**Recent Updates of the Calibration-Free Evapotranspiration Mapping (CREMAP) Method**

Jozsef Szilagyi

[32] Schilling, K. E, & Libra, R. D. (2003). Increased baseflow in Iowa over the second half

[33] Skiles, J. W, & Hanson, J. D. (1994). Responses of arid and semiarid watersheds to in‐ creasing carbon dioxide and climate change as shown by simulation studies. *Clim.*

[34] Spronken-smith, R. A, & Oke, T. R. (1998). The thermal regime of urban parks in two

[35] Stephenson, N. L. (1990). Climatic control of vegetation distribution: the role of the

[36] Swank, W. T, & Douglass, J. E. (1974). Streamflow greatly reduced by converting de‐

[37] Trimble, S. W, Weirich, F, & Hoag, B. L. (1987). Reforestation and the reduction of water yield on the Southern Piedmont since c. 1940. *Water Resour. Res.* , 23, 425-437.

[38] Turner, K. M. (1991). Annual evapotranspiration of native vegetation in a Mediterra‐

[39] US Geological Survey (USGS). (2012a). USGS Real-time data for Missouri: USGS Re‐

[40] US Geological Survey (USGS). (2012b). USGS Land Cover Institute (LCI): US Land

[41] US Water Resources Council. (1978). *The Nation's Water Resources, 1975-2000: second*

[42] Van Bavel, C. H. M. (1961). Lysimetric measurements of evapotranspiration rates in

[43] Vandike, J. E. (1995). Missouri State Water Plan Series, Surface Water Resources of Missouri. *Water Resources Report*, Missouri Department of Natural Resources, , 1(45),

[44] Wahl, K. L, Thomas, W. O, & Hirsch, R. M. (1995). *The stream-gaging program of the US*

[45] Ward, A. D, & Trimble, S. W. (2004). *Environmental hydrology*, 2nd ed. CRC Press, Boca

[46] Wicht, C. L. (1941). Diurnal fluctuation in Jonkershoek streams due to evaporation

*national water assessment.* US Water Resources Council, Washington, DC.

cities with different summer climates*. Int. J. Rem. Sens.* , 19, 3039-3053.

of the 20th century. *J. Am. Water Resour. As.* , 39, 851-860.

ciduous hardwood stands to pine. *Science*. , 185, 857-859.

al-time data for Missouri, http://waterdata.usgs.gov/mo/nwis/rt.

the eastern United States. *Soil Sci. Soc. Am. Proc.* , 25, 138-141.

*Geological Survey*. US Geological Survey Circular 1123, , 22.

and transpiration. *J. S. Aft. For. Assoc*. , 7, 34-49.

nean-type climate. *Water Resour. Bull.* , 27, 1-6.

Cover, http://landcover.usgs.gov/uslandcover.php.

*Change*. , 26, 377-397.

22 Evapotranspiration - An Overview

122.

Raton, Florida, , 475.

water balance. *Am. Nat.* , 135, 649-670.

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/52392

### **1. Introduction**

This study is the revision of an earlier evapotranspiration (ET) estimation technique [1], called Calibration-Free Evapotranspiration Mapping (CREMAP), applied for Nebraska (Fig‐ ure 1). Major differences between the current and previous versions are


In principle, the recent modeling period could have been extended to include 2010 and 2011, however, the multi-institutional research project [2] that provided the monthly incoming global radiation values was terminated in 2010, thus no radiation data are available after June 2010 from that source. Rather than looking for alternative data sources, the original 10 year long modeling period, i.e., 2000-2009, was kept, thus ensuring that the same data types were employed throughout the study.

In the earlier version of the ET maps it was assumed that the ET rates in the winter time are negligible when one is concerned with the mean annual value. In the light of the present version of ET mapping, this assumption was found true only partially: there are regions within Nebraska for which winter ET indeed seems to be negligible (mostly the north-cen‐ tral and north-western parts) in comparison with water-balance data, while in other regions it is not so. These latter regions include parts of Nebraska (mostly the south and south-west portion) with the highest winter-time daily maximum temperatures and/or with most abun‐ dant precipitation (eastern, south-eastern portion of the state). As a result the precipitation (P) recycling ratio (i.e., ET / P) rose from a previously estimated mean annual value of 93% to 95%, leaving an estimated 5% of the precipitation to emerge as runoff (Ro) in the streams.

Naturally, as any estimation method, the current approach is not perfect. In the Pine Ridge Escarpment and in the Niobrara River Breaks regions (Figure 1) the ET estimates (similarly to the previous version of the ET map) had to be corrected via comparison with precipita‐ tion data because otherwise they would overestimate ET rates by about 10-20%. The reason is in the gross violation of the underlying hypotheses of the current ET estimation method in areas of very rough terrain. After the corrections in these distinct geomorphic regions, it is believed that the resulting ET rates are quite reasonable across the whole state. Overall, the method yields a state-representative ET rate value of 549 mm/yr, within 2% of the simplified water balance (P – Ro) derived rate of 538 mm/yr, employing the USGS [3] values of com‐ puted runoff for catchments with level-8 hydrologic unit codes (HUC), and explains 87% of the observed spatial variance of the water balance ET values among the HUC-8 catchments (there are 70 such watersheds within the state) for the same period.

The transformation requires the specification of two anchor points in the Ts versus ET plane (Figure 2). The first anchor point is defined by the spatially averaged daytime surface tem‐ perature, <Ts>, and the corresponding regionally representative ET rate, E, from WREVAP. (The original FORTRAN source code can be downloaded from the personal website of the author: snr.unl.edu/ szilagyi/szilagyi.htm). The second anchor point comes from the surface temperature, Tsw, of a completely wet cell and the corresponding wet-environment evapora‐ tion, Ew, (defined by the Priestley-Taylor [9] equation with a coefficient value of 1.2). The two points identify the linear transformations of the Ts pixel values into ET rates for each month. The resulting line is extended to the right, since in about half the number of the pix‐ els ET is less than the regional mean, E. A monthly time-step is ideal because most of the watershed- or large-scale hydrologic models work at this time-resolution, plus a monthly averaging further reduces any lingering cloud effect in the 8-day composited Ts values. Wet cells within Nebraska were identified over Lake McConaughy and the Lewis and Clark Lake on the Missouri River (Figure 1). An inverse-distance weighting method was subse‐ quently used to calculate the Tsw value to be assigned to a given MODIS cell for the linear

Recent Updates of the Calibration-Free Evapotranspiration Mapping (CREMAP) Method

http://dx.doi.org/10.5772/52392

25

**Figure 2.** Schematics of the linear transformation of the MODIS daytime surface temperature values into ET rates (af‐

The core assumption of CREMAP is that the surface temperature of any MODIS cell is pre‐ dominantly defined by the rate of evapotranspiration due to the large value of the latent heat of vaporization for water and that the energy (Qn) available at the surface for sensible (i.e., heat convection) and latent heat (i.e., evapotranspiration) transfers are roughly even among the cells of a flat-to-rolling terrain. Heat conduction into the soil is typically negligi‐ ble over a 24-hour period, and here considered negligible over the daytime hours as well.

transformation.

ter [1]), applied in CREMAP.

