1. Introduction
Medium-range (1–2 weeks ahead) reference evapotranspiration ETo forecasts can provide valuable information for water resource and irrigation management. Such ETo forecasts can be incorporated into hydrological models, water demand models, and irrigation scheduling models to reduce risk and improve reliability of decision making (e.g., Srivastava et al. 2014). When adequate meteorological data input are provided, ETo can be estimated using the Food and Agriculture Organization (FAO) Irrigation and Drainage Paper 56 (FAO-56) Penman–Monteith (PM) equation, which is considered to be the standard method to compute ETo (Allen et al. 1998).
Daily medium-range ETo forecasts can be made using statistical models or numerical weather prediction (NWP) models. A typical statistical model may use prior ETo values calculated from ground-based observations to make a forecast (e.g., Trajkovic et al. 2003). The main drawbacks of such statistical models are that they are black-box models and cannot be implemented in other locations without local training (e.g., Kumar et al. 2011), and the ground-based observations are often not available (e.g., Srivastava et al. 2013). In recent years, several works have been conducted to predict daily ETo using weather forecast data as inputs to the PM equation. The operational forecast products include the Experimental Forecast Reference Evapotranspiration (FRET) produced by the National Weather Service using outputs of the NWP models (e.g., www.wrh.noaa.gov/forecast/evap/FRET/FRET.php?wfo=sto). Many studies mainly included public weather forecast messages (Cai et al. 2007, 2009) and forecasts from mesoscale NWP models (Ishak et al. 2010; Silva et al. 2010; Srivastava et al. 2013) to predict ETo. However, the availability of the complete public weather forecast messages for the PM equation could not always be guaranteed over a large area at fine resolution (Cai et al. 2007), and while mesoscale NWP models could produce sufficient meteorological data for the PM equation over a large region at a high resolution, it has been noted to be very time consuming and the output suffered from systematic errors (Ishak et al. 2010; Silva et al. 2010).
As an alternative to the above methods, a retrospective forecast (reforecast) archive of a global NWP could be used to forecast daily ETo and correct systematic errors. Archives of the first-generation reforecast of the Global Forecast System (GFS; hereafter reforecast1; Hamill et al. 2006) with a forecast analog technique (Hamill and Whitaker 2006) have been applied to produce skillful ensemble forecasts of daily ETo at high resolution (Tian and Martinez 2012a,b). However, because the reforecast1 did not include sufficient meteorological variables for the PM equation, the forecasting skill was largely impaired because of the need to approximate several variables. The second-generation reforecast dataset (hereafter reforecast2) was recently developed through archiving the forecast outputs of the operational 2012 Global Ensemble Forecast System (GEFS; Hamill et al. 2013). Compared to reforecast1, reforecast2 used a newer version of the weather forecast model and archived a larger set of output data at a higher spatial and temporal resolution (Hamill et al. 2013). Thus, using the forecast analog technique with reforecast2 could potentially improve the daily ETo forecast skill.
In this study, we downscaled and bias corrected medium-range probabilistic forecasts of daily ETo at high spatial resolution using the forecast analog approach with the reforecast2 dataset in the southeastern United States [SEUS; Alabama, Georgia (GA), Florida (FL), North Carolina (NC), and South Carolina]. The ETo was calculated using the PM equation and the probabilistic forecasts of daily ETo were evaluated compared to the climatology of the forcing dataset of phase 2 of the North American Land Data Assimilation System (NLDAS-2) for all months and leads over the SEUS. A water deficit forecast driven by the ETo forecasts was evaluated to explore its usefulness for water management.
2. Data
Study area and an example of a subset of 16 GEFS grid points and corresponding NLDAS-2 grid points in the Tampa Bay area.
Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-0119.1
Because long-term continuous daily observed data for ETo estimation were generally not available over the SEUS, we used the forcing dataset of the NLDAS-2 (Xia et al. 2012a,b) as a surrogate for observations. The forcing data of NLDAS-2 has a resolution of 0.125° × 0.125° (~12 km; Fig. 1) over North America. We obtained relevant variables at an hourly time step (temperature, Rs, and u10) over the SEUS (25°–37°N, 89°–75°W). Daily Tmax and Tmin were obtained by comparing 1-h values on each day, daily Tmean was the average of daily Tmax and Tmin, and daily Rs and u10 were converted by averaging hourly values into daily values. The u10 was converted to u2 using Eq. (1).
Observations from two weather stations in the SEUS (Fig. 2) were selected to compare with the NLDAS-2 ETo, Tmax, Tmin, Rs, and Wind extracted at the same locations. These two stations included Lake Alfred, FL (28.10°N, 81.71°W), and Raleigh, NC (38.88°N, 78.79°W). The Lake Alfred station data was from the Florida Automated Weather Network, and the Clayton station (identification CLAY) data was from the North Carolina Climate Retrieval and Observations Network of the Southeast Database (NC CRONOS). Both stations are daily observations covering the period from 1 January 1998 to 31 December 2012. Both of the Lake Alfred and Clayton stations included Tmax, Tmin, dewpoint temperature Tdew, Rs, Wind, and ETo, where ETo was calculated by the FAO-56 PM equation.
Locations of the observed stations and selected locations for WD forecast.
Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-0119.1
3. Methods
a. ETo calculation
Box-and-whisker plots of the NLDAS-2 ea(Tmin) (red) and the NLDAS-2 ea(SH) (blue) in 12 months at (a) Saint Leo, FL, and (b) Smithfield, NC.
Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-0119.1
b. The analog method
The fine-resolution ETo forecasts were produced using a moving spatial window forecast analog approach (Hamill and Whitaker 2006; Hamill et al. 2006). This method is briefly described below. The first step was to find the closest analog dates for one lead day forecast within a domain of 16 grid points of GEFS (Fig. 1). That is, the root-mean-square error (RMSE) over the 16 grid points of GEFS was computed by comparing a given day’s ETo forecast with the historical ETo forecasts within a ±45-day window of the same day of the year at the same lead. For example, a 15 February 2012 forecast at lead day 5 over central Florida (the 16 GEFS grid points) was compared against the reforecasts from 1 January to 1 April between 1985 and 2011 (i.e., 2457 forecasts) at the same lead day. The RMSE between the current forecast and each reforecast was computed and averaged over the 16 grid points in Fig. 1. The analog dates for the day’s ETo forecast were selected as the 75 dates with the lowest RMSE. In the second step, the analogs for the forecast of the day were selected on the dates of the 75 analogs at each of the grid points of the NLDAS-2 dataset in Fig. 1. Thus, 75 analogs were chosen for this forecast to generate an ensemble forecast for each grid point of the NLDAS-2. This process was repeated for the other forecast lead days and the other locations across the SEUS, and the forecast over the entire SEUS were generated by tiling together the local analog forecasts. Leave-one-out cross validation was conducted by excluding the current year from the list of potential analogs.
c. Forecast verification
d. Irrigation scheduling model
Because ARID assumes a reference grass having a 400-mm soil layer with evenly distributed roots, it only requires site-specific weather data as a site-specific input. Following Woli et al. (2012), default values for the other parameters were used in this study (DC = 0.55 m3 m−3 day−1, Z = 400 mm, RCN = 65, MUF = 0.096 day−1, θwp = 0.06 m3 m−3, and θfc = 0.12 m3 m−3). The 27 years of daily WDs (from 1 October 1985 to 31 September 2012) at five locations in the SEUS (Fig. 2), including Smithfield, NC (35.52°N, 78.35°W); Gainesville, GA (34.30°N, 83.86°W); Tifton, GA (31.45°N, 83.48°W); Saint Leo, FL (28.34°N, 82.26°W); and Perrine, FL (25.58°N, 80.44°W), were calculated using the ARID model with the input from the daily NLDAS-2 precipitation (aggregated from hourly precipitation; mm day−1) and ETo (mm day−1).
e. Evaluation of analog forecast of WD





4. Results
a. Comparison between observations and NLDAS-2
Figure 4 shows a comparison of the observed and NLDAS-2 daily ETo, Tmax, Tmin, Rs, and Wind for 12 months at Lake Alfred, FL, and Clayton, NC, in the SEUS. While the NLDAS-2 ETo showed greater positive bias at the Lake Alfred station than the Clayton station throughout the year, the Tmax and Tmin matched quite well with the observations at both stations. The Rs showed higher bias at the Lake Alfred station than the Clayton station throughout the year. The wind also showed slightly smaller positive bias at the Clayton station than the Lake Alfred station across all months. Because ETo was estimated by the FAO-56 PM equation with the inputs of Tmax, Tmin, Rs, and Wind, any bias of ETo was due to one or more of these variables. At the Lake Alfred station in Florida, the high bias of ETo was likely caused by the high bias of both Rs and Wind. The ETo bias was relatively lower in the Clayton station than the bias at the Lake Alfred station, which was likely due to only Wind showing positive bias at this station.
Box-and-whisker plots of NLDAS-2 (red) and observations (blue) for ETo, Tmax, Tmin, Rs, and Wind in 12 months at (a) Alfred Lake, FL, and (b) Clayton, NC.
Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-0119.1
b. Skill of the analog ETo forecast
Figure 5 shows the skill scores as a function of month and lead day. For lead day 1, the lower and upper tercile forecast skills (BSS) were above 0.4 in cool months and above 0.2 in warm months (Figs. 5b,d); the lower and upper extreme forecast skills (BSS) were between 0.2 and 0.4 throughout the year, with the skill higher in cool months than in warm months (Figs. 5a,e); the middle tercile forecast skills (BSS) were the lowest among the five categories, with the skill scores above 0 and below 0.2 (Fig. 5c); and the overall forecast skill (LEPS skill score) was above 40% in cool months and above 20% in warm months. The forecast skills for tercile, extreme, and overall forecasts were generally positive up to lead day 7, with the skill scores higher in cool months than in warm months and the skill decreased with the increase in lead day.
BSS and LEPS skill score (%) as a function of month and lead day. (a)–(e) The BSS reflected the extreme and tercile forecasting skill. (f) The LEPS skill score reflected the overall forecasting skill.
Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-0119.1
Figure 6 shows the reliability and ROC diagrams for tercile and extreme forecasts for lead days 1 and 5. While the reliability curves showed slight overforecasting bias, the curves were along the diagonal for all five categorical forecasts at lead days 1 and 5 (Figs. 6a,b), which indicated the forecast probability matched very well with the observed relative frequency. All ROC curves with the exception of the middle tercile forecasts were far toward the upper-left corner for both lead days 1 and 5 (Figs. 6c,d), indicating the upper and lower tercile and extreme forecasts had very good resolution and could discriminate between events and nonevents very well. While the reliability and ROC curves all showed high skill at lead day 5, the BSS only showed modest skill. Our explanation is that the reliability and ROC curves were created by pooling the forecasts and observations of all grid points and months instead of evaluating at each grid point and month before averaging, so that the variability of ETo across locations and seasons produced artificially high skill (Hamill and Juras 2006).
(a),(b) Reliability and (c),(d) ROC diagrams for tercile and extreme forecasts at lead days 1 and 5.
Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-0119.1
The skill scores for each grid point were calculated by averaging over all months for different lead days. Figure 7 shows the overall, tercile, and extreme forecast skill for each grid point over the SEUS for four lead days. The skill decreased with the increase of lead days. All forecasts indicated the Florida peninsula showed the lowest skill, and the northern portion of the study area generally showed higher skill than the southern.
(top) LEPS skill score (%) and (below) BSS over the SEUS. The LEPS skill score reflected the overall forecasting skill. The BSS reflected the tercile and extreme forecasting skill.
Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-0119.1
c. Evaluation of WD forecast
Table 1 shows the evaluation of the analog forecasts and climatology of WDs (mm) at lead days 1 and 5 at five locations in the SEUS. The analog forecast showed better E, RMSE, and r factor than climatology at all the five locations, with the stations in Georgia and North Carolina showing better performance than the two stations in Florida for both lead days 1 and 5. In terms of the E and RMSE, which evaluates the deterministic forecast, the analog-based WD forecast is more accurate than the climatology-based WD forecast. There is a trade-off between the p factor and r factor, that is, the percent of observations falling within the upper and lower boundaries of the ensemble and the width of the boundaries of the ensemble. While the climatology ensemble only shows a slightly higher p factor than the analog ensemble forecast, the analog ensemble forecast shows much lower r factor than the climatology ensemble. This indicates the analog ensemble forecast has a much narrower boundary than the climatology ensemble but includes a similar percent of observations as the climatology ensemble, that is, the analog ensemble forecast achieved a better trade-off than the climatology ensemble.
Evaluation of ensemble and deterministic forecast of water deficits (mm) at five locations in the SEUS.
5. Concluding remarks
In this work, daily medium-range probabilistic ETo forecasts at high resolution were produced using the analog approach with the reforecast2 dataset. The daily ETo probabilistic forecast showed skill up to lead day 7. The WD forecasts were generated using the daily ETo analog forecast at five locations in the SEUS. The analog-based WD forecast showed high accuracy and small uncertainty at lead days 1 and 5. Because the WD is considered to be the amount of water needed for irrigation, this WD forecast based on the ETo analog forecast will be useful for irrigation scheduling.
The daily ETo forecast showed higher skill in cool months than in warm months. The lower skill in warm months than in cool months was likely due to convective heating. Convective heating is more frequent in summertime than in wintertime. Such convection could cause different weather conditions such as cloudiness and rainfall at small scales, which may not have been well captured by the GEFS model resolution. Over space, the skill was higher in the north than in the south of the SEUS, with the Florida peninsula showing the lowest skill. This is probably due to the influence of the sea breeze over the Florida peninsula (Marshall et al. 2004; Misra et al. 2011).
Compared to the reforecast1 ETo using either natural analogs of the ensemble-mean forecast (reforecast1a; Tian and Martinez 2012a) or constructed analogs of all forecast members (reforecast1b; Tian and Martinez 2012b), the skills of reforecast2 were greatly improved throughout the year (Fig. 8). For example, the overall forecast skill (LEPS skill score) for lead day 1 in January increased from 28% (reforecast1a) and 37% (reforecast1b) to 43%. Moreover, the ETo forecasts using reforecast1a could only produce skillful forecasts up to lead day 5. In contrast to the reforecast1a and reforecast1b ETo, the reforecast2 ETo did not show the lowest skill in the mountainous regions at the confluence of North Carolina, South Carolina, and Georgia, and the skill of reforecast2 was higher than reforecast1 at all locations over the SEUS (Fig. 8). In moving from the reforecast1 data used in Tian and Martinez (2012a) to the reforecast2 data here, the improvement of ETo forecast skill is due to various reasons. First, the reforecast2 dataset was generated by the operational version GEFS (Hamill et al. 2011), which has more advanced configurations with higher horizontal and vertical resolution and more advanced methods for data assimilation and ensemble initialization than the 1998 version GFS used by reforecast1. Second, reforecast2 provided more of the required variables for the PM equation, including Tmax, Tmin, and Rs, so that only one approximation (using Tmin to replace Tdew) was made in this study. By contrast, reforecast1 had a number of variables (Tmax, Tmin, Rs, Tdew, and RH) that needed to be approximated in order to use the PM equation (Tian and Martinez 2012a). Third, reforecast2 (~100 km) has a much higher spatial resolution than reforecast1 (~250 km). Therefore, the analogs could be selected from a smaller spatial domain (reforecast2), which was more likely to find appropriate analogs compared to a larger spatial domain (reforecast1).
Comparisons of LEPS skill scores (%) for reforecast2, reforecast1a, and reforecast2b at lead days (a) 1 and (b) 5 throughout the year. (c) Comparisons of LEPS skill scores (%) for (left) reforecast2, (middle) reforecast1a, and (right) reforecast1b at lead days (top) 1 and (bottom) 5 over the SEUS.
Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-0119.1
For the forecast verification, the use of the forcing dataset of NLDAS-2 instead of the North American Regional Reanalysis (NARR) as used by Tian and Martinez (2012a,b) could also affect the forecast. The NLDAS-2 forcing data were based on the interpolation of the NARR fields. The Rs was bias corrected from the interpolated NARR using satellite-derived Rs (Xia et al. 2012a) over each grid cell using the ratio of their monthly average diurnal cycle. The details of the method for bias correction can be found in Berg et al. (2003) and Pinker et al. (2003). The NLDAS-2 2-m temperature was directly interpolated from NARR with adjustments to account for the vertical difference between the NARR and NLDAS-2 fields of terrain height (Xia et al. 2012b). Nevertheless, the downscaled and bias-corrected ETo forecasts produced by this work are still affected by the biases in the NLDAS-2 fields. By comparing the NLDAS-2 fields with station-based observations, we can see biases for ETo, Rs, and Wind in Florida. Because the ETo was calculated by the PM equation, the biases of Rs and Wind would be the major contribution to the biases of ETo. The ETo has a smaller bias in North Carolina than in Florida, which was due to the smaller bias of Rs and Wind. While the forcing dataset of NLDAS-2 showed bias, we should note that the skill of the forecast is not related to the bias of the NLDAS-2 data, because the NLDAS-2 data were used for both validation and the selection of forecast analogs.
It is worth noting that further research could be conducted to find the optimum number of analogs and size of the search window to improve the ETo forecast skill (e.g., Hamill et al. 2006). Also, ETo forecasts could be verified using ground-based observations rather than the forcing data of NLDAS-2. However, such ground-based observations would need to be of a similar length of the reforecast2 dataset in order for forecast analog methods to be effective. In this work, Tmin was used to approximate Tdew, which was found to be generally valid for the humid SEUS. This approximation should be validated before being applied to other, less humid locations (Allen et al. 1998).
Acknowledgments
This research was supported by the NOAA/Climate Program Office SARP and RISA program Grants NA10OAR4310171 and NA12OAR4310130. The second-generation NOAA Global Ensemble Forecast System Reforecast was provided by the NOAA/ESRL/PSD, Boulder, Colorado (www.esrl.noaa.gov/psd/forecasts/reforecast2/). The forcing data of NLDAS-2 used in this effort were acquired as part of the activities of NASA’s Science Mission Directorate and are archived and distributed by the Goddard Earth Sciences (GES) Data and Information Services Center (DISC). The authors thank three anonymous reviewers for their valuable comments.
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