O 30 2D 1930
50
70
90
YEAR •
THORNTHWAITE
--
AET
TItORNTHWAITE
~ THORNTHWAITE PAN
PET
PARTITIONED BY RIO T lBO T 150 140
|
13o 110 ] 100 ]
,,a
80
<
60 50 40J 30 ~ 2O I 1930
-, • 5'0
70
90
YEAR •
THORNTHWAITE
AET
~ THOBNTHWAITE B10T
Fig. 5. Temporal changes in AET estimated by water balance and PET estimated by the modified Thornthwaite PET estimates, 1937-1986.
TABLE 7 Descriptive statistics of modified Thornthwaite PET estimates and regression relationships with AET estimated by water balance, 1937-1986 Modified Thornthwaite
Mean (mm)
Standard deviation (mm)
Coefficient of variation
Ratio
/P
Ratio AET/
Dependent variable: A E T (mm) Constant
Coefficient
R2
r.m.s.e.
17.535 - 18.291
0.792 1.218
0.626 0.746
14.0 11.3
(%) Pan BlOT
86.5 86.0
20.2 14.7
23.3 17.1
0.80 0.79
0.99 1.00
r.m.s.e, is root mean square error, BIOT is biotemperature.
EVAPOTRANSPIRATION IN THE OKEFENOKEE SWAMP WATERSHED
311
paralleled AET estimated by the water balance approach during the study period. Although developed for humid tropical and subtropical regions, the Holdridge method overestimated evapotranspiration in the Okefenokee Swamp watershed. If Holdridge PET estimates are used in a watershed water balance model for this area, runoff would be underestimated. Of the methods examined, Thornthwaite PET had the highest R 2 value of 0.817 when correlated with the AET and a long-term average only 0.8% higher than that of the AET. Although the Thornthwaite method may overestimate PET in winter and underestimate it in summer, seasonal errors can be reduced by partitioning annual PET into monthly values according to monthly variations in pan evaporation or temperature. The Blaney-Criddle method was originally designed for irrigated crops under a dry and advective environment. Therefore, it tends to overestimate evapotranspiration in humid areas such as the Okefenokee Swamp watershed. In this study, a crop coefficient of 1.50 rendered good PET estimates for the Okefenokee Swamp watershed with the lowest error among the methods examined. Results from this study indicate that the Blaney-Criddle method can be used in humid regions if crop coefficients are determined for this environment. Pan evaporation had the lowest R 2 value when correlated with AET, but its error was relatively low. A pan coefficient of 0.71 was estimated for the Okefenokee area. Tifton, where pan evaporation is measured, is 120 km from the study area. Therefore, it may not represent actual conditions in the Okefenokee Swamp watershed. This may explain the wide scatter of points in the plot between AET and pan evaporation, and the low R 2 value between these two variables. As pan evaporation is not measured at all weather stations, data availability will restrict the application of pan evaporation in local studies.
REFERENCES Blaney, H.F. and Criddle, W.D., 1950. Determining Water Requirements in Irrigated Area from Climatological Irrigation Data. US Department of Agriculture, Soil Conservation Service Tech. Pap. No. 96, 48 pp. Blood, E.R., 1982. Surface Water Hydrology and Biogeochemistry of the Okefenokee Swamp, Watershed. Okefenokee Ecosystem Investigations, Department of Zoology and Institute of Ecology, University of Georgia, Athens, Tech. Rep. No. 7, 194 pp. Dagg, M. and Blackie, J.R., 1970. Estimates of evaporation in East Africa in relation to climatological classification. Geogr. J., 136: 227-234. Dunne, T. and Leopold, L. B., 1978. Water in Environmental Planning. W.H. Freeman and Co., New York, 818 pp. Holdridge, L.R., 1962. The determination of atmospheric water movements. Ecology, 43: 1-9.
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Hyatt, R.A., 1984. Hydrology and Geochemistry of the Okefenokee Swamp Basin. Okefenokee Ecosystem Investigations. Department of Zoology and Institute of Ecology, University of Georgia, Athens, Technical Rep. No. 17, 361 pp. National Oceanic and Atmospheric Administration (NOAA), 1937-1986. Climatological Data for Georgia, Vols. 41-90 (including publications of the same title published by the US Weather Bureau), Ashville, NC. Pelton, W.L., King, K.M. and Tanner, C.B., 1960. An evaluation of the Thornthwaite method for determining potential evapotranspiration. Agron. J., 52: 387-395. Rosenberg, N.J., Blad, B.L. and Verma, S.B., 1983. Microclimate: The Biological Environment. Wiley, New York, 495 pp. Rykiel, Jr., E.J., 1977. The Okefenokee watershed: water balance and nutrient budgets. Ph.D. Dissertation, University of Georgia, Athens, 246 pp. Saxton, K.E. and McGuinness, J.L., 1982. Evapotranspiration. In: C.T. Haan, H.P. Johnson and D.L. Brakensiek (Eds.), Hydrologic Modeling of Small Watersheds. ASAE, St. Joseph, Michigan, pp. 229-273. Shih, S.F., Allen, L.H., Hammond, L.C., Jones, J.W., Rogers, J.S. and Smajstrla, A.G., 1983. Basinwide water requirement estimation in southern Florida. Trans. ASAE, 26: 760-766. Soil Conservation Service, 1970. Irrigation Water Requirements. US Department of Agriculture, Technical Release No. 21. Sun, C.-H., 1986. COASTAL--A Distributed Hydrologic Simulation Model for Lower Coastal Plain Watersheds in Georgia. Okefenokee Ecosystem Investigations. Department of Zoology and Institute of Ecology, University of Georgia, Athens, Tech. Rep. No. 19, 217 pp. Thornthwaite, C.W., 1948. An approach toward a rational classification of climate. Geogr. Rev., 38: 55-94. Yu, K.B., 1986. The Hydrology of the Okefenokee Swamp Watershed with Emphasis on Groundwater Flow. Okefenokee Ecosystem Investigations. Department of Zoology and Institute of Ecology, University of Georgia, Athens, Tech. Rep. No. 20, 226 pp.