### **2. Description of the current ET estimation method**

An ET estimation method had been proposed by Bouchet [4], employing the complementary relationship (CR) of evaporation which was subsequently formulated for practical regionalscale ET applications by Brutsaert & Stricker [5] and Morton et al. [6]. In this study the WRE‐ VAP program of [6] was applied for the estimation of the regional-scale ET rates at monthly periods. Disaggregation of the regional ET value in space is based on the Moderate Resolu‐ tion Imaging Spectroradiometer (MODIS) data [7] that have a nominal spatial resolution of about 1 km. The disaggregation is achieved by a linear transformation of the 8-day compos‐ ited MODIS daytime surface temperature (Ts) values into actual ET rates on a monthly basis [1, 8] by first aggregating the composited Ts data into monthly mean values. Compositing is used for eliminating cloud effects in the resulting composite data by removing suspicious, low pixel-values in the averaging over each eight-day period. See [7] for more detail of data collection and characteristics.

**Figure 1.** Stream network and selected geomorphic regions of Nebraska. MC: McConaughy Reservoir; LC: Lewis and Clark Reservoir; L: Lincoln; O: Omaha.

The transformation requires the specification of two anchor points in the Ts versus ET plane (Figure 2). The first anchor point is defined by the spatially averaged daytime surface tem‐ perature, <Ts>, and the corresponding regionally representative ET rate, E, from WREVAP. (The original FORTRAN source code can be downloaded from the personal website of the author: snr.unl.edu/ szilagyi/szilagyi.htm). The second anchor point comes from the surface temperature, Tsw, of a completely wet cell and the corresponding wet-environment evapora‐ tion, Ew, (defined by the Priestley-Taylor [9] equation with a coefficient value of 1.2). The two points identify the linear transformations of the Ts pixel values into ET rates for each month. The resulting line is extended to the right, since in about half the number of the pix‐ els ET is less than the regional mean, E. A monthly time-step is ideal because most of the watershed- or large-scale hydrologic models work at this time-resolution, plus a monthly averaging further reduces any lingering cloud effect in the 8-day composited Ts values. Wet cells within Nebraska were identified over Lake McConaughy and the Lewis and Clark Lake on the Missouri River (Figure 1). An inverse-distance weighting method was subse‐ quently used to calculate the Tsw value to be assigned to a given MODIS cell for the linear transformation.

Naturally, as any estimation method, the current approach is not perfect. In the Pine Ridge Escarpment and in the Niobrara River Breaks regions (Figure 1) the ET estimates (similarly to the previous version of the ET map) had to be corrected via comparison with precipita‐ tion data because otherwise they would overestimate ET rates by about 10-20%. The reason is in the gross violation of the underlying hypotheses of the current ET estimation method in areas of very rough terrain. After the corrections in these distinct geomorphic regions, it is believed that the resulting ET rates are quite reasonable across the whole state. Overall, the method yields a state-representative ET rate value of 549 mm/yr, within 2% of the simplified water balance (P – Ro) derived rate of 538 mm/yr, employing the USGS [3] values of com‐ puted runoff for catchments with level-8 hydrologic unit codes (HUC), and explains 87% of the observed spatial variance of the water balance ET values among the HUC-8 catchments

An ET estimation method had been proposed by Bouchet [4], employing the complementary relationship (CR) of evaporation which was subsequently formulated for practical regionalscale ET applications by Brutsaert & Stricker [5] and Morton et al. [6]. In this study the WRE‐ VAP program of [6] was applied for the estimation of the regional-scale ET rates at monthly periods. Disaggregation of the regional ET value in space is based on the Moderate Resolu‐ tion Imaging Spectroradiometer (MODIS) data [7] that have a nominal spatial resolution of about 1 km. The disaggregation is achieved by a linear transformation of the 8-day compos‐ ited MODIS daytime surface temperature (Ts) values into actual ET rates on a monthly basis [1, 8] by first aggregating the composited Ts data into monthly mean values. Compositing is used for eliminating cloud effects in the resulting composite data by removing suspicious, low pixel-values in the averaging over each eight-day period. See [7] for more detail of data

**Figure 1.** Stream network and selected geomorphic regions of Nebraska. MC: McConaughy Reservoir; LC: Lewis and

(there are 70 such watersheds within the state) for the same period.

**2. Description of the current ET estimation method**

collection and characteristics.

24 Evapotranspiration - An Overview

Clark Reservoir; L: Lincoln; O: Omaha.

**Figure 2.** Schematics of the linear transformation of the MODIS daytime surface temperature values into ET rates (af‐ ter [1]), applied in CREMAP.

The core assumption of CREMAP is that the surface temperature of any MODIS cell is pre‐ dominantly defined by the rate of evapotranspiration due to the large value of the latent heat of vaporization for water and that the energy (Qn) available at the surface for sensible (i.e., heat convection) and latent heat (i.e., evapotranspiration) transfers are roughly even among the cells of a flat-to-rolling terrain. Heat conduction into the soil is typically negligi‐ ble over a 24-hour period, and here considered negligible over the daytime hours as well. This last assumption is most likely true for fully vegetated surfaces where soil heat conduc‐ tion is small throughout the day, and is less valid for bare soil and open water surfaces. While a spatially constant Qn term at first seems to be an overly stringent requirement in practical applications due to spatial changes in vegetation cover as well as slope and aspect of the land surface, Qn will change only negligibly in space provided the surface albedo (i.e., the ratio of in- and outgoing short-wave radiation) value also changes negligibly among the pixels over a flat or rolling terrain. For the study region, the MODIS pixel size of about 1 km may indeed ensure a largely constant Qn value among the pixels since the observed stand‐ ard deviation in the mean monthly (warm season) surface albedo value of 17% is only 1.2% among the MODIS cells.

performed only in a selected set of points, which was chosen as each tenth MODIS cell in space (both row-, and column-wise). The remaining cells were then filled up with spatial mean values, linearly interpolated first by row among the selected MODIS-cell values, and then by column, involving the already interpolated values in the rows as well. Near the eastern and southern boundaries of the state any necessary spatial extrapolation was done by the gradi‐ ent method (i.e., keeping the first two terms of the Taylor-expansion). This "sampling" sped

Recent Updates of the Calibration-Free Evapotranspiration Mapping (CREMAP) Method

http://dx.doi.org/10.5772/52392

27

Care had to be exercised with the choice of the radius of influence. Rather than applying a constant radius, a spatially changing one was required because near the boundary of the state the "window" becomes asymmetrical around the MODIS cells, therefore the radius changed linearly with distance to these boundaries from a starting value of 25 cells up to a maximum of 125 cells (at a rate of 4/5 cell by each line or column) in the central portion of the domain. It was simpler to define a rectangular region around each designated MODIS cell, rather than a circular one, therefore the radius of influence is half the side-length of the

