**2.3. Calculation of seasonal ET**

The splining of ETrF between image dates was done using an ERDAS Modelmaker code that implemented a standard cubic spline algorithm. The spline function produced a continuous curvilinear function for each pixel between each date that was continuous in both first and second derivatives. The function intersected each pixel data point. Daily reference ET (ETr) for the splining was computed from daily weather data obtained from the Twin Falls, Idaho Agrimet automated weather station for year 2000 for the Idaho study. For Nebraska, daily ETr was computed using hourly weather data from the 23 weather stations obtained from the High Plains Regional Climate Center (HPRCC) Automated Weather Data Network (AWDN), where a daily ETr surface was computed using cubic spline interpolation. In all cases, ETr was calculated using the ASCE (2005) standardized Penman-Monteith alfalfa reference ET equation [21–24], and that same equation had been originally used to calibrate the METRIC model during the production of ETrF.

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**Table 1.**

*platform.*

*Influence of Landsat Revisit Frequency on Time-Integration of Evapotranspiration…*

**integration using both paths and landsats**

L7 \* \*

L7 \* \*

L7 \* \*

L7 \* \*

L7 \* \*

L7 \* \*

L7 \* \*

L7 \* \*

L7 \* \*

L7 \* \*

L7 \* \*

L7 \* \*

*Asterisks indicate the dates used in a particular integration run to estimate monthly and growing season ET.\*\*In this run, two synthetic ETrF images were created using constant values and placed at dates November 01, 2000 (ETrF = 0.25) and November 10, 2000 (ETrF = 0.1) to provide endpoints for the cubic spline. \*\*\*In this run, four synthetic images were created using constant values and placed at dates March 20, 2000 (ETrF = 0.1); March 31, 2000 (ETrF = 0.1); November 01, 2000 (ETrF = 0.25) and November 10, 2000 (ETrF = 0.1) to provide* 

*Selection of Landsat images used to time-integrate ET for the Idaho study area, showing collection path and* 

L7 \* \*

**Run 2: Time integration using path 39 and both landsats\*\***

L5 \* \* \*

L5 \* \* \*

L5 \* \* \*

L5 \* \* \*

L5 \* \* \*

L5 \* \* \*

L5 \* \* \*

**Run 3: Time integration using path 40 and both landsats**

**Run 4: Time integration using path 40 and landsat L5\*\*\***

*DOI: http://dx.doi.org/10.5772/intechopen.80946*

1 April 01, 2000

2 April 08, 2000

3 May 02, 2000

4 May 03, 2000

5 June 03, 2000

6 June 04, 2000

7 June 19, 2000

8 June 20, 2000

9 July 05, 2000

10 July 21, 2000

11 July 22, 2000

13 August 07, 2000

14 August 14, 2000

15 August 22, 2000

16 August 23, 2000

17 September 07, 2000

18 September 08, 2000

19 September 15, 2008

20 September 16, 2000

21 October 17, 2000

*endpoints for the cubic spline.*

**Dates Sensor Run 1: Time** 


*Influence of Landsat Revisit Frequency on Time-Integration of Evapotranspiration… DOI: http://dx.doi.org/10.5772/intechopen.80946*

*Asterisks indicate the dates used in a particular integration run to estimate monthly and growing season ET.\*\*In this run, two synthetic ETrF images were created using constant values and placed at dates November 01, 2000* 

*(ETrF = 0.25) and November 10, 2000 (ETrF = 0.1) to provide endpoints for the cubic spline. \*\*\*In this run, four synthetic images were created using constant values and placed at dates March 20, 2000 (ETrF = 0.1); March 31, 2000 (ETrF = 0.1); November 01, 2000 (ETrF = 0.25) and November 10, 2000 (ETrF = 0.1) to provide endpoints for the cubic spline.*

**Table 1.**

*Selection of Landsat images used to time-integrate ET for the Idaho study area, showing collection path and platform.*

*Advanced Evapotranspiration Methods and Applications*

*irrigated fields are fields using primarily ground water a water source.*

that had not been processed by METRIC due to the close coincidence of other clear images in time. An example is June 28, 2000 for path 39, which was not processed. Therefore, the list of images in **Table 1** is not all inclusive. However, the absence of images should not impact the accuracy of the baseline estimation of timeintegrated ET because there are sufficient data points to afford a relatively accurate

*Close-up view of the Nebraska study area extent. The white line is the Central Platte NRD boundary. Bright red areas are cultivated fields and the lighter areas are rangeland. The areas of high densities of fields are irrigated areas along the Platte River, which is visible along the southern boundary of the Central Platte NRD. Those fields utilize a combination of ground water and surface water. Areas of more sparse densities of* 

**Table 2** lists the selection of Landsat images used to time-integrate ET in the Nebraska study area. As with the Idaho study area, year 2002 was selected for analysis because it was a year when both Landsat 5 and 7 satellites were in operation and fully functioning. Asterisks in **Table 2** indicate dates that they were used in a

Most of the imagery listed were clear images for the small study area and did not require mitigation for clouds. The exceptions were June 27, 2002 and August 6, 2002 from path 30, with both images having significant cloud cover over the study area. Cloud-covered areas in the imagery were masked out by manually tracing around the cloud areas and filling those cloud areas with a value recognizable in the timeintegration models as invalid. The masked out areas were replaced with data from a previous or following image date during the spline function in the time-integration.

particular integration run to estimate monthly and growing season ET.

The splining of ETrF between image dates was done using an ERDAS Modelmaker code that implemented a standard cubic spline algorithm. The spline function produced a continuous curvilinear function for each pixel between each date that was continuous in both first and second derivatives. The function intersected each pixel data point. Daily reference ET (ETr) for the splining was computed from daily weather data obtained from the Twin Falls, Idaho Agrimet automated weather station for year 2000 for the Idaho study. For Nebraska, daily ETr was computed using hourly weather data from the 23 weather stations obtained from the High Plains Regional Climate Center (HPRCC) Automated Weather Data Network (AWDN), where a daily ETr surface was computed using cubic spline interpolation. In all cases, ETr was calculated using the ASCE (2005) standardized Penman-Monteith alfalfa reference ET equation [21–24], and that same equation had been originally used to calibrate the METRIC model during the production of ETrF.

**54**

interpolation.

**Figure 4.**

**2.3. Calculation of seasonal ET**


#### **Table 2.**

*Selection of Landsat images used to time-integrate ET for the Nebraska study area, showing collection path and platform.*

Three to four integration runs were made for the study areas, as described in the next section. The integration runs utilized (1) both Landsat 5 and 7 imagery from both paths; (2) both Landsat 5 and 7 imagery from one path or the other; and

**57**

agriculture.

*Influence of Landsat Revisit Frequency on Time-Integration of Evapotranspiration…*

(3) imagery from only one Landsat 5 from one path only. The first integration run approximated a condition, where four images are collected each 16 days. This is a condition that would occur with four Landsat satellites in orbit with the current path width or with two Landsat satellites in orbit, each having a 'double-wide' path of approximately 300 km. The second and third integration runs approximated the condition where two currently formulated Landsats are in orbit at any one time, for the center of a WRS path. The last condition represents the condition, where only

In the Idaho study area, ET was integrated over the April 1–October 31 period to form monthly ET for April through October. The absence of clear images for the study area during late March and early April and during late October and early November for some of the time integration runs required the use of 'synthetic' images to represent ET conditions during these periods. The synthetic images were required to anchor the spline function prior to April and following October. The synthetic images were created for the Idaho study area by applying a daily soil water balance model for a bare soil condition [11] representing surface conditions during Idaho winters and late falls, where nearly all vegetation is dormant due to freezing. The daily soil water balance model used the FAO-56 evaporation model [11] and was applied to 18 weather stations in the region and an evaporation surface was created using inverse distance interpolation. The average ETrF during the late March to early April and from late October to early November periods was determined by averaging the simulated evaporation rates over those periods. Those synthetic images were then used as beginning and ending points for the spline interpolation

No synthetic images were required for the full two-Landsat/two-path integration for the Idaho study area, as sufficient image dates during early April and late October were available. In the double satellite/single path integration, however, synthetic ETrF images were required at the end of the growing season to provide endpoints for the cubic spline, and were placed on dates November 01, 2000 (ETrF averaged 0.25) and November 10, 2000 (ETrF averaged 0.1). For the run using only Landsat 5 data and for path 40 only, synthetic images were required at both the beginning and end of the growing season. In this run, four synthetic images were placed on dates March 20, 2000 (ETrF averaged 0.1); March 31, 2000 (ETrF averaged 0.1); November 01, 2000 (ETrF averaged 0.25); and November 10, 2000 (ETrF

For the Nebraska study area, ET was integrated over the May–September period, representing the shorter growing season for the predominately corn and soybean crop rotation there, as opposed to the April–October growing period for Idaho crops. As with Idaho, ETrF for bare soil was also estimated for the Nebraska study area using the FAO-56 style evaporation model for the purpose of creating synthetic images for April 1, April 15, October 15, and November 15. These dates and synthetic images were used in each of the time-integration analyses to approximate ET conditions during those general periods so that the spline function could be applied

In both study areas, about 1500 data points were sampled. The points were selected from the interiors of irrigated fields, with one point per field. Pixels were located far from field edges to avoid contamination of thermal pixels from thermal information from outside the field. Nearly all of the Idaho sample locations were in agricultural fields, with about 15 sample points taken from desert rangeland. Irrigated agriculture was emphasized in this study due to its importance in water resources management. In the Nebraska data set, about 100 sample pixels were selected from rangeland and riparian areas each. The rest were from irrigated

averaged 0.1) to provide endpoints for the cubic spline.

with spans covering May–September.

*DOI: http://dx.doi.org/10.5772/intechopen.80946*

one Landsat satellite is in orbit.

process.
