Validation and Bias Correction of Forecast Reference Evapotranspiration for Agricultural Applications in Nevada | Journal of Water Resources Planning and Management | Vol 148, No 11

IntroductionThe 2017 Census of Agriculture stated that the total area of irrigated land in the US is approximately 23 million ha (58 million acres) (NASS 2019); the associated water rights are worth over $200 billion (Allen et al. 2015). Accurate operational estimates of agricultural evapotranspiration (ET) are therefore a national necessity. Further, the western US faces increasing pressure to conserve water and reduce consumptive water use in the face of prolonged drought and a changing climate (Blumler 2018). Because irrigated agriculture consumes most permitted water rights in the western US (Dieter et al. 2018), the biggest opportunity to save water is through reducing consumptive uses of irrigation, particularly through the use of new technologies such as in situ field monitoring, high-resolution weather forecasts, and precision irrigation systems (Allmaras et al. 2018).Accurately measuring ET to estimate consumptive use can be difficult and expensive, so most agricultural regions lack actual ET measurements. To overcome this limitation, reference evapotranspiration (ET0) is commonly used to estimate actual ET in support of irrigation scheduling (Hobbins and Huntington 2016). A form of evaporative demand, ET0 is parameterized to represent the ET from a well-watered reference crop (Allen et al. 2005), and it is generated from local weather data observations of temperature, humidity, wind speed, and solar radiation. The generated values are then used as an evaporative index to permit decision makers such as engineers, hydrologists, and water managers to predict ET for agricultural areas that are well-watered (Allen et al. 2005). For agricultural applications, accurate forecasts of ET can help support and complement conservation efforts by identifying optimal times and days for irrigation, optimizing application amounts, and providing for data-informed deficit irrigation.Global weather forecast models provide the variables needed to compute ET0, but at too coarse a spatial resolution for agricultural applications, necessitating downscaling (e.g., Tian and Martinez 2014). Gridded high-resolution (5 km) forecasts of meteorological variables from the National Weather Service (NWS 2018) were first produced in 2003 with the development of the National Digital Forecast Database (NDFD) (Glahn and Ruth 2003); the forecast reference evapotranspiration (FRET) was added as an operational output variable in 2016. However, thus far, studies validating FRET have been limited to California (Krone-Davis et al. 2012; Hamouda et al. 2022) and New Mexico (Engle et al. 2019) and have focused on annual or seasonal comparison with observations, and these studies have yet to assess the individual drivers used to compute FRET.Weather forecasts in general do not assimilate agricultural land information into their modeling systems. Irrigation increases ET and affects land surface-atmospheric feedbacks (Ozdogan and Rodell 2010). Even in highly advective arid environments, land surface-atmospheric feedbacks and near-surface boundary layer conditioning within irrigated areas has been well-documented (Allen et al. 1983; Temesgen et al. 1999; Szilagyi and Schepers 2014; Huntington et al. 2015, 2018). The near-surface (i.e., 2-m) air temperature is lower, humidity is higher, and wind speeds are lower in irrigated areas than in surrounding arid landscapes. These differences are typical when comparing reanalysis data with agricultural weather station–derived variables and ET0 (Lewis et al. 2014; Blankenau 2017).They also follow well-known complementary theory, where an increase in actual ET results in a decrease in evaporative demand (i.e., ET0) (Brutsaert and Parlange 1998; Hobbins et al. 2004; Hobbins and Huntington 2016). Abatzoglou (2011) also noted a positive bias in ET0 derived from a reanalysis hybrid of the North American Land Data Assimilation System (NLDAS) (Mitchell et al. 2004) and the Parameter Regression on Independent Slopes Model (PRISM) (Daly et al. 2002) when compared with ET0 computed from data collected from US Bureau of Reclamation’s AgriMET stations in the US Pacific Northwest. Despite this common knowledge within the ET community, researchers and practitioners routinely and erroneously apply reference ET equations to estimate well-watered reference and potential crop ET using ambient weather data representative of water-limited arid conditions, rather than using weather data representative of local agricultural conditions. This practice can lead to excess irrigation and wasted water supply.A bias-corrected FRET product has the potential to reduce avoidable nonbeneficial consumptive uses by informing irrigators when to vary the application rate of conventional high-pressure or newer low-energy precision application (LEPA) center-pivot irrigation systems, when to turn the irrigation systems off completely on days when ET0 is forecast to be low or to continue application on days where ET0 is forecast to be high (M. P. Plaskett, personal communication, 2019). Current practice in Nevada is to run conventional irrigation systems at constant speeds and pumping rates throughout the day. Therefore, integrating the 7-day FRET into irrigation management and operations and implementing LEPA systems has the greatest potential to reduce application rates and nonbeneficial consumptive uses beyond typical reported values of 20% to 30% (Lyle and Bordovsky 1983; Fipps and New 1990; Rajan et al. 2015).In this study, we examine the forecast skill of FRET and NDFD compared against agricultural weather station observations in Nevada. We build upon existing studies that have assessed FRET by (1) using the individual NDFD ET0 drivers to determine which variables are contributing most to forecast errors, (2) performing comparisons monthly (as opposed to seasonal or annual), and (3) providing a method to apply a bias-correction to ET0 forecasts. First, the collection of ET0 observations and data QC is described, followed by a description of NDFD and FRET. Then, we describe the results of the skill analysis over Nevada and provide a station-based case study. Finally, we show a comparison of the forecast errors before and after bias correction.Data and MethodsReference Evapotranspiration Observations and Quality ControlDaily weather observations were gathered from the Nevada Integrated Climate and Evapotranspiration Network (NICE Net, Desert Research Institute, n.d.-a) run by the Desert Research Institute (Fig. 1). The network consists of 18 agricultural weather stations located throughout Nevada and one station located in eastern California [Fig. 1(a)]. NICE Net stations were installed beginning in 2010 to collect weather data representative of agricultural areas in Nevada and enable a more accurate estimation of agricultural water use across the state. Stations are typically located on the edges of irrigated fields [Figs. 1(b and c)] to capture the modified near-surface boundary layer weather conditions associated with irrigated lands in arid regions. NICE Net stations collect measurements of solar radiation, air temperature at 2 m, relative humidity at 2 m, wind speed at 3 m, and precipitation, barometric pressure, and soil temperature and soil moisture at multiple depths. Daily records were downloaded for the period of record at each station. Station metadata can be found in Table 1.Table 1. NICE Net station metadataTable 1. NICE Net station metadataStation nameStation IDElevation (m)Station start dateMoapa ValleyNMOA399February 2010Mason WMANMAS1,319April 2010Truckee MeadowsNSPA1,338May 2010Pahranagat NWRNPWL983July 2010Carson ValleyNCVA1,426August 2010Smith ValleyNSMV1,489August 2010Snake ValleyNSNA1,579August 2010Rogers SpringNROG689September 2010Paradise ValleyNPVA1,341November 2010Sand Spring ValleyNSSV1,466December 2010Steptoe Valley NorthNSTV1,785March 2011Steptoe Valley WMANSWM1,966March 2011Antelope ValleyNANV1,485June 2011North Spring ValleyNSPA1,338June 2011Clover ValleyNCLV1,721September 2011Bridgeport ValleyCBVA1,980July 2012Hualapai FlatNHUA1,236October 2012Reese River ValleyNREE1,847May 2014Weather station data were subject to quality assurance and quality control (QAQC) following QAQC recommendations and guidelines of Allen (1996), Allen et al. (2011), and ASCE (Allen et al. 2005), which are specific to agricultural weather data. Weather data were visualized and QAQCed using open-source Python software developed by DRI (pyWeatherQAQC, Desert Research Institute, n.d.-b).Corrections for omissions of agricultural weather data are common and necessary prior to computing ET0 (Allen 1996; Allen et al. 2005, 2011). As a specific example, the pyranometer recording solar radiation data may experience frequent accumulations of debris on the lens, or it may experience voltage spikes, sensor drift, or local environmental obstructions (Allen 2008). The ASCE equation requires wind speeds for a 2-m height, so wind speeds measured at a 3-m height were logarithmically transformed following guidelines of Allen et al. (2005). Details of QAQC procedures and recommendations for best results are found within the code documentation (Desert Research Institute, n.d.-b).After completion of weather data QAQC, meteorological variables were used to compute ET0 using the ASCE standardized Penman-Monteith (ASCE-PM) reference ET equation (Allen et al. 2005) for a short-grass reference crop using open-source Python software developed by DRI called the ASCE Standardized Reference Evapotranspiration Script version 0.3.10 (Desert Research Institute, n.d.-b), and is defined as follows: (1) ET0=0.480Δ(Rn−G)+γCnT+273u2(es−ea)Δ+γ(1+Cdu2)where T = daily mean temperature at 2-m height (°C); u2 = daily mean wind speed at 2-m height (m s−1); Rn = daily average net radiation (MJ m−2 day−1); G = soil heat flux density (MJ m−2 day−1); es = daily mean saturation vapor pressure at 2-m height (kPa); ea = daily mean actual vapor pressure at 2-m height (kPa); Δ = slope of the saturation vapor pressure-temperature curve (kPa °C−1); γ = psychrometric constant (kPa °C−1); Cn=900  K mms3 Mg−1  day−1 for a short-grass reference; and Cd=0.34 m s−1 for a short-grass reference.Reference ET from the National Digital Forecast DatabaseIn 2003, the NWS began producing the NDFD (Glahn and Ruth 2003) to supplement the text-only forecasts previously available. NDFD provides continuous spatial grids across Contiguous United States (CONUS) that are mosaicked together from individual NWS Weather Forecast Offices at high resolution (5 km) with forecasts updated hourly and issued for lead times of 1–7 days. For applications such as forecasting ET0 for agricultural water-use estimates, the high spatial resolution of the NDFD is beneficial and eliminates the need to downscale. In 2016, the NWS began producing an operational FRET) (Hobbins 2010), computed from NDFD elements and based on ET0. The main issue with conducting a skill analysis of FRET is its short period of record (shorter than 5 years) and consequent small sample size. Most NICE Net stations have 8–10 years of data to compare against. Another limitation of using just FRET for a skill analysis is that biases and forecast errors cannot be attributed to the individual drivers of ET0. We therefore decided to compute ET0 offline based on NDFD elements to provide a more robust skill analysis and development of bias-correction factors, and to examine the skill and biases of the NDFD drivers of ET0. A comparison of FRET with the ET0 computed in this study from NDFD variables is presented in Fig. 2 and shows strong relationships between the two. For the main study results, we show ET0 computed offline using NDFD elements and show the FRET results in Appendix I.From the NDFD archive (Desert Research Institute, n.d.-b), we used daily maximum temperature (Tmax), daily minimum temperature (Tmin), wind speed at 10 m, percent sky cover, and vapor pressure extracted from the grid point nearest to each observing station. Forecast lead times of 1–6 days were evaluated. Calculations of ET0 were done in the same way as for observations, with the following exception: NDFD does not provide incoming shortwave radiation (Rin), so we had to estimate it from sky cover first. We followed the methods of Hobbins (2010) to estimate Rin to replicate the methods used in FRET calculations as follows: (2) Rin=Rtoa(1−asaCCdaily100)where Rtoa = extraterrestrial shortwave radiation estimated based on Walter et al. (2000); asa =calibrated constant (0.71); and CCdaily = mean cloud cover (%) during daylight hours estimated from Brutsaert (2013).Skill AnalysisForecasts of NDFD ET0 and the drivers were compared against observations to assess skill of the forecasts. Skill was assessed at leads 1–6 days and for each month of the year. Samples for skill analysis were grouped by using all days in each month for the period of record, which provided sample sizes of about 150–250 data points per month at each location. The following three statistical measures were used to gauge the skill of NDFD forecasts: the correlation coefficient (R) based on the Pearson correlation; root-mean square error (RMSE); and bias. Bias was computed as the difference (NDFD−Observations) for Tmax and Tmin and as the ratio (NDFD/Observations) for all other variables.Bias Correction of NDFD ET0 to Observed ET0We show how a bias-correction approach can be applied to NDFD ET0 forecasts. We did not bias-correct the individual drivers used to compute ET0; just the resultant ET0 values were bias-corrected. Bias ratios computed for each month and lead time were applied to NDFD ET0 forecasts at the daily time step. This method has been previously applied to bias-correct historical gridded weather data and gridded climate projections (Huntington et al. 2016, 2018). Forecasts and observations were pooled by month using the full period of record at each station point, and a mean ET0(ET0¯) was computed for each. The bias ratio (BR) for each month was then computed as follows: (3) BR=(ET0¯)NDFD(ET0¯)ObservedFor example, at Carson Valley (NCVA in Table 1) in June, there were at total of 235 observations (2010–2020); for each NDFD lead time, the (ET0¯) was computed over those 235 data points and divided by the station (ET0¯) for June. The bias-corrected data (ET0BC) for June would be obtained by dividing the NDFD daily forecasts (ET0NDFD) by the monthly BR(4) The RMSE for the original forecasts were then compared with the RMSE of the bias-corrected forecasts to examine improvements in the forecasted ET0 quantities.ResultsGrowing Season Forecast SkillThe correlation between NDFD and observed ET0 for each month (May–October) and lead time (1–6 days) is shown in Fig. 3. As expected, we found a general pattern of correlation decreasing at longer lead times. Forecasts in the month of May were the most skillful of all growing season months with R values of 0.7–0.9 during the first 4 days and a notable drop in skill for Days 5 and 6. The summer months, particularly July and August, showed a large drop in forecast skill at all lead times with R values rarely exceeding 0.7 and often in the 0.4–0.6 range even at a lead of 1 day. In September and October, skill improved again. The lower skill during July and August is concerning for agricultural applications given that climatologically, ET0 reaches a peak during these months and irrigation rates are highest. Results showing FRET compared with observations can be found in Appendix I.To examine possible sources of the lower correlations during summer, we used July as an example and plotted the correlations for ET0 along with all the drivers in Fig. 4. Overall, Tmax, solar radiation, and vapor pressure consistently had the strongest correlations, whereas Tmin and wind speed had the lowest correlations. This result shows that Tmin and wind speed were likely the main contributors to the degraded ET0 correlations.Fig. 5 shows the NDFD ET0 RMSE for each month (May–October) and lead time (1–6 days). RMSE generally increased with lead time, although for some stations, RMSE remained steady over all leads or even decreased. Like the correlation analysis, the RMSE was overall greatest during the summer months. For summer, when absolute values of ET0 were the highest, RMSE ranged from 0.65 to 1.96  mm/day. At some stations, high RMSE was found during all months and lead times, including Moapa Valley (NMOA), Reese River Valley (NREE), and Rogers Spring (NROG). Results showing FRET RMSE can be found in Appendix I.Maximum and minimum temperature biases for each month (and growing season mean) at a lead of 1 day are shown in Figs. 6(a and b). Because monthly bias patterns were similar at all lead times and indicate systematic bias in NDFD, we chose to focus on 1-day leads, which are likely the most applicable for agricultural applications. We found a distinct seasonal pattern in bias for both Tmax and Tmin. For Tmin, biases ranged from −0.53°C to +4.62°C, but were mostly positive (warm) with consistently larger values found during the growing season; for Tmax, biases ranged from −1.90°C to +1.83°C, with negative (cool) biases often found in October–April and positive (warm) biases during May–September. Warm Tmin biases during the growing season are due to NDFD not accounting for the well-watered and vegetated land-surface conditions at station locations, which leads to lower overnight temperatures than the surrounding arid landscapes of Nevada. Similarly, daytime high temperatures (Tmax) tend to be higher in arid landscapes than in irrigated areas. Scale mismatches between station and 5-km grid values will also inherently lead to gridded data biases that do not capture microclimates.Bias ratios for vapor pressure, wind speed, solar radiation, and ET0 for each month (and growing season mean) at a 1-day lead are shown in Figs. 6(c–f). Starting with vapor pressure [Fig. 6(c)], we found consistently low NDFD bias during the growing season. Some larger vapor pressure bias ratios were found to be less than 0.75 (25%); however, smaller biases of 0.9–1.0 (<10%) were more common. The low growing-season biases in NDFD reflect the general arid bias with lower humidity relative to observations. Wind speed biases [Fig. 6(d)] were variable, but NDFD wind speed was higher than observations for the most part. At several locations, we found wind speed bias ratios to consistently exceed 1.25 during all months. At other locations, wind speed biases were far more reasonable, remaining within ±10% of observations.Solar radiation [Fig. 6(e)] had the most consistent magnitude of biases when considering variations across all stations; biases were generally low, with a notably larger bias during the spring months. ET0 biases [Fig. 6(f)] (FRET results are given in Appendix I) were also quite variable but often fell within ±10% of observations during the growing season. Next, we present a case study for an individual station to help understand how each driver contributes to NDFD ET0 biases and errors.Smith Valley, Nevada, Case StudyThe Smith Valley NICE Net station (NSMV) is used next as a case study to examine contributions of forecast skill from individual drivers. A daily time series from July 2018 at NSMV is shown in Fig. 7 with the lead 1-day NDFD forecast overlaid. At the monthly scale, we found good agreement between the ET0 totals from observations (202 mm) and NDFD (207 mm). Although this is encouraging, it is the daily variations that will be most important to producers for irrigation scheduling. In general, observed ET0 variability seemed to be captured well, with an exception being July 20–22. A light precipitation event occurred on July 20 with 3.3 mm of rainfall observed. During this period, the observed ET0 declined to a minimum of 4.0  mm/day on July 20, whereas NDFD always exceeded 5.4  mm/day and showed no pronounced drop off. NDFD Tmax declined but not as sharply as observed, whereas NDFD Tmin showed a steady high bias.Observed Tmin variations earlier in the month were not well captured by NDFD. There was a large dip in observed solar radiation on July 20 (121  W/m2) due to clouds that NDFD did not capture (a similar situation occurred earlier in the month), which coincides with the ET0 minimum. Even if the sensitivity of ET0 to solar radiation is low, cloudy days not being well resolved in NDFD will impact other variables such as Tmax, Tmin, and vapor pressure, ultimately contributing to a less accurate forecast for that day.The coefficient of variation (COV) was computed by month (daily values averaged to the month) for ET0 and each driver and is shown in Fig. 8 for NSMV. We found that NDFD was able to capture the seasonal pattern of lowest ET0 variability in the summer months and highest during the winter, with NDFD consistently having less variability than observations throughout the entire year [Fig. 8(a)]. Of the five drivers of ET0, the closest match was for Tmax, with a difference within ±0%. NDFD Tmin also followed the observed seasonal COV cycle but was consistently much lower (20%–40%) than observed. Wind speed and solar radiation from NDFD also consistently varied less than observed values. The underprediction of Tmin, wind speed, and solar radiation COV is one factor in the reduction of forecast skill from NDFD. Results may vary at other sites (for example, at NMOA, wind speed is actually overpredicted) (Appendix II), but Tmin, wind speed, and solar radiation consistently drive the reductions in forecast skill.Forecast Skill Improvements with Bias CorrectionBias ratios computed for ET0 were applied to the NDFD ET0, and RMSE was recalculated using the bias-corrected results. Fig. 9 shows the change (%) in RMSE after the bias correction was applied (results using FRET are given in Appendix I). Decreases in RMSE were found at most locations with 5%–30% reductions in error common. Reese River Valley, Nevada (NREE), consistently had reductions in RMSE of >30% at all lead times for June–August with a 48%–50% reduction at leads of 1–3 days in June. Minor increases in error were found in some locations; these changes were negligible, with a maximum increase in RMSE of 0.73%.Results presented in Fig. 9 show RMSE for the period of record. This does not ensure that for a real-time forecast application every single bias-corrected value will improve. Some forecasts will improve, and others will get worse, but on average there should be improvements. Also, real-time forecasted values will be independent of the values used to compute the historical bias ratios shown here, which could slightly reduce the skill shown in this paper. These results suggest that, overall, a real-time application of a monthly bias-correction ratio to NDFD ET0 forecasts could improve estimates of ET0 quantities needed for accurate irrigation scheduling and water conservation.DiscussionThere are several caveats and limitations to the approach described here before it could be used in an operational agricultural application. First, we obtained observed weather data from agricultural weather stations that are representative of well-watered conditions found throughout irrigated western US farms. However, most farms do not have reliable weather stations to use for bias correction of forecasts. Although a potential solution is to use the bias-correction ratios based on the nearest weather station, many farms will still be tens or hundreds of kilometers away from these stations. A second option could be to use historical ET0 estimates from high-resolution gridded climate data (e.g., Abatzoglou 2011) that are bias-corrected to nearby agricultural weather stations to create farm-specific or even field-specific bias ratios.A limitation of NDFD and FRET is that forecasts are deterministic and provide no level of uncertainty or confidence. Although some users may prefer to see a single forecast value, there is strong support showing ensemble forecasts are more skillful than deterministic forecasts, especially at longer lead times (e.g., Zhu 2005; Gneiting and Raftery 2005; Boucher et al. 2011). Ensemble forecast systems are costly to run and time-consuming compared with a single deterministic run, which is one reason they are rarely run at high resolution over large domains. In the case of NDFD, its high spatial resolution and short lead times (1–5 days, where deterministic forecasts are comparable to ensemble means) used for irrigation scheduling might be sufficient. Future studies should compare ensemble and deterministic ET0 forecasts for agricultural applications.Intuitively, improving irrigation efficiency by using ET0 forecasts would also lead to less water loss in the form of ET. Paradoxically, improving irrigation efficiencies often causes an increase in ET, even though the amount of applied water decreases (Grafton et al. 2018; Ward and Pulido-Velazquez 2008). Understanding this irrigation-efficiency paradox requires a detailed look at the relationships among crop ET, irrigation uniformity, avoidable and unavoidable consumptive uses, and beneficial and nonbeneficial consumptive uses. Burt et al. (1997) examined these relationships and identified avoidable nonbeneficial consumptive uses, including bare-soil evaporation, sprinkler wind drift, and canopy-interception losses. These losses could be reduced with conversion to LEPA techniques (Lyle and Bordovsky 1981; Bordovsky 2019). However, converting to LEPA requires significant investment ($5,000–$20,000 per center pivot), and although the Nevada Department of Agriculture recently began a drought and water conservation grant program per recommendations by the Nevada Drought Forum (Drozdoff et al. 2015), conversion has been slow across the state, and it may take decades before it is the primary irrigation method from groundwater.From the perspective of agricultural producers, ET0 forecasts can be used for irrigation scheduling (e.g., Wang and Cai 2009; Anupoju et al. 2021; Hamouda et al. 2022). During periods of high ET0, water limited pivots (typically due to low well yield) can run nearly 24 h a day, 7 days a week to provide the crop with sufficient water. Knowledge of the coming week’s ET0 is useful information to help growers to apply the amount of water necessary to meet atmospheric demand but at the most efficient times of day. The grower will have confidence that enough water is provided for the coming week to satisfy the atmospheric demand while choosing the best times to irrigate such as at night or when wind speed is low.Summary and ConclusionsThis study provided an evaluation of ET0 forecasts derived from NDFD inputs and the FRET product compared with observations from the NICE Net. We also demonstrated the value of implementing a bias-correction method to improve RMSE. We showed results from NDFD in the main paper (with FRET given in Appendix I) because NDFD allowed for a longer period of record as well as analysis of the individual drivers of ET0, which ultimately control resultant ET0 quantities.ET0 forecasts were reasonably well correlated to observations during most of the growing season, with notable declines in correlations during July and August, and generally decreasing correlations with lead time. Systematic biases were found in Tmax, Tmin, vapor pressure, and solar radiation from NDFD. An arid bias that arises due to NDFD not accounting for irrigated lands and the associated modified near-surface boundary layer was apparent in NDFD Tmin, which is biased high year-round (often exceeding +3°C in summer), and during the growing season Tmax typically biased high and vapor pressure biased low.A case study revealed that observed daily variability in Tmin, solar radiation, wind speed, and ET0 was underestimated by NDFD and is likely a key factor in reducing the skill of the forecast ET0 (also supported by the skill analysis of each driver). Solar radiation on cloudy days showed minimal decreases in NDFD compared with observations, which has a cascading effect impacting all other variables and the estimated ET0. Other studies have documented this observed effect of how clouds have a strong influence on diurnal temperature ranges (Dai et al. 1999; Zhou et al. 2009; Tang and Leng 2013). The poor representation of convective clouds in NDFD could be a result of the model physics not capturing the physical processes, the crude estimate of solar radiation from percent sky cover, a grid scale/point scale mismatch, or a combination of all of these.Application of bias-correction ratios to ET0 generally reduced RMSE daily values by 5%–30%. Testing other bias-correction methods (e.g., Durai and Bhradwaj 2014) or correcting the ET0 input variables first (e.g., Yang et al. 2021) is recommended in future studies to determine if other methods may provide better forecast skill than the ratio method used in this study. It is yet to be seen whether the level of skill from these bias-corrected forecasts is sufficient to aid farmers in irrigation scheduling and water-conservation efforts. 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