Once the spatial mean values were available for each MODIS cell, the actual linear transfor‐ mation of the Ts to ET values was performed for each month (except the winter months). The linear transformation of the Ts values into ET rates assumes a negligible change in the ra value among the cells. As was mentioned above, ra is directly proportional –up to a constant and with a negative slope— to the logarithm of z0m under neutral stability conditions of the atmosphere, provided the wind speed at the blending height (about 200 m above the ground) is near constant within the region [11]. The momentum roughness height, z0m, of each MODIS cell has been estimated over the state (Figure 3) with the help of a 1-km digital elevation model, as the natural logarithm of the standard deviation in the elevation values among the 25 neighboring cells surrounding a given cell, including the chosen cell itself. The mini‐ mum value of z0m has been set to 0.4 m, so when the estimate became smaller than this lower limit (possible for flat regions), the value was replaced by 0.4 m. Note that the z0m = 0.4 m value is the upper interval value for a "prairie or short crops with scattered bushes and tree clumps" in Table 2.6 of [13]. The rugged hills regions of Nebraska (e.g., the Pine Ridge and the Pine Bluffs, just to name a few) are characterized (Figure 3) by the largest z0m values (larger than 3 m), covering the 3-4 m range for "Fore-Alpine terrain (200-300 m) with scat‐ tered tree stands" of [13]. Since the ra estimates are proportional (up to a constant) to the logarithm of the z0m values, their change among the MODIS cells is much subdued: about 67% of the time they are within 5% of their spatial mean and more than 94% of the time they remain within 15% (Figure 4), supporting the original assumption of the present ET

Cells that had ra values smaller than 95% of the mean ra value (involved about 20% of all cells) were identified, and the corresponding ET values corrected by the relative change in ra, considering that the sum of the latent (LE) and sensible heat (H) values are assumed to be constant among the cells (equaling Qn) and that H is proportional to dTz / ra [11], where dTz is the vertical gradient of the air temperature above the surface, itself taken proportional to Ts. The reason that only the "overestimates" of ET are corrected is that the linear transforma‐

up calculations by at least two orders of magnitude.

resulting square.

mapping method.

A further assumption of the method is that the vertical gradient of the air temperature near the surface is linearly related to the surface temperature [10, 11], thus sensible heat (H) transfer across the land-atmosphere interface, provided changes in the aerodynamic resist‐ ance (ra) among the MODIS pixels are moderate, can also be taken a linear function of Ts. This can be so because under neutral atmospheric conditions (attained for time-steps a day or longer) ra depends linearly on the logarithm of the momentum roughness length, z0m [11], thus any change in z0m between pixels becomes significantly dampened in the ra value due to the logarithm. Consequently, the latent heat (LE) transfer itself becomes a linear function of Ts under a spatially constant net energy (Qn) term required by the CR, therefore Qn = H + LE, from which LE = mTs + c follows, m and c being constants for the computational time step, i.e., a month here, within a region.

8-day composited MODIS daytime surface temperature data were collected over the 2000 – 2009 period. The 8-day composited pixel values were averaged for each month to obtain one surface temperature per pixel per month, except for December, January, and February. The winter months were left out of the linear transformations because then the ground may have patchy snow cover which violates the constant Qn assumption since the albedo of snow is markedly different from that of the land. Therefore in the wintertime the WREVAP-derived regional ET rates were employed without any further disaggregation by surface tempera‐ tures but, rather, with a subsequent correction, discussed later.

Mean annual precipitation, mean monthly maximum/minimum air and dew-point tempera‐ ture values came from the PRISM database [12] at 2.5-min spatial resolution. Mean monthly incident global radiation data at half-degree resolution were downloaded from the GCIP/SRB site [2]. While previously [1] the regions were defined by subdividing the state into eight distinct areas (a largely arbitrary process) for the calculation of the regionally representative values of the mean monthly air temperature, humidity and radiation data, required by WRE‐ VAP, now such a subdivision is not necessary. Instead, a "radius of influence" is defined over which the regional values are calculated separately for each designated MODIS cell, very similar to a temporal moving-average process, but now in two dimensions of space. In prin‐ ciple, such a spatial averaging could be performed for each MODIS cell, in practice howev‐ er, it becomes computationally overwhelming on the PC, and it is also unnecessary, since the spatial averages form a 2-D signal of small gradient, making possible that "sampling" (i.e., the actual calculation of the spatial mean values including the WREVAP-calculated ET rate) is performed only in a selected set of points, which was chosen as each tenth MODIS cell in space (both row-, and column-wise). The remaining cells were then filled up with spatial mean values, linearly interpolated first by row among the selected MODIS-cell values, and then by column, involving the already interpolated values in the rows as well. Near the eastern and southern boundaries of the state any necessary spatial extrapolation was done by the gradi‐ ent method (i.e., keeping the first two terms of the Taylor-expansion). This "sampling" sped up calculations by at least two orders of magnitude.

This last assumption is most likely true for fully vegetated surfaces where soil heat conduc‐ tion is small throughout the day, and is less valid for bare soil and open water surfaces. While a spatially constant Qn term at first seems to be an overly stringent requirement in practical applications due to spatial changes in vegetation cover as well as slope and aspect of the land surface, Qn will change only negligibly in space provided the surface albedo (i.e., the ratio of in- and outgoing short-wave radiation) value also changes negligibly among the pixels over a flat or rolling terrain. For the study region, the MODIS pixel size of about 1 km may indeed ensure a largely constant Qn value among the pixels since the observed stand‐ ard deviation in the mean monthly (warm season) surface albedo value of 17% is only 1.2%

A further assumption of the method is that the vertical gradient of the air temperature near the surface is linearly related to the surface temperature [10, 11], thus sensible heat (H) transfer across the land-atmosphere interface, provided changes in the aerodynamic resist‐ ance (ra) among the MODIS pixels are moderate, can also be taken a linear function of Ts. This can be so because under neutral atmospheric conditions (attained for time-steps a day or longer) ra depends linearly on the logarithm of the momentum roughness length, z0m [11], thus any change in z0m between pixels becomes significantly dampened in the ra value due to the logarithm. Consequently, the latent heat (LE) transfer itself becomes a linear function of Ts under a spatially constant net energy (Qn) term required by the CR, therefore Qn = H + LE, from which LE = mTs + c follows, m and c being constants for the computational time

8-day composited MODIS daytime surface temperature data were collected over the 2000 – 2009 period. The 8-day composited pixel values were averaged for each month to obtain one surface temperature per pixel per month, except for December, January, and February. The winter months were left out of the linear transformations because then the ground may have patchy snow cover which violates the constant Qn assumption since the albedo of snow is markedly different from that of the land. Therefore in the wintertime the WREVAP-derived regional ET rates were employed without any further disaggregation by surface tempera‐

Mean annual precipitation, mean monthly maximum/minimum air and dew-point tempera‐ ture values came from the PRISM database [12] at 2.5-min spatial resolution. Mean monthly incident global radiation data at half-degree resolution were downloaded from the GCIP/SRB site [2]. While previously [1] the regions were defined by subdividing the state into eight distinct areas (a largely arbitrary process) for the calculation of the regionally representative values of the mean monthly air temperature, humidity and radiation data, required by WRE‐ VAP, now such a subdivision is not necessary. Instead, a "radius of influence" is defined over which the regional values are calculated separately for each designated MODIS cell, very similar to a temporal moving-average process, but now in two dimensions of space. In prin‐ ciple, such a spatial averaging could be performed for each MODIS cell, in practice howev‐ er, it becomes computationally overwhelming on the PC, and it is also unnecessary, since the spatial averages form a 2-D signal of small gradient, making possible that "sampling" (i.e., the actual calculation of the spatial mean values including the WREVAP-calculated ET rate) is

among the MODIS cells.

26 Evapotranspiration - An Overview

step, i.e., a month here, within a region.

tures but, rather, with a subsequent correction, discussed later.

