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  • View in gallery

    Example of a subset of 16 grid points covering the Tampa Bay area. The small points denote where NLDAS-2 data are available. Large black squares denote where the CFSv2 reforecast data are available.

  • View in gallery

    Comparison of skill scores of five CFSv2 downscaled variables—Tmean, Tmax, Tmin, Rs, and Wind— by (a)–(d) the SD and (e)–(h) the SDBC methods as a function of consecutive three-month periods (January–March to December–February) for 0-month lead time: (a) MSESS for SD; BSS for SD (b) below, (c) near, and (d) above normal; (e) MSESS for SDBC; and BSS for SDBC (f) below, (g) near, and (h) above normal.

  • View in gallery

    Comparison of skill scores of downscaled ETo by the SD and SDBC methods as a function of consecutive three-month periods (January–March to December–February) for 0-month lead time: (a) MSESS and BSS (b) below, (c) near, and (d) above normal.

  • View in gallery

    The average skill scores of the downscaled CFSv2 variables—(top to bottom) Tmean, Tmax, Tmin, Rs, and Wind— by the SD method for the deterministic and tercile forecasts across the SEUS: (left to right) MSESS and BSS below, near, and above normal.

  • View in gallery

    As in Fig. 4, but for the SDBC method.

  • View in gallery

    The average skill scores of the downscaled CFSv2 ETo by the SD and SDBC methods—(top to bottom) SD ETo1, SD ETo2, SDBC ETo1, and SDBC ETo2 variables—for the deterministic and tercile forecasts across the SEUS: (left to right) MESS, BSS below, BSS near, and BSS above normal.

  • View in gallery

    The average of absolute sensitivity coefficients for (left to right) Tmean, Tmax, Tmin, Rs, and Wind over all consecutive three-month periods (January–March to December–February) in the SEUS.

  • View in gallery

    As in Fig. 4, but as a function of consecutive three-month periods (January–March to December–February) and lead times of 0–9 months. The thick contour denotes 0 skill.

  • View in gallery

    As in Fig. 8, but for the SDBC method.

  • View in gallery

    The average skill scores of (top) ETo1 and (bottom) ETo2 by the SD method as a function of consecutive three-month periods (January–March to December–February) and lead times of 0–9 months for the deterministic and tercile forecasts across the SEUS: (left to right) MSESS and BSS below, near, and above normal. The thick contour denotes 0 skill.

  • View in gallery

    As in Fig. 10, but for the SDBC method.

  • View in gallery

    The skill scores of downscaled ETo1 (black) and ETo2 (gray) by the SDBC method as a function of consecutive three-month periods (January–March to December–February) for 0-month lead during ENSO events: (a) MSESS and BSS (b) below, (c) near, and (d) above normal.

  • View in gallery

    As in Fig. 10, but by the SDBC method. The forecast initial season is during ENSO events.

  • View in gallery

    As in Fig. 13, but the forecast target season is during ENSO events.

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Seasonal Prediction of Regional Reference Evapotranspiration Based on Climate Forecast System Version 2

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  • 1 Department of Agricultural and Biological Engineering, University of Florida, Gainesville, Florida
  • | 2 Department of Agricultural and Biological Engineering, and Water Institute, University of Florida, Gainesville, Florida
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Abstract

Reference evapotranspiration (ETo) is an important hydroclimatic variable for water planning and management. This research explored the potential of using the Climate Forecast System, version 2 (CFSv2), for seasonal predictions of ETo over the states of Alabama, Georgia, and Florida. The 12-km ETo forecasts were produced by downscaling coarse-scale ETo forecasts from the CFSv2 retrospective forecast archive and by downscaling CFSv2 maximum temperature (Tmax), minimum temperature (Tmin), mean temperature (Tmean), solar radiation (Rs), and wind speed (Wind) individually and calculating ETo using those downscaled variables. All the ETo forecasts were calculated using the Penman–Monteith equation. Sensitivity coefficients were evaluated to quantify how and how much does each of the variables influence ETo. Two statistical downscaling methods were tested: 1) spatial disaggregation (SD) and 2) spatial disaggregation with quantile mapping bias correction (SDBC). The downscaled ETo from the coarse-scale ETo showed similar skill to those by first downscaling individual variables and then calculating ETo. The sensitivity coefficients showed Tmax and Rs had the greatest influence on ETo, followed by Tmin and Tmean, and Wind. The downscaled Tmax showed highest predictability, followed by Tmean, Tmin, Rs, and Wind. SDBC had slightly better performance than SD for both probabilistic and deterministic forecasts. The skill was locally and seasonally dependent. The CFSv2-based ETo forecasts showed higher predictability in cold seasons than in warm seasons. The CFSv2 model could better predict ETo in cold seasons during El Niño–Southern Oscillation (ENSO) events only when the forecast initial condition was in either the El Niño or La Niña phase of ENSO.

Corresponding author address: Di Tian, Department of Agricultural and Biological Engineering, University of Florida, P.O. Box 110570, Gainesville, FL 32611-0570. E-mail: tiandi@ufl.edu

Abstract

Reference evapotranspiration (ETo) is an important hydroclimatic variable for water planning and management. This research explored the potential of using the Climate Forecast System, version 2 (CFSv2), for seasonal predictions of ETo over the states of Alabama, Georgia, and Florida. The 12-km ETo forecasts were produced by downscaling coarse-scale ETo forecasts from the CFSv2 retrospective forecast archive and by downscaling CFSv2 maximum temperature (Tmax), minimum temperature (Tmin), mean temperature (Tmean), solar radiation (Rs), and wind speed (Wind) individually and calculating ETo using those downscaled variables. All the ETo forecasts were calculated using the Penman–Monteith equation. Sensitivity coefficients were evaluated to quantify how and how much does each of the variables influence ETo. Two statistical downscaling methods were tested: 1) spatial disaggregation (SD) and 2) spatial disaggregation with quantile mapping bias correction (SDBC). The downscaled ETo from the coarse-scale ETo showed similar skill to those by first downscaling individual variables and then calculating ETo. The sensitivity coefficients showed Tmax and Rs had the greatest influence on ETo, followed by Tmin and Tmean, and Wind. The downscaled Tmax showed highest predictability, followed by Tmean, Tmin, Rs, and Wind. SDBC had slightly better performance than SD for both probabilistic and deterministic forecasts. The skill was locally and seasonally dependent. The CFSv2-based ETo forecasts showed higher predictability in cold seasons than in warm seasons. The CFSv2 model could better predict ETo in cold seasons during El Niño–Southern Oscillation (ENSO) events only when the forecast initial condition was in either the El Niño or La Niña phase of ENSO.

Corresponding author address: Di Tian, Department of Agricultural and Biological Engineering, University of Florida, P.O. Box 110570, Gainesville, FL 32611-0570. E-mail: tiandi@ufl.edu

1. Introduction

Reference evapotranspiration (ETo) is defined as the evapotranspiration from a hypothetical reference crop in an adequately watered condition (Allen et al. 1998). ETo is one of the most important hydroclimatic variables for scheduling irrigation, driving hydrologic and crop models, and estimating actual evapotranspiration for a region (Gong et al. 2006). If ETo can be predicted a few months in advance, it would be beneficial for the water management and irrigation communities for making long-term planning decisions. There are many methods to estimate ETo. The Food and Agriculture Organization (FAO) Irrigation and Drainage Paper 56 (FAO-56) Penman–Monteith (PM) equation (Allen et al. 1998) is considered a globally valid standardized method to estimate ETo and was adopted by the FAO of the United Nations. A major limitation of this method is that it requires a large amount of climatic data input at the land surface level, including air temperature, wind speed, solar radiation, and dewpoint temperature or relative humidity, which are often not available in many regions.

