Assessing Calibration Uncertainty and Automation for Estimating ...

JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION Vol. 49, No. 3

AMERICAN WATER RESOURCES ASSOCIATION June 2013

ASSESSING CALIBRATION UNCERTAINTY AND AUTOMATION FOR ESTIMATING EVAPOTRANSPIRATION FROM AGRICULTURAL AREAS USING METRIC1

Charles G. Morton, Justin L. Huntington, Greg M. Pohll, Richard G. Allen, Kenneth C. McGwire, and Scott D. Bassett2

ABSTRACT: Agricultural irrigation accounts for a large fraction of the total water use in the western United States. The Mapping Evapotranspiration at high Resolution with Internalized Calibration (METRIC) remote sensing energy balance model is being used to estimate historical agricultural water use in western Nevada to evaluate basin-wide water budgets. Each METRIC evapotranspiration (ET) estimate must be calibrated by a trained user, which requires some iterative time investment and results in variation in ET estimates between users. An automated calibration algorithm for the METRIC model was designed to generate ET estimates comparable to those from trained users by mimicking the manual calibration process. Automated calibration allows for rapid generation of METRIC ET estimates with minimal manual intervention, as well as uncertainty and sensitivity analysis of the model. The variation in ET estimates generated by the automated calibration algorithm was found to be similar to the variation in manual ET estimates. Results indicate that uncertainty was highest for fields with low ET levels and lowest for fields with high ET levels, with a seasonal mean uncertainty of approximately 5% for all fields. In addition, in a blind comparison, automated daily and seasonal ET estimates compared well with flux tower measurement ET data at multiple sites. Automated methods can generate first-order ET estimates that are similar to time intensive manual efforts with less time investment. (KEY TERMS: evapotranspiration; uncertainty analysis; remote sensing; surface energy balance.) Morton, Charles G., Justin L. Huntington, Greg M. Pohll, Richard G. Allen, Kenneth C. McGwire, and Scott D. Bassett, 2013. Assessing Calibration Uncertainty and Automation for Estimating Evapotranspiration from Agricultural Areas Using METRIC. Journal of the American Water Resources Association (JAWRA) 49(3): 549-562. DOI: 10.1111/jawr.12054

piration (ET) from irrigated lands as increasing demands are placed on finite water supplies. Local, state, and federal water resource agencies in Nevada and across the western United States (U.S.) require accurate ET estimates for evaluating basin water budgets, water resource modeling, transfers of irrigation

INTRODUCTION

Irrigation accounts for over 80% of all the water rights in Nevada. As such, it is important to accurately estimate water use in the form of evapotrans-

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Paper No. JAWRA-12-0110-P of the Journal of the American Water Resources Association (JAWRA). Received May 4, 2012; accepted February 20, 2013. © 2013 American Water Resources Association. Discussions are open until six months from print publication. 2 Respectively, Staff Research Scientist (Morton), Division of Earth and Ecosystem Science, Desert Research Institute, 2215 Raggio Parkway, Reno, Nevada 89512; Assistant Research Professor (Huntington), Research Professor (Pohll), Division of Hydrologic Sciences, Desert Research Institute, Reno, Nevada; Research Professor (Allen), Department of Biological and Agricultural Engineering, University of Idaho, Kimberly, Idaho; Associate Research Professor (McGwire), Division of Earth and Ecosystem Science, Desert Research Institute, Reno, Nevada; and Assistant Professor (Bassett), Department of Geography, University of Nevada, Reno, Nevada (E-Mail/Morton: charles. [email protected]).

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generated much more quickly for a large number of Landsat images, either over a long time period or for a large area. Automation allows for more efficient operational ET estimates that would save time and cost. In addition, automated calibration methods can allow for more thorough testing of the uncertainty and sensitivity of the METRIC model. Typically, each METRIC derived ET estimate for a single Landsat TM scene is made by a single user, which makes it difficult to directly assess the uncertainty in ET estimates caused by model error as opposed to those caused by user error. METRIC ET estimates derived from a limited number of users can provide an initial indication of the uncertainty in estimated ET; however, additional independent calibrations are required to accurately characterize the uncertainty. An automated calibration algorithm was developed to generate a large number of calibrations comparable to those from an existing user population. The automated calibration algorithm was parameterized using statistics from manually calibrated images from six users covering multiple years and Landsat TM scenes in western Nevada. An additional set of calibrations for a single year made by five users was reserved to independently assess how well the automated calibration algorithm captured the variation of ET among different user calibrations. Finally, to test the accuracy of the automated method, automatically calibrated daily and seasonal ET estimates were compared to ET measurements derived from Bowen ratio and eddy correlation micrometeorological stations at multiple sites in Mason Valley and Carson Valley, Nevada (Figure 1).

water for municipal use, and negotiation and litigation of water right permits and applications (Huntington and Allen, 2010). The Nevada Division of Water Resources and the Desert Research Institute are working to develop accurate estimates of actual historical consumptive water use (i.e., ET) from irrigated lands in western Nevada (Figure 1). ET is being estimated from Landsat Thematic Mapper (TM) satellite imagery using the Mapping Evapotranspiration at high Resolution with Internalized Calibration (METRIC) model (Allen et al., 2007b). A constraint in applying the current METRIC model is the requirement for a calibration process, which requires human oversight and can require significant time investment, especially for new users. Currently, trained users must calibrate the METRIC model for each Landsat TM image, where the calibrations among users are independent and therefore not identical. Also, if any changes are made to the METRIC input parameters, data, or models, the ET estimate may need to be recalibrated. This article describes an automated calibration algorithm for the METRIC model that can be used to characterize the uncertainty in ET estimates in agricultural areas introduced from calibration by different users, and to explore the potential of using METRIC more efficiently in operational ET estimates. This automated approach allows METRIC ET estimates to be

BACKGROUND

Evapotranspiration can be measured at a point scale using weighing lysimeters, energy balance Bowen ratio, or micrometeorological eddy correlation techniques. Agricultural fields do not all have similar water availability, crop type, soil type, cutting cycles, and farming and irrigation practice, so a single, point-scale ET estimate will not capture all of the variation in ET over a basin or region. Reference ET (ETr) and crop coefficient (Kc) curves are commonly used to estimate ET based on the potential ET, crop type, and crop stage (Allen et al., 1998; Allen et al., 2005a). The ETr and Kc curve approach is representative of a crop grown under optimal water supply and soil conditions, and therefore may not be representative of actual conditions, especially under conditions of water stress, salinity, or disease (Tasumi et al., 2005a; Allen et al., 2007b).

FIGURE 1. Study Area Map Showing the Agricultural Areas, Measured Evapotranspiration (ET) Sites, and the Fallon AgriMet Site.

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ESTIMATING EVAPOTRANSPIRATION

Remotely sensed measurements of the visible and infrared wavelengths of the electromagnetic spectrum from satellites or aircraft can be used to estimate ET over large areas. Accuracy of these estimates can be limited by the resolution of the sensor, multiday time interval between measurements, scattering and absorption of radiation by the atmosphere, and difficulty in estimating the turbulent fluxes that impact ET. The simplest approaches empirically correlate ET to a parameter that can be measured by a satellite sensor, such as surface temperature (TS) or a vegetation index such as the Normalized Difference Vegetation Index (NDVI) (Glenn et al., 2007; Senay et al., 2007; Groeneveld et al., 2007). While temperature and vegetation index approaches are useful in their simplicity, their accuracy is limited because vegetation index approaches do not account for evaporation from the soil, and temperature approaches omit the impacts of albedo, aerodynamic roughness, and ground heat flux. These drawbacks may create error and bias in estimates where accurate quantification is needed. In contrast, remotely sensed shortwave and thermal data can be used to estimate ET as the residual of the full surface energy balance (SEB) kE ¼ Rn G H

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would be possible given the available energy (Rn G). The METRIC model is generally applied using Landsat 5 TM or Landsat 7 Enhanced Thematic Mapper Plus (ETM+) satellite imagery. The TM and ETM+ images have a 30 m visible and shortwave pixel size while the thermal band pixel size is 120 m for TM and 60 m for ETM+, which makes it well suited for estimating ET from individual agricultural fields in the western U.S. Landsat 5 and Landsat 7 each have a 16-day return cycle which, especially in the arid western U.S., typically provides adequate images during the growing cycle to capture crop green up and harvesting cycles such as alfalfa cuttings. The only other data needed to run METRIC are a digital elevation model (DEM), a general land use map, and hourly or daily weather data to compute ETr. A detailed description of the METRIC model and applications can be found in Allen et al. (2007a, b). To solve for kE in Equation (1), Rn and G are first estimated from the Landsat imagery, DEM, and land use map. H is then estimated using a one-dimensional bulk aerodynamic function H¼

ð1Þ

qcp dT rah

ð2Þ

where q is the air density (kg/m3), cp is the specific heat of air at constant pressure (J/kg K), dT is the vertical near surface temperature difference (K), and rah is the aerodynamic resistance (s/m). The sensible heat flux (H) is estimated by calculating dT for each pixel as a linear function of TS. To develop the dT vs. TS relationship that calibrates the METRIC model, a trained user applies the Calibration using InverseModeling at Extreme Conditions (CIMEC) procedure (Allen et al., 2007b, 2011) by selecting two anchor points where kE is known so that Equation (1) can be solved for H and then Equation (2) can be inverted to solve for dT. The “cold pixel” calibration anchor point is identified in an agricultural field having full vegetation cover where essentially all available energy (Rn G) goes to evaporative cooling. Typically, the ET rate at the cold pixel is set 5% greater than the ETr because the ETr does not account for ET from a wet canopy or soil, for example due to recent irrigation (Tasumi et al., 2005a; Allen et al., 2007b). The “hot pixel” calibration anchor point is identified in a bare agricultural field having little or no vegetation cover where there is little evaporative cooling and substantial surface heating. Typically the ET rate at the hot pixel is set as 0-10% of the ETr for a dry condition to account for residual soil moisture, especially when located in an agricultural field, which is required to best match soil heat flux algorithms used

where kE is the latent heat flux consumed by ET (W/ m2), Rn is the net radiation from the sun, atmosphere, and surface (W/m2), G is the heat flux into the ground (W/m2), and H is the sensible heat flux to the air (W/m2). One such model, the Surface Energy Balance Algorithm for Land (SEBAL) developed by Bastiaanssen (1995), has been tested and widely applied (Bastiaanssen et al., 1998a, b; Bastiaanssen, 2000; Bastiaanssen et al., 2005). A thorough review of the different SEB approaches for estimating ET is given by Kalma et al. (2008). The METRIC model is a remotely sensed energy balance approach for estimating ET that has been extensively applied for water management in the western U.S. It was developed by the University of Idaho in conjunction with the Idaho Department of Water Resources to support water management, hydrologic modeling, and water rights transfers throughout Idaho (Allen et al., 2005b; Tasumi et al., 2005b; Allen et al., 2007a). METRIC was derived from SEBAL, however, it relies on local weather data to calibrate and interpolate ET estimates in time using an alfalfa ETr, which is calculated hourly with the ASCE standardized Penman-Monteith equation (ASCE-EWRI, 2005). The use of ETr for calibration in METRIC is desirable in semiarid and arid climates because advection of warm air from surrounding dry areas can result in more ET from irrigated fields than JOURNAL

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ETinst ETr 24 ETr

ð3Þ

where the ratio of ETinst (mm) to ETr (mm) is the reference ET fraction (ETrF) measured at the satellite overpass time and ETr24 is the cumulative ETr for the day (mm). The ETrF is equivalent to the Kc and is assumed to remain relatively constant throughout the day (Allen et al., 2007b). The use of ETr to extrapolate daily ET from ETinst, as well as to compute seasonal ET from the daily ET is advantageous because ETr accounts for hourly and daily changes in solar radiation, wind speed, and vapor pressure deficit. In addition, ETr is commonly used by water managers in the western U.S. (Allen et al., 2007b). METRIC has been applied in the states of Idaho, California, New Mexico, Montana, Nebraska, Wyoming, Texas, Florida, Colorado, Nevada, and Oregon to produce field-scale ET information needed for water rights management and hydrologic studies (Allen et al., 2007a; Anderson et al., 2012).

DATA

The METRIC ET estimates from six trained users were used to parameterize and test the user-based automated calibration algorithm. Three of the users were students who were recently trained in applying METRIC, and three were more experienced in METRIC background and applications, ET measurement, and ET estimation. This pool of users is representative of the different types of users and experience levels that would likely be applying the METRIC model. METRIC ET estimates were derived for TM and ETM+ images from multiple years for the Fallon/ Mason Valley study area and the Mason Valley/Smith Valley study area (Figure 1). For each run of METRIC, ETrF values for all agricultural pixels within the study areas were statistically analyzed to develop the automated algorithm. ET estimates made by five trained users for a single year (2006) for the Fallon/ Mason Valley study areas were withheld for subsequent validation of the method. Evapotranspiration data measured by Maurer et al. (2006) at six sites in Carson Valley (Figure 1) were used to compare and validate ET derived with the automated algorithm. ET measurements for part of 2003 and the full growing season of 2004 were made using the Bowen ratio energy budget method at sites ET2, ET3, and ET8. ET measurements were also made during part of 2004 using the eddy correlation method at sites ET4, ET5, ET6, and ET8. Sites ET2 and ET5 are flood-irrigated alfalfa fields, sites ET3, ET4, and ET8 are flood-irrigated pasture, and site ET6 is a nonirrigated pasture. The Bowen ratio

STUDY AREA

The project study focused on agricultural areas in the Walker River and Carson River watersheds of western Nevada, principally in four areas: Fallon, Mason Valley, Smith Valley, and Carson Valley. Primary crops included alfalfa and pasture grass, with smaller acreages of corn, garlic, and onions. Riparian and phreatophytic shrub areas along the rivers’ corridors are primarily comprised of cottonwood, willow, greasewood, sagebrush, rabbitbrush, and bitterbrush. Most water for irrigation is supplied by Carson and Walker Rivers, although there is groundwater pumping to supplement surface water supplies in all four areas. Mean annual precipitation is approximately 15 cm/yr, with an average maximum temperature of JAWRA

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33°C occurring in July and average minimum of 8°C occurring in January. The typical growing season begins in late March to April, with killing frost occurring in late October to November. Three study areas and date ranges were selected based on Landsat scene footprints and the availability of measured agricultural ET data (Figure 1). The first study area included Mason Valley and Fallon and used path 42/row 33 TM imagery. The second study area included Mason Valley and Smith Valley and used path 43/row 33 TM imagery. Mason Valley and Smith Valley are positioned in the overlap of the two Landsat path footprints. This was taken as an opportunity to generate two separate seasonal estimates for each path/row rather than generating a single METRIC estimate with a higher temporal sampling. The third area was focused solely on the Carson Valley and used path 43/row 33 TM and ETM+ imagery.

in METRIC that were developed from agricultural data (Allen et al., 2007b, 2013). The CIMEC process factors out many of the biases in the energy balance, especially in TS. To balance Equation (1) at the calibration points when ET is set by the user, biases present in Rn G and TS are propagated into the dT vs. TS relationship so that H will equalize the SEB. The same dT vs. TS relationship is then used to calculate H for the entire image and much of the bias is subsequently canceled out of the final kE image (Allen et al., 2007b, 2011). The instantaneous ET (ETinst) estimate for each Landsat image is calculated via kE in Equation (1). For each image, daily ET (ET24) is calculated as ET24 ¼

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and eddy correlation daily ET measurements were assumed by Maurer et al. (2006) to be accurate to within 12% of actual ET rates based on literature and a direct comparison of Bowen ratio and eddy correlation measurements at site ET8 in the spring of 2004. Maurer et al. (2006) did not state how they addressed the closure error in the eddy correlation measurements. Bowen ratio ET data were collected in Mason Valley by Allander et al. (2009) at two sites for 2005 and 2006. Sites B01 and B11 were located near the middle of flood-irrigated alfalfa fields, however, site B01 was only irrigated in 2005 and was fallow in 2006. Uncertainty for the ET measurements was not reported for B01 and B11, however, it was assumed to be similar to the 12% uncertainty reported by Maurer et al. (2006). For both measured ET datasets, there were significant periods of missing data ranging from a few days (sites B11, ET3, and ET8) to multiple months (sites ET4, ET5, and ET6). Although periods of missing data were estimated by Maurer et al. (2006) and Allander et al. (2009), the estimated ET values were not used for this study and those dates were excluded from the daily and seasonal ET comparisons. For each of the study areas and years of image analysis, nonagricultural areas were masked using digitized field boundaries so that only agricultural areas were included in the analysis. A 120 m buffer of the outer edges of the fields was also masked to prevent contamination of thermal pixels by nonagricultural areas. Cloud and snow masks were applied to each scene so that only areas free of snow, clouds, and cloud shadows were analyzed. Individual yearly land use maps updated from the U.S. Geological Survey (USGS) 2006 National Land Cover Dataset were used for estimating the surface roughness in METRIC. Hourly ETr computed using measured solar radiation, temperature, humidity, and wind speed collected at the AgriMet site in Fallon, Nevada was used for all study areas and years. Rigorous quality assurance and quality control of weather data used to compute ETr was exercised following ASCE-EWRI (2005) and Allen et al. (2011).

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ETrF values, adjusting hot and cold pixel calibration points, and rerunning METRIC in a process similar to that of a trained user, so that the resulting distribution of ETrF is similar to the distributions derived from multiple users for the same image date (Figure 2). Both the manual and automated approaches assume that at least one field within the study area is at or exceeding the reference condition during the growing season, meaning it is at full cover, recently irrigated, and has an ETrF exceeding 1.0. The cold pixel calibration point is typically placed at a high ETrF pixel value, such as 1.0 or 1.05, so that only a small percentage of fields are greater than the reference, a condition that commonly exists in areas having wet soil and low albedo. The majority of fields have an ETrF less than 1.0 due to crop cuttings, growing cycles, water stress, or disease. Likewise, the hot pixel calibration point is typically placed at a low ETrF value, such as 0.05 or 0.1, as even bare agricultural fields will often have some minimal ET rate due to residual evaporation driven by negative matrix potential gradients, soil moisture redistribution, and diffusive processes near the surface (Allen et al., 2007b). The hot pixel calibration condition is not as well defined as the cold condition because there is considerable variation in the TS, NDVI, and albedo due to differences in soil type and condition, fallow vegetation cover, and soil moisture. A second assumption of the algorithm is that the majority of METRIC derived ET estimates from different users are all equally valid. For the majority of

METHODS

Automated Calibration Algorithm Development

FIGURE 2. Example of Reference Evapotranspiration Fraction (ETrF) Distributions from Five Trained Users for Day of Year (DOY) 169, 2006 for All Agricultural Pixels in the Study Area. Vertical bars indicate the ETrF calibration thresholds of 0.1 and 1.05. Tail size percentages are calculated as the percentage of agricultural pixels with ETrF values outside the calibration thresholds. For these five calibrations, the cold tail size percentages range from 0 to 2% while the hot tail size percentages range from 1 to 7.5%.

The algorithm computes the percentage of agricultural pixels with ETrF values outside fixed thresholds as the primary measure for adjusting the calibration. Each automated METRIC ET estimate is calibrated by iteratively checking the distribution of agricultural JOURNAL

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MORTON, HUNTINGTON, POHLL, ALLEN, MCGWIRE, scenes and study areas, there were no measured ET data to compare against user ET estimates. Even when ET measurements existed, the combination of measurement errors, data gaps, and limited number of sampling sites made it difficult to directly assess the accuracy of each suite of ET estimates. Figure 2 shows an example of the estimated agricultural ETrF distributions for a single Landsat TM scene from five users. As the figure indicates, there were significant variations in the ETrF distributions, even between trained users of the METRIC model. A third assumption is that for all ETrF distributions from multiple users, the percentage of agricultural pixels with ETrF values outside fixed thresholds will be relatively constant across image dates and study areas, as will be shown later. Visually, this percentage is represented as tail sizes at the extremes of the ETrF distribution. Figure 2 shows how the tails of the ETrF distributions compare for the five users and indicates the range of the percentage of the agricultural pixels with ETrF values outside the fixed calibration thresholds of 0.1 and 1.05. As Figure 2 illustrates, users can generate a range of different calibrations for the same scene, and the tail size percentages are a measure of that variation. The automated approach was based on distributions at the tails because it is similar to how a user would typically assess a METRIC calibration by considering the number of fields with ETrF values that fell outside the typical ETrF ranges. The thresholds on ETrF were set to 0.1 and 1.05, as these values are commonly assigned to calibrate scenes during the growing season (Allen et al., 2011). Because calibrations and ET estimates were derived from multiple users, seasons, years, and different Landsat scenes, an opportunity existed to test whether the third assumption, that the tail size percentages were constant during the growing season, was appropriate. Figure 3 illustrates the distribution of hot and cold tail size percentages by month for the existing user calibrations. It is evident from Figure 3 that for periods outside the April 1st-October 31st growing season, the tail size percentages were larger and more varied. Based on Figure 3 and to ensure the assumptions of the METRIC model were supported (Allen et al., 2007b), the calibrations for dates that were outside April 1-October 31 were excluded. The spread of the remaining user calibration tail size percentages is fairly consistent throughout the growing season months (Figure 3). Therefore, it was concluded that a single hot and cold tail size distribution could be tested for application to the entire growing season. These calibrations were used to develop separate empirical cumulative distribution functions (CDFs) for hot and cold pixel tail sizes (Figure 4). This JAWRA

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FIGURE 3. Boxplots of User Cold (a) and Hot (b) Calibration Tail Size Percentages by Month. The number of user calibrations are also listed below each month. Only calibrations that were within the April 1-October 31 growing season were used to parameterize the automated calibration algorithm.

empirical CDF describes the proportion of a population whose values are less than a given value. The empirical CDFs were generated by sorting the tail size percentage values and then calculating the probability as the position of each value in the sorted list divided by the total number of values. As Figure 4 illustrates, for about 80% of the calibrations, generally 0-2% of agricultural pixels exceed the 1.05 threshold and 0-8% lie below the 0.1 thresholds. Although fields can have an ETrF greater than 1.05 (Allen et al., 2007b), the approximately 20% of calibrations that have more than 2% of agricultural 554

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pixels outside the 1.05 threshold (Figure 4) are likely caused by inexperienced users. For generating final ET estimates, these calibrations would be either removed or recalibrated, but they were intentionally included in this project to capture the variation in calibrations from our pool of users. The hot calibration tail sizes tended to have more variation than the cold calibration tail sizes, which is likely a result of the hot calibration condition not being as well defined. The physical reasons for this are discussed later. For each Landsat scene, the automated method selects initial calibration points based on simple NDVI and TS thresholds similar to the procedures outlined by Allen et al. (2013). First, the buffered and masked digitized field boundaries are used to specify an area of interest (AOI) instead of AOI steps 1 and 2 by Allen et al. (2013). Then, steps 1-3 for the cold calibration point and steps 1, 2, and 4 for the hot calibration point from Allen et al. (2013) are applied to generate regions of suitable calibration point locations. Within each region, a random point is selected and assigned as the initial calibration point. As long as the initial calibration points satisfy the basic NDVI and TS criteria of Allen et al. (2013), they will generate a suitable initial ETrF for further processing by the automated algorithm. METRIC is run using these initial calibration points to produce an initial ETrF map of the study area. After identifying initial calibration points for each Landsat scene, a Monte Carlo simulation approach is used to generate unique ET estimates. For each Monte Carlo iteration, the automated method selects target hot and cold pixel tail sizes by randomly OF THE



generating probability values of 0-1 from a uniform distribution and assigning the corresponding target tail size percentage from the CDFs generated from the users (Figure 4). In an iterative process (Figure 5), the method calculates the target ETrF values corresponding to the target tail sizes in the ETrF distribution, selects new hot and cold pixel locations with the target ETrF value, runs METRIC, and checks the tail sizes of the resulting distribution of agricultural ETrF values until the tail size percentages are within 0.1% of the target thresholds selected from Figure 4. The first iteration typically resulted in values within 1% of the targets, while the second iteration was typically within 0.1%. To ensure that the calibration points are at reasonable locations, the algorithm forced the cold calibration point to be at pixels with an NDVI greater than 0.4. This was primarily done to avoid placing the cold calibration point in flooded fields that had low NDVI with an ETrF potentially much greater than the reference of 1.05 due to low albedo and TS. Based on the existing user calibrations, no user selected a cold calibration pixel with an NDVI value less than 0.56. The NDVI threshold of 0.4 used by the algorithm is intentionally set below the user calibration NDVI minimum of 0.56 so that the algorithm has flexibility in finding calibration point locations that resulted in the target tail size percentages while maintaining realistic calibration point conditions (i.e., not associated with flooded fields). Cold calibration pixels with relatively low NDVI values (