Care had to be exercised with the choice of the radius of influence. Rather than applying a constant radius, a spatially changing one was required because near the boundary of the state the "window" becomes asymmetrical around the MODIS cells, therefore the radius changed linearly with distance to these boundaries from a starting value of 25 cells up to a maximum of 125 cells (at a rate of 4/5 cell by each line or column) in the central portion of the domain. It was simpler to define a rectangular region around each designated MODIS cell, rather than a circular one, therefore the radius of influence is half the side-length of the resulting square.

Once the spatial mean values were available for each MODIS cell, the actual linear transfor‐ mation of the Ts to ET values was performed for each month (except the winter months). The linear transformation of the Ts values into ET rates assumes a negligible change in the ra value among the cells. As was mentioned above, ra is directly proportional –up to a constant and with a negative slope— to the logarithm of z0m under neutral stability conditions of the atmosphere, provided the wind speed at the blending height (about 200 m above the ground) is near constant within the region [11]. The momentum roughness height, z0m, of each MODIS cell has been estimated over the state (Figure 3) with the help of a 1-km digital elevation model, as the natural logarithm of the standard deviation in the elevation values among the 25 neighboring cells surrounding a given cell, including the chosen cell itself. The mini‐ mum value of z0m has been set to 0.4 m, so when the estimate became smaller than this lower limit (possible for flat regions), the value was replaced by 0.4 m. Note that the z0m = 0.4 m value is the upper interval value for a "prairie or short crops with scattered bushes and tree clumps" in Table 2.6 of [13]. The rugged hills regions of Nebraska (e.g., the Pine Ridge and the Pine Bluffs, just to name a few) are characterized (Figure 3) by the largest z0m values (larger than 3 m), covering the 3-4 m range for "Fore-Alpine terrain (200-300 m) with scat‐ tered tree stands" of [13]. Since the ra estimates are proportional (up to a constant) to the logarithm of the z0m values, their change among the MODIS cells is much subdued: about 67% of the time they are within 5% of their spatial mean and more than 94% of the time they remain within 15% (Figure 4), supporting the original assumption of the present ET mapping method.

Cells that had ra values smaller than 95% of the mean ra value (involved about 20% of all cells) were identified, and the corresponding ET values corrected by the relative change in ra, considering that the sum of the latent (LE) and sensible heat (H) values are assumed to be constant among the cells (equaling Qn) and that H is proportional to dTz / ra [11], where dTz is the vertical gradient of the air temperature above the surface, itself taken proportional to Ts. The reason that only the "overestimates" of ET are corrected is that the linear transforma‐ tion of the Ts values into ET rates seems to be more sensitive to more rugged-than-average terrain than to smoother one. That is why the most rugged part of Nebraska, i.e., the Pine Ridge, required an additional (to the above) 10% ET adjustment if no Ponderosa Pine was detected in the 3x3-cell region of the land use-land cover map around a given cell, and a 20% cut if it was. The assumption is that in this extremely rugged region cells with other than Ponderosa pine designation, may still contain scattered trees, if in the vicinity there are pine-forested areas plus the air turbulence, enhanced by the rugged terrain, may have a wake with a characteristic length of about a km. Within the Niobrara River Breaks region (less rugged than the Pine Ridge) only a 10% additional ET adjustment was applied without regard if the cell-surroundings are pine-covered or not. The underlying reasons of these de‐ viations may be (after accepting that the PRISM precipitation values are correct) the way z0m is estimated, perhaps a DEM with a finer resolution would yield better results.

Or maybe the type of vegetation, even at a 1-km resolution, has relevance (similar to plotscale applications), in addition to the primary elevation variance. Or even, due to the en‐ larged surface area of the rugged terrain, the global radiation value should be reduced, which would lower ET. This topic certainly requires further research.

> **Figure 4.** Relative histograms of the momentum roughness height (z0m) and the relative change in the aerodynamic resistance (ra) around its spatial mean value [m(ra)] across Nebraska, estimated from a 1-km resolution digital elevation

Recent Updates of the Calibration-Free Evapotranspiration Mapping (CREMAP) Method

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29

The WREVAP model is based on the complementary relationship [4] which performs the worst in the cold winter months [8, 14, 15], thus the resulting WREVAP-obtained winter ET rates become the most uncertain. A yet unpublished study by the present author, involving the Republican River basin, indicated that inclusion of the winter ET rates of WREVAP im‐ proved the mean annual ET estimates in comparison with water balance derived [3, 12] da‐ ta. Other studies [1, 16] also indicated that WREVAP somewhat overestimates ET rates in the Nebraska Sand Hills region even without inclusion of the winter months. Finally, a wa‐ ter balance based [3, 12] verification of the current ET estimates indicated that the WREVAPprovided winter ET rates are necessary in the most humid eastern, south-eastern part of the state. Based on these comparisons, the WREVAP winter months were fully included in the mean annual ET rates [besides the wettest part of the state, defined by (Psm – ETWREVAP) > 50 mm] for the Republican River basin, and for areas where the mean monthly daytime maxi‐ mum temperature values exceeded 5 ºC. The latter area almost fully covers the Republican River basin, plus the south and south-western part of the panhandle region. Psm designates the spatially smoothed precipitation values of PRISM, applying a 30-by-30-cell window, to filter out the unrealistic grainy structure of the PRISM precipitation field (Figure 5) due probably to its spatial interpolation method. No winter ET rates were included in the mean annual ET values wherever (Psm – ETWREVAP) < 10 mm; and a 50% reduction of the WREVAP winter ET rates were used for areas where [10 mm < (Psm – ETWREVAP) < 50 mm] held true.

model.

**Figure 3.** Estimated values of the a) momentum roughness height (z0m), and; b) relative change in the aerodynamic resistance (ra) around the state-wide mean. The numbers along the left and bottom edge of the panels are the MODIS cell numbers.

A final correction was applied for cells of "extreme" elevation. Namely, when the elevation of a cell differed from the regional mean value by more than 100 m, its surface temperature was corrected by 0.01 Kelvin per meter, reflecting the dry-adiabatic cooling rate of the air.

tion of the Ts values into ET rates seems to be more sensitive to more rugged-than-average terrain than to smoother one. That is why the most rugged part of Nebraska, i.e., the Pine Ridge, required an additional (to the above) 10% ET adjustment if no Ponderosa Pine was detected in the 3x3-cell region of the land use-land cover map around a given cell, and a 20% cut if it was. The assumption is that in this extremely rugged region cells with other than Ponderosa pine designation, may still contain scattered trees, if in the vicinity there are pine-forested areas plus the air turbulence, enhanced by the rugged terrain, may have a wake with a characteristic length of about a km. Within the Niobrara River Breaks region (less rugged than the Pine Ridge) only a 10% additional ET adjustment was applied without regard if the cell-surroundings are pine-covered or not. The underlying reasons of these de‐ viations may be (after accepting that the PRISM precipitation values are correct) the way z0m

Or maybe the type of vegetation, even at a 1-km resolution, has relevance (similar to plotscale applications), in addition to the primary elevation variance. Or even, due to the en‐ larged surface area of the rugged terrain, the global radiation value should be reduced,

**Figure 3.** Estimated values of the a) momentum roughness height (z0m), and; b) relative change in the aerodynamic resistance (ra) around the state-wide mean. The numbers along the left and bottom edge of the panels are the MODIS

A final correction was applied for cells of "extreme" elevation. Namely, when the elevation of a cell differed from the regional mean value by more than 100 m, its surface temperature was corrected by 0.01 Kelvin per meter, reflecting the dry-adiabatic cooling rate of the air.

cell numbers.

28 Evapotranspiration - An Overview

is estimated, perhaps a DEM with a finer resolution would yield better results.

which would lower ET. This topic certainly requires further research.

**Figure 4.** Relative histograms of the momentum roughness height (z0m) and the relative change in the aerodynamic resistance (ra) around its spatial mean value [m(ra)] across Nebraska, estimated from a 1-km resolution digital elevation model.

The WREVAP model is based on the complementary relationship [4] which performs the worst in the cold winter months [8, 14, 15], thus the resulting WREVAP-obtained winter ET rates become the most uncertain. A yet unpublished study by the present author, involving the Republican River basin, indicated that inclusion of the winter ET rates of WREVAP im‐ proved the mean annual ET estimates in comparison with water balance derived [3, 12] da‐ ta. Other studies [1, 16] also indicated that WREVAP somewhat overestimates ET rates in the Nebraska Sand Hills region even without inclusion of the winter months. Finally, a wa‐ ter balance based [3, 12] verification of the current ET estimates indicated that the WREVAPprovided winter ET rates are necessary in the most humid eastern, south-eastern part of the state. Based on these comparisons, the WREVAP winter months were fully included in the mean annual ET rates [besides the wettest part of the state, defined by (Psm – ETWREVAP) > 50 mm] for the Republican River basin, and for areas where the mean monthly daytime maxi‐ mum temperature values exceeded 5 ºC. The latter area almost fully covers the Republican River basin, plus the south and south-western part of the panhandle region. Psm designates the spatially smoothed precipitation values of PRISM, applying a 30-by-30-cell window, to filter out the unrealistic grainy structure of the PRISM precipitation field (Figure 5) due probably to its spatial interpolation method. No winter ET rates were included in the mean annual ET values wherever (Psm – ETWREVAP) < 10 mm; and a 50% reduction of the WREVAP winter ET rates were used for areas where [10 mm < (Psm – ETWREVAP) < 50 mm] held true.

Elkhorn, and partly the Republican) and their valleys in ET rates. The reason, beside the presence of the open water surface, is in the relatively small distance to the groundwater ta‐ ble in these river valleys, enabling the root system of the vegetation to tap into it, plus in the accompanying large-scale irrigation within the valleys. The river valleys on the ET scale are followed by areas of intensive irrigation, reaching 750 mm a year. The driest regions, with the smallest rate of ET in eastern Nebraska are the urban areas of Omaha and Lincoln (Fig‐ ure 1), where the built in surfaces enhance surface runoff. The eastern outline of the Sand Hills is clearly visible, as well as the sandy areas (the elongated green-colored features) be‐ tween the Loup and the Platte Rivers. The sandy soil, due to its large porosity favors deep

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Figure 7 depicts the monthly ET rates from January through December. In July and August the irrigated plots in south-central Nebraska can evaporate as intensively as the open water surfaces. Even in September, when most of the produce has been harvested, the soil through its enhanced moisture due to summer irrigation, evaporates more than the surrounding, non-irrigated land. In November the distribution of ET rates becomes zonal and follows the

While in absolute numbers the south-central portion of the state produces the highest ET rates, the picture changes significantly, when one looks at the ET to precipitation (so-called

percolation of the water often out of reach of the vegetation.

**Figure 7.** Estimated mean monthly ET rates (mm) in Nebraska., 2000-2009.

precipitation recycling) ratios of Figure 8.

precipitation distribution.

**Figure 5.** Distribution of the mean annual precipitation (mm) values across Nebraska from the PRISM data, 2000-2009. The state-wide mean annual precipitation rate is 577 mm.

### **3. Results and conclusion**

The mean annual ET rates across Nebraska are displayed in Figure 6. By and large, ET fol‐ lows the distribution of precipitation, as expected. Most of the ET values are between 250-500 mm in the panhandle, around

**Figure 6.** Estimated mean annual ET rates (mm) in Nebraska (2000-2009). The state-wide mean ET value is 549 mm/yr.

500-650 mm in the middle of the state and near 650 mm in the eastern portion of it. Locally, however, there are large differences due to land use and land cover variance. The sizeable reservoirs (McConaughy, Lewis and Clarke, Harlan County, Swanson, Calamus, etc.) large enough to fully accommodate a MODIS cell, display the largest ET rates, around 1000 mm annually. The reservoirs/lakes are followed by the wider rivers (i.e., Platte, Missouri, Loups, Elkhorn, and partly the Republican) and their valleys in ET rates. The reason, beside the presence of the open water surface, is in the relatively small distance to the groundwater ta‐ ble in these river valleys, enabling the root system of the vegetation to tap into it, plus in the accompanying large-scale irrigation within the valleys. The river valleys on the ET scale are followed by areas of intensive irrigation, reaching 750 mm a year. The driest regions, with the smallest rate of ET in eastern Nebraska are the urban areas of Omaha and Lincoln (Fig‐ ure 1), where the built in surfaces enhance surface runoff. The eastern outline of the Sand Hills is clearly visible, as well as the sandy areas (the elongated green-colored features) be‐ tween the Loup and the Platte Rivers. The sandy soil, due to its large porosity favors deep percolation of the water often out of reach of the vegetation.

Figure 7 depicts the monthly ET rates from January through December. In July and August the irrigated plots in south-central Nebraska can evaporate as intensively as the open water surfaces. Even in September, when most of the produce has been harvested, the soil through its enhanced moisture due to summer irrigation, evaporates more than the surrounding, non-irrigated land. In November the distribution of ET rates becomes zonal and follows the precipitation distribution.

**Figure 7.** Estimated mean monthly ET rates (mm) in Nebraska., 2000-2009.

**Figure 5.** Distribution of the mean annual precipitation (mm) values across Nebraska from the PRISM data,

The mean annual ET rates across Nebraska are displayed in Figure 6. By and large, ET fol‐ lows the distribution of precipitation, as expected. Most of the ET values are between

**Figure 6.** Estimated mean annual ET rates (mm) in Nebraska (2000-2009). The state-wide mean ET value is 549 mm/yr.

500-650 mm in the middle of the state and near 650 mm in the eastern portion of it. Locally, however, there are large differences due to land use and land cover variance. The sizeable reservoirs (McConaughy, Lewis and Clarke, Harlan County, Swanson, Calamus, etc.) large enough to fully accommodate a MODIS cell, display the largest ET rates, around 1000 mm annually. The reservoirs/lakes are followed by the wider rivers (i.e., Platte, Missouri, Loups,

2000-2009. The state-wide mean annual precipitation rate is 577 mm.

**3. Results and conclusion**

30 Evapotranspiration - An Overview

250-500 mm in the panhandle, around

While in absolute numbers the south-central portion of the state produces the highest ET rates, the picture changes significantly, when one looks at the ET to precipitation (so-called precipitation recycling) ratios of Figure 8.

The lines in Figure 9 designate areas (after [17]) where groundwater decline was at least 3, 5, 8 m over the 2000-2009 period. Naturally, in heavily irrigated areas close to major streams (e.g., North- and South Platte, Platte River), such groundwater depletions are absent (but not around Lake McConaughy, where reservoir water levels have been below normal most of 2000-2009) since the chief source of the irrigation water is the stream itself. Figure 10 dis‐

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As seen in Figure 10, not all land areas with larger than unity ratios are connected to irrigation, good examples are the Sand Hills wetlands. Similarly, not all areas that come up with values larger than 100% do actually evaporate more than they receive from precipita‐ tion. Such an area is the table-land just south of the western edge of Lake McConaughy, between the North- and South-Platte Rivers (please, refer to Figure 8 for corresponding precipitation recycling ratios, the colors of Figure 10 are slightly off because it was pro‐ duced by a different software that enabled marking the irrigated areas on top of the ra‐ tios). In this area irrigation is largely absent (or at least it was in 2005, the date of the irrigation data), yet the ratio is between 100-120%. The error may be caused by several factors, name‐ ly a) the well-known, often 10% underestimation of precipitation; b) inaccuracy of the ET estimates, and; c) problems with the spatial interpolation of the measured precipitation values. The latter is well demonstrated in Figure 5, which shows that in the southern pan‐ handle region there can be a difference of 125 mm (about 25-30% of the annual value) in the precipitation values within a distance of 30 km or less. Added to this uncertainty is the wide-spread underestimation of precipitation, especially in windy areas where a measura‐ ble portion of the raindrops (and especially snowflakes) is swept away from the rain gage. Finally, the present ET estimates have an error term (discussed further later) of about plus/ minus (±) 5-10%. Employing a ±5% error in the latter, another -5% underestimation in the measured precipitation values together with yet another independent ±5% error in the inter‐ polated values, the resulting ET / P ratio may contain an error of -5% to 16%, coinciding well with the error extent found in the table-land area. Therefore, the ratios in Figure 8 must

A comparison with the previous version [1] of the mean annual ET map (Figure 11) reveals that the largest differences are found in the Republican River basin and the southern pan‐ handle region, where now the full values of the WREVAP-estimated winter-time ET rates

plays the distribution of irrigated land, overlain the ET / P values.

**Figure 10.** Irrigated land (marked in black) distribution [after 18, 19] in Nebraska, 2005.

be treated with this uncertainty in mind.

**Figure 8.** Estimated mean annual ET to precipitation ratios (%), 2000-2009. The state-wide mean ratio is 95%.

**Figure 9.** Distribution of areas with the largest observed groundwater decline (at least 3 m, to up to 8 m) over the 2000-2009 period, overlain the ET / P map. For the correct color to ratio correspondence, please, use the colors in Figure 8 instead of the current ones.

Lake McConaughy is the clear winner (followed by smaller lakes in the vicinity), evaporat‐ ing about twice as much as it receives from precipitation. It does not mean, of course, that the other small lakes in the area would not evaporate as much as Lake McConaughy per unit area, they probably evaporate even more (the smaller the lake the larger typically its evaporation rate, provided other environmental factors are equal), but their size inhibits MODIS to detect their surface temperatures without "contamination" from the surrounding land. Note again the eastern outline of the Sand Hills and the elongated sandy areas be‐ tween the Loup and Platte Rivers as areas of relatively low ET rates. The two urban areas of Omaha and Lincoln are clearly visible again.

Two large irrigated areas stand out clearly as the most intensive water users (relative to pre‐ cipitation), one in the Republican River basin and the other in the North-Platte River valley of the panhandle. In these areas ET rates significantly exceed (up to 50%) precipitation rates. Another significant irrigated area in Box Butte County (at the western edge of the Sand Hills) plus the one in the Republican River basin coincide largely with regions of extensive groundwater depletions, displayed in Figure 9.

The lines in Figure 9 designate areas (after [17]) where groundwater decline was at least 3, 5, 8 m over the 2000-2009 period. Naturally, in heavily irrigated areas close to major streams (e.g., North- and South Platte, Platte River), such groundwater depletions are absent (but not around Lake McConaughy, where reservoir water levels have been below normal most of 2000-2009) since the chief source of the irrigation water is the stream itself. Figure 10 dis‐ plays the distribution of irrigated land, overlain the ET / P values.

**Figure 10.** Irrigated land (marked in black) distribution [after 18, 19] in Nebraska, 2005.

**Figure 8.** Estimated mean annual ET to precipitation ratios (%), 2000-2009. The state-wide mean ratio is 95%.

**Figure 9.** Distribution of areas with the largest observed groundwater decline (at least 3 m, to up to 8 m) over the 2000-2009 period, overlain the ET / P map. For the correct color to ratio correspondence, please, use the colors in

Lake McConaughy is the clear winner (followed by smaller lakes in the vicinity), evaporat‐ ing about twice as much as it receives from precipitation. It does not mean, of course, that the other small lakes in the area would not evaporate as much as Lake McConaughy per unit area, they probably evaporate even more (the smaller the lake the larger typically its evaporation rate, provided other environmental factors are equal), but their size inhibits MODIS to detect their surface temperatures without "contamination" from the surrounding land. Note again the eastern outline of the Sand Hills and the elongated sandy areas be‐ tween the Loup and Platte Rivers as areas of relatively low ET rates. The two urban areas of

Two large irrigated areas stand out clearly as the most intensive water users (relative to pre‐ cipitation), one in the Republican River basin and the other in the North-Platte River valley of the panhandle. In these areas ET rates significantly exceed (up to 50%) precipitation rates. Another significant irrigated area in Box Butte County (at the western edge of the Sand Hills) plus the one in the Republican River basin coincide largely with regions of extensive

Figure 8 instead of the current ones.

32 Evapotranspiration - An Overview

Omaha and Lincoln are clearly visible again.

groundwater depletions, displayed in Figure 9.

As seen in Figure 10, not all land areas with larger than unity ratios are connected to irrigation, good examples are the Sand Hills wetlands. Similarly, not all areas that come up with values larger than 100% do actually evaporate more than they receive from precipita‐ tion. Such an area is the table-land just south of the western edge of Lake McConaughy, between the North- and South-Platte Rivers (please, refer to Figure 8 for corresponding precipitation recycling ratios, the colors of Figure 10 are slightly off because it was pro‐ duced by a different software that enabled marking the irrigated areas on top of the ra‐ tios). In this area irrigation is largely absent (or at least it was in 2005, the date of the irrigation data), yet the ratio is between 100-120%. The error may be caused by several factors, name‐ ly a) the well-known, often 10% underestimation of precipitation; b) inaccuracy of the ET estimates, and; c) problems with the spatial interpolation of the measured precipitation values. The latter is well demonstrated in Figure 5, which shows that in the southern pan‐ handle region there can be a difference of 125 mm (about 25-30% of the annual value) in the precipitation values within a distance of 30 km or less. Added to this uncertainty is the wide-spread underestimation of precipitation, especially in windy areas where a measura‐ ble portion of the raindrops (and especially snowflakes) is swept away from the rain gage. Finally, the present ET estimates have an error term (discussed further later) of about plus/ minus (±) 5-10%. Employing a ±5% error in the latter, another -5% underestimation in the measured precipitation values together with yet another independent ±5% error in the inter‐ polated values, the resulting ET / P ratio may contain an error of -5% to 16%, coinciding well with the error extent found in the table-land area. Therefore, the ratios in Figure 8 must be treated with this uncertainty in mind.

A comparison with the previous version [1] of the mean annual ET map (Figure 11) reveals that the largest differences are found in the Republican River basin and the southern pan‐ handle region, where now the full values of the WREVAP-estimated winter-time ET rates were added to the warm-season values (March-November). Note that the procedures used for preparing the two maps are different (application of a radius of influence around each MODIS cell versus distinct geographic regions) as was explained above. The perceptible di‐ agonal and level straight lines suggest some problems with the interpolation method em‐ ployed in the previous ET map.

**Figure 12.** Water balance derived (P – Ro) mean annual ET rates (mm) of the USGS HUC-8 watersheds in Nebraska,

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Note also that a systematic underestimation of the precipitation rates automatically leads to a virtual overestimation of the ET rates by the present method during verification. Another problem with the verification is that the watershed area employed for the transformation of the discharge values into water depth, may also be somewhat uncertain, since the ground‐ water catchment does not always overlap perfectly with the surface-water catchment de‐ lineated by the help of surface elevation values. Probably that is why the largest over- and under-estimation of ET is found within the Sand Hills, in catchments very close to each oth‐ er. Also, the USGS watershed runoff values employ simplifications that may cause serious errors in the estimated watershed runoff rate, such as found for the Lower Republican basin in Kansas (not shown here), where USGS reports a mean runoff rate of 5 mm/yr for 2000-2009, while a Kansas Geological Survey study [20] found a mean annual runoff rate of

**Figure 13.** Distribution of the estimation error (mm) in the mean annual ET rates among the USGS HUC-8 watersheds

2000-2009.

106 mm/yr, an almost twenty-fold difference.

within Nebraska, 2000-2009.

**Figure 11.** Differences in the present and previous [1] mean annual ET maps (mm). Mean is 18.5 mm.

Verification of the estimated mean annual ET rates can be best performed on a watershedby-watershed basis by subtracting the stream discharge values (expressed in mm) from the mean precipitation values of the catchments, assuming that groundwater level changes are negligible over the study period, i.e., 2000-2009. As seen above, the latter is not true in many regions within Nebraska, but a transformation of these groundwater-level changes into wa‐ ter depth values would require the state-wide distribution of the specific yield value (also called drainable porosity, defined by dividing the drained water volume value with that of the control volume, fully saturated with water at the start of drainage) of the water bearing aquifer, a hydro-geological parameter not available for the whole state. Figure 12 displays the water-balance derived ET rates employing the PRISM precipitation values [12] and USGS-derived watershed-representative runoff values [3] for the HUC-8 watersheds within Nebraska, while Figure 13 displays the spatial distribution of estimation error (predicted mi‐ nus water-balance derived) of the CREMAP ET values among the same catchments. As seen, in the majority of the watersheds the estimation error is within 30 mm of the "observed" val‐ ue. The largest overestimation takes place for watersheds within the Missouri River basin, within the Sand Hills, and within and just north of the Republican River basin. The latter area corresponds to one of the most severe groundwater depletion regions within the state, where the "missing" water certainly contributes to elevated ET rates, not detectable by the simplified water balance approach.

were added to the warm-season values (March-November). Note that the procedures used for preparing the two maps are different (application of a radius of influence around each MODIS cell versus distinct geographic regions) as was explained above. The perceptible di‐ agonal and level straight lines suggest some problems with the interpolation method em‐

**Figure 11.** Differences in the present and previous [1] mean annual ET maps (mm). Mean is 18.5 mm.

Verification of the estimated mean annual ET rates can be best performed on a watershedby-watershed basis by subtracting the stream discharge values (expressed in mm) from the mean precipitation values of the catchments, assuming that groundwater level changes are negligible over the study period, i.e., 2000-2009. As seen above, the latter is not true in many regions within Nebraska, but a transformation of these groundwater-level changes into wa‐ ter depth values would require the state-wide distribution of the specific yield value (also called drainable porosity, defined by dividing the drained water volume value with that of the control volume, fully saturated with water at the start of drainage) of the water bearing aquifer, a hydro-geological parameter not available for the whole state. Figure 12 displays the water-balance derived ET rates employing the PRISM precipitation values [12] and USGS-derived watershed-representative runoff values [3] for the HUC-8 watersheds within Nebraska, while Figure 13 displays the spatial distribution of estimation error (predicted mi‐ nus water-balance derived) of the CREMAP ET values among the same catchments. As seen, in the majority of the watersheds the estimation error is within 30 mm of the "observed" val‐ ue. The largest overestimation takes place for watersheds within the Missouri River basin, within the Sand Hills, and within and just north of the Republican River basin. The latter area corresponds to one of the most severe groundwater depletion regions within the state, where the "missing" water certainly contributes to elevated ET rates, not detectable by the

ployed in the previous ET map.

34 Evapotranspiration - An Overview

simplified water balance approach.

**Figure 12.** Water balance derived (P – Ro) mean annual ET rates (mm) of the USGS HUC-8 watersheds in Nebraska, 2000-2009.

Note also that a systematic underestimation of the precipitation rates automatically leads to a virtual overestimation of the ET rates by the present method during verification. Another problem with the verification is that the watershed area employed for the transformation of the discharge values into water depth, may also be somewhat uncertain, since the ground‐ water catchment does not always overlap perfectly with the surface-water catchment de‐ lineated by the help of surface elevation values. Probably that is why the largest over- and under-estimation of ET is found within the Sand Hills, in catchments very close to each oth‐ er. Also, the USGS watershed runoff values employ simplifications that may cause serious errors in the estimated watershed runoff rate, such as found for the Lower Republican basin in Kansas (not shown here), where USGS reports a mean runoff rate of 5 mm/yr for 2000-2009, while a Kansas Geological Survey study [20] found a mean annual runoff rate of 106 mm/yr, an almost twenty-fold difference.

**Figure 13.** Distribution of the estimation error (mm) in the mean annual ET rates among the USGS HUC-8 watersheds within Nebraska, 2000-2009.

Figure 14 summarizes the ET verification results. It can be seen that in the vast majority of the USGS HUC-8 watersheds the estimated values are within 10% of the simplified water balance derived values. Five of the seven overestimates (above the upper intermittent line) of Figure 14, found between 400 and 500 mm, correspond to the large groundwater deple‐ tion area in and around the Republican River basin, displayed in Figure 9, so in those cases the CREMAP ET estimates may better represent reality than the simplified water balance derived values. The explained variance, R2 , has a value of 0.87, meaning that 87% of the spa‐ tial variance found in the HUC-8 water-balance derived ET values is explained by the CRE‐ MAP estimates. In summary, the annual and monthly ET maps are recommended for use in future regional-scale water-balance calculations with the resolution and accuracy of the esti‐ mates kept in mind. The maps are certainly not recommended for reading off individual cell values, because the exact cell coordinates maybe slightly off due to the geographically refer‐ enced data manipulations necessary to produce those maps. For example, the author found some problem with coordinate referencing when cells are extracted from a grid employing another grid with differing cell size. The maps are best suited for studies of spatial scale larger than one km.

ed to the scientific program of the "Development of quality-oriented and harmonized R+D+I strategy and functional model at BME" project. This project is supported by the New Szeche‐

Recent Updates of the Calibration-Free Evapotranspiration Mapping (CREMAP) Method

http://dx.doi.org/10.5772/52392

37

*Disclaimer*: The views, conclusions, and opinions expressed in this study are solely those of the writer and not the University of Nebraska, state of Nebraska, or any political subdivi‐

1 Department of Hydraulic and Water Resources Engineering, Budapest University of Tech‐

[1] Szilagyi, J., Kovacs, A., & Jozsa, J. (2011). A calibration-free evapotranspiration map‐ ping (CREMAP) technique. In: Labedzki L. (ed.) Evapotranspiration. Rijeka: InTech Available from http://www.intechopen.com/books/show/title/evapotranspiration (ac‐

[2] GEWEX Continental Scale International Project (2012). Surface Radiation Budget. GCIP-SRB. http://metosrv2.umd.edu/~srb/gcip/cgi-bin/historic.cgiaccessed 28 June).

[3] United States Geological Survey, USGS. (2012). Computed runoff. http://water‐

[4] Bouchet, R. J. (1963). Evapotranspiration reelle, evapotranspiration potentielle, et

[5] Brutsaert, W., & Stricker, H. (1979). An Advection-Aridity approach to estimate ac‐

[6] Morton, F., Ricard, F., & Fogarasi, S. (1985). Operational estimates of areal evapo‐ transpiration and lake evaporation- Program WREVAP. *National Hydrological Re‐*

[7] National Aeronautics and Space Administration. (2012). Moderate Resolution Imag‐ ing Spectroradiometer. MODIS data. http://modis.gsfc.nasa.govaccessed 28 June).

tual regional evapotranspiration. *Water Resources Research*, 15, 443-449.

2 School of Natural Resources, University of Nebraska-Lincoln, Lincoln, Nebraska, USA

nyi Plan (Project ID: TAMOP-4.2.1/B-09/1/KMR-2010-0002).

Address all correspondence to: jszilagyi1@unl.edu

nology and Economics, Budapest, Hungary

cessed 28 June 2012)., 257-274.

watch.usgs.gov/new/accessed 28 June).

*search Institute (Ottawa, Canada) Paper*, 24.

production agricole. *Annales Agronomique*, 14, 543-824.

sion thereof.

**Author details**

Jozsef Szilagyi1,2\*

**References**

**Figure 14.** 14. Regression plot of the water-balance derived and CREMAP-estimated mean annual ET rates (mm) among the USGS HUC-8 catchments. R2 is the portion of the spatial variance of the water balance ET rates that is ex‐ plained by the CREMAP estimates. The upper and lower envelope lines designate the P – Ro value plus or minus 10%.

### **Acknowledgements**

This work has been supported by the Hungarian Scientific Research Fund (OTKA, #83376) and the Agricultural Research Division of the University of Nebraska. This work is connect‐ ed to the scientific program of the "Development of quality-oriented and harmonized R+D+I strategy and functional model at BME" project. This project is supported by the New Szeche‐ nyi Plan (Project ID: TAMOP-4.2.1/B-09/1/KMR-2010-0002).

*Disclaimer*: The views, conclusions, and opinions expressed in this study are solely those of the writer and not the University of Nebraska, state of Nebraska, or any political subdivi‐ sion thereof.

### **Author details**

Figure 14 summarizes the ET verification results. It can be seen that in the vast majority of the USGS HUC-8 watersheds the estimated values are within 10% of the simplified water balance derived values. Five of the seven overestimates (above the upper intermittent line) of Figure 14, found between 400 and 500 mm, correspond to the large groundwater deple‐ tion area in and around the Republican River basin, displayed in Figure 9, so in those cases the CREMAP ET estimates may better represent reality than the simplified water balance

tial variance found in the HUC-8 water-balance derived ET values is explained by the CRE‐ MAP estimates. In summary, the annual and monthly ET maps are recommended for use in future regional-scale water-balance calculations with the resolution and accuracy of the esti‐ mates kept in mind. The maps are certainly not recommended for reading off individual cell values, because the exact cell coordinates maybe slightly off due to the geographically refer‐ enced data manipulations necessary to produce those maps. For example, the author found some problem with coordinate referencing when cells are extracted from a grid employing another grid with differing cell size. The maps are best suited for studies of spatial scale

**Figure 14.** 14. Regression plot of the water-balance derived and CREMAP-estimated mean annual ET rates (mm) among the USGS HUC-8 catchments. R2 is the portion of the spatial variance of the water balance ET rates that is ex‐ plained by the CREMAP estimates. The upper and lower envelope lines designate the P – Ro value plus or minus 10%.

This work has been supported by the Hungarian Scientific Research Fund (OTKA, #83376) and the Agricultural Research Division of the University of Nebraska. This work is connect‐

, has a value of 0.87, meaning that 87% of the spa‐

derived values. The explained variance, R2

larger than one km.

36 Evapotranspiration - An Overview

**Acknowledgements**

Jozsef Szilagyi1,2\*

Address all correspondence to: jszilagyi1@unl.edu

1 Department of Hydraulic and Water Resources Engineering, Budapest University of Tech‐ nology and Economics, Budapest, Hungary

2 School of Natural Resources, University of Nebraska-Lincoln, Lincoln, Nebraska, USA

### **References**


[8] Szilagyi, J., & Jozsa, J. (2009). Estimating spatially distributed monthly evapotranspi‐ ration rates by linear transformations of MODIS daytime land surface temperature data. *Hydrology and Earth System Science*, 13(5), 629-637.

**Chapter 3**

**Quantifying the Evapotranspiration**

**Component of the Water Balance of**

Nebo Jovanovic, Richard Bugan and Sumaya Israel

Additional information is available at the end of the chapter

the water balance as part of a sensitive ecosystem.

http://dx.doi.org/10.5772/53405

**1. Introduction**

**Atlantis Sand Plain Fynbos (South Africa)**

The Cape Floral Kingdom, which experiences the Mediterranean climate of the Western Cape (South Africa), is home to about 9,000 species of the fynbos and succulent karoo bi‐ omes, 68% of which are endemic [1]. Vegetation types or veld types of the Cape Floral Kingdom are commonly classified as Mountain Fynbos, Coastal Fynbos, Strandveld and Coastal Rhenosterbosveld. The fynbos biome includes three large taxonomic groups: i) proteoids (tall, deep-rooted shrubs), ii) ericoids (fine leaves, shallow-rooted shrubs), and iii) restioids (graminoids) [2]. Future climate predictions indicate that the Western Cape region will become warmer, drier and subject to more extreme droughts [3,4], with po‐ tential risks of species extinctions and range shifts [5]. It is therefore imperative to con‐ sider the adaptation mechanisms of these species to drought and their contribution to

The physiological and morphological adaptation of fynbos to drought has been studied in the past. Differences in plant-water relations of two species of Protea (*Protea susannae* and *Protea compacta*) have been previously studied [6]. These two species exhibited differ‐ ent water use adaptation strategies, indicating that habitat specialization plays an impor‐ tant role in their distributions across landscapes. A similar plant-water behavior was observed in different species occurring in riparian zones and hillslopes, as they extract water from deeper soil layers through a well-developed root system [7]. Plant-water rela‐ tions of several dominant fynbos species were investigated [8], where it was demonstrat‐ ed that deep-rooted and isohydric species of fynbos tolerate drought better than shallowrooted and anisohidric species. Rhenosterbos (*Elytropappus Rhinocerotis*) and its impacts

> © 2013 Jovanovic et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2013 Jovanovic et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