Coupled ocean–land–atmosphere general circulation models (CGCMs) combine models for the ocean, atmosphere, land surface, and sea ice and run from several months to 1 year ahead to produce seasonal forecasts (Troccoli 2010). CGCMs have been operationally implemented at major weather and climate forecast centers around the world (Palmer et al. 2004; Saha et al. 2006; Yuan et al. 2011). Recently, the National Centers for Environmental Prediction (NCEP) of the National Oceanic and Atmospheric Administration (NOAA) has improved the physics and resolution of its operational CGCM and updated the forecast system to the Climate Forecast System, version 2 (CFSv2; Saha et al. 2010, 2014; Yuan et al. 2011). There are 29 yr (1982–2010) of retrospective forecasts (reforecasts or hindcasts) of CFSv2 that are archived by the National Climatic Data Center (NCDC). Recent studies have used the archived CFSv2 reforecasts for different applications such as evaluating the seasonal forecast skill of soil moisture (Mo et al. 2012), the South American monsoon (Jones et al. 2012), meteorological drought (Yoon et al. 2012), streamflow (Yuan and Wood 2012a; Yuan et al. 2013), East Asian winter monsoon (Jiang et al. 2013), summer heat waves (Luo and Zhang 2012), and tornado occurrence (Tippett et al. 2012). While the CFSv2 has shown the potential to improve seasonal forecast skill for many applications, studies using CFSv2 to predict seasonal ETo have not been conducted to date.

Seasonal predictions of CFSv2 land surface variables can provide valuable information for ETo forecasts. The archived reforecasts of CFSv2 land surface variables (e.g., temperature, wind speed, and solar radiation) provide all of the variables necessary for the FAO-56 PM equation to assess the predictability for ETo seasonal forecasts. Because of the upgraded physics and resolution, the CFSv2 has been shown to have the ability to predict near-surface air temperature and precipitation for hydrological forecasting at long leads (Yuan and Wood 2012b; Yuan et al. 2011). Besides near-surface air temperature, other land surface variables such as solar radiation and wind speed are important to forecast ETo. However, the predictability of these land surface variables for ETo forecasts has not yet been assessed.

ETo seasonal predictions are often needed at the local scale. Because CFSv2 has the horizontal resolution of T126 (equivalent to nearly 100 km), it is too coarse to meet local forecasting needs. To provide local predictions of seasonal ETo, CFSv2 forecasts need to be spatially downscaled. In general, there are two categories of downscaling methods: statistical and dynamical (Fowler et al. 2007). Statistical downscaling employs statistical relationships between the output of a CGCM and local observations and is computationally efficient and straightforward to apply. The statistical downscaling step can also be used to correct systematic bias between CGCM output and observations. One limitation to statistical downscaling methods is that they need long-term continuous forecast archives and observations to establish the statistical relationships. For dynamical downscaling, a CGCM provides the boundary and initial conditions to a regional climate model (RCM) and the RCM runs at a finer resolution to produce local-scale forecasts. The errors in the CGCM are typically propagated to the RCM and influence predictions (Hwang et al. 2011; Yoon et al. 2012). RCMs also have their own errors. Thus, dynamical downscaling requires additional statistical bias correction and is computationally intensive.

There are multiple methods for statistical downscaling and bias correction. The bias correction and spatial disaggregation (BCSD) method is an interpolation-based downscaling technique that has been extensively applied in hydrologic prediction studies (e.g., Christensen et al. 2004; Salathe et al. 2007; Maurer and Hidalgo 2008; Wood et al. 2002, 2004; Yoon et al. 2012). The BCSD method consists of bias correction using quantile mapping and then spatial disaggregation, which works effectively to correct both mean and variance of the forecasts using observations. Abatzoglou and Brown (2012) developed the spatial disaggregation with bias correction (SDBC) method by reversing the order of the BCSD procedures. This modification improved downscaling skill for reproducing local-scale temporal statistics of precipitation (Hwang and Graham 2013). The spatial disaggregation (SD) from the BCSD or SDBC methods could be adapted to an independent method by spatially interpolating the anomalies of forecasts to a finer resolution and then producing the downscaled forecasts by adding the observed climatology to the interpolated forecast anomalies. Besides the interpolation-based downscaling methods, there are parametric approaches (Schaake et al. 2007; Wood and Schaake 2008) and Bayesian merging techniques (Coelho et al. 2004; Luo and Wood 2008; Luo et al. 2007) that have also been used in downscaling seasonal climate forecasts. While the natural analog and constructed analog downscaling methods have shown good performance (Abatzoglou and Brown 2012; Hidalgo et al. 2008; Maurer and Hidalgo 2008; Maurer et al. 2010; Tian and Martinez 2012a, 2012b), the seasonal reforecast datasets are generally not long enough to perform those analog-based downscaling methods since there is a limited number of potential historical analogs.

The objectives of this study were 1) to evaluate the ability of the CFSv2 to produce downscaled ETo seasonal predictions from 0 to 9 months lead, 2) to assess the predictability of the relevant CFSv2 land surface and reference height variables for ETo forecasts, and 3) to compare the skill from two interpolation-based statistical downscaling methods to downscale CFSv2 forecasts. As members of the Southeast Climate Consortium (SECC), our goal was to develop an improved understanding of seasonal climate variability and climate predictability at local to regional scales across the southeastern United States (SEUS). Therefore, the study region includes Alabama, Georgia, and Florida in the SEUS. Sections 2 and 3 describe the data and methods used in this work. The results are presented in section 4. Conclusions and a discussion are given in section 5.

2. Data

The availability of the long-term archived CFSv2 reforecasts makes it feasible to conduct statistical downscaling. The forcing dataset of phase 2 of the North American Land Data Assimilation System (NLDAS-2) were used as observations to verify and correct errors of the downscaled forecasts.

a. NCEP CFSv2 forecasts

The CFSv2 is a fully coupled land–ocean–atmosphere dynamical seasonal prediction system (Saha et al. 2014). The CFSv2 reforecast archive consists of the NCEP Global Forecast System, the Geophysical Fluid Dynamics Laboratory Modular Ocean Model version 5.0 coupled with a two-layer sea ice model, and the four-layer Noah land surface model (Yuan et al. 2011). The reforecast includes model forecasts from January 1982 to December 2010 with 9-month leads at a T126 resolution (roughly 100 km). The reforecast of monthly means have 28 members in November and 24 members in other months with initial conditions of the 0000, 0600, 1200, and 1800 UTC cycles for every 5 days, starting from the last month after the seventh. For example, the 24 ensemble members for January are the four cycles for each of 12, 17, 22, and 27 December and 1 and 6 January. The near-surface variables of CFSv2 reforecast including 2-m maximum temperature (Tmax; K), minimum temperature (Tmin; K), mean temperature (Tmean; K), surface solar radiation (Rs; W m−2), and 10-m wind speed (u10; m s−1) are potentially useful to forecast ETo. Wind speed at 2-m height (u2, or referred to hereafter as Wind) was estimated from u10 (Allen et al. 1998):
e1
where z is the measurement height (10 m). The monthly means of those variables were converted to seasonal means by taking the moving average of the three months from January 1982 to December 2010. For the convenience of manipulation, all of those variables were regridded to 1.0° × 1.0° resolution (Fig. 1).
Fig. 1.
Fig. 1.

Example of a subset of 16 grid points covering the Tampa Bay area. The small points denote where NLDAS-2 data are available. Large black squares denote where the CFSv2 reforecast data are available.

Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-087.1

b. Forcing dataset of NLDAS-2

The 0.125° × 0.125° resolution (approximately 12 km) NLDAS-2 forcing dataset (Xia et al. 2012b,c; Fig. 1) was taken as a surrogate for long-term observations to use both for forecast verification and bias correction (as described in section 3). NLDAS-2 integrates a large quantity of observation-based and model reanalysis data to drive land surface models and executes at 0.125° × 0.125° grid spacing over North America with an hourly time step. The NLDAS-2 data provides the same land surface variables as CFSv2 reforecasts required for ETo estimation, including 2-m Tmax, Tmin, Tmean, u10, and Rs. The u10 was converted to u2 using Eq. (1). For this work, we used 30 yr of data from January 1982 to December 2011 because CFSv2 has a 9-month lead. The NLDAS-2 hourly data were aggregated into daily data and then averaged to monthly means. The monthly means were converted to seasonal means as was done for CFSv2 reforecasts.

The NLDAS-2 fields used in this study were based on the interpolation of the 3-h time step North American Regional Reanalysis (NARR; 0.3° × 0.3°; Mesinger et al. 2006; Xia et al. 2012b). The NLDAS-2 Rs was bias corrected using satellite-derived Rs by Pinker et al. (2003) over each grid cell using the ratio of their monthly average diurnal cycle (Xia et al. 2012b); all other NLDAS-2 fields used in this study were directly interpolated from NARR with or without adjustments to account for the vertical difference between the NARR and NLDAS-2 fields of terrain height (Xia et al. 2012a). The methods of the spatial and temporal interpolation and vertical adjustment were adopted from Cosgrove et al. (2003). Since the NARR data are a hybrid product of model simulations and observations, they contain known biases for either output fields (e.g., Markovic et al. 2009; Vivoni et al. 2008; Zhu and Lettenmaier 2007) or estimated ETo (Tian and Martinez 2012b). Thus, biases from the NARR would be propagated to the NLDAS-2 fields and consequently affect ETo estimation in this study. High biases of Rs and precipitation were found in the prior generation of forcing of the NLDAS-2 (Luo et al. 2003). The validation for the NLDAS-2 fields is still ongoing by the research community.

3. Methods

a. ETo estimation methods

The original PM approach (Jensen et al. 1990; Monteith 1964; Shuttleworth 1993) was derived from a “big leaf” assumption of evapotranspiration whereby a single surface resistance and a single aerodynamic resistance term represent the transport properties of the vegetated surface, where the vegetated surface is assumed to be complete and uniform. Since the PM equation approximates the stomatal resistance of the entire plant canopy as a single surface resistance, it takes an inherently macroscale view of the evapotranspiration process, which is appropriate for application at large scales such as that of CGCMs (e.g., Kingston et al. 2009; Sperna Weiland et al. 2012). The original PM equation is written as
e2
where evapotranspiration (λET; W m−2) can be converted into ET (mm) by dividing by the latent heat of vaporization of water λ (J kg−1), Δ (Pa K−1) is the slope of the plot of saturated vapor pressure against air temperature, Rn is the net radiation (W m−2), ρa is the density of air (kg m−3), cp is the specific heat of air at constant pressure (J kg−1 K−1), D is the vapor-pressure deficit (Pa), and γ is the psychometric constant (Pa K−1). The variables ra and rs are the aerodynamic and surface resistances (s m−1), respectively. The FAO developed the concept of reference evapotranspiration and the standardized FAO-56 PM equation by defining the grass reference crop as a hypothetical crop with an assumed height of 0.12 m and standardized height for wind speed, temperature, and humidity measurements at 2 m under well-watered conditions. The ET rates of various vegetation covers are related to the ETo by means of crop coefficients. By introducing this grass reference crop, the FAO-56 PM equation was derived from Eq. (2) (derivation procedure is shown in the appendix) and has the form
e3
where ETo is the reference evapotranspiration (mm day−1), Rn is the net radiation at the crop surface (MJ m−2 day−1) and is determined from the difference between net shortwave radiation (assuming a constant albedo of 0.23) and net outgoing longwave radiation calculated following Allen et al. (1998), G is soil heat flux density (MJ m−2 day−1) and was considered to be negligible for the calculations, T is the mean air temperature at 2-m height (°C), u2 is wind speed at 2-m height (m s−1), es is saturation vapor pressure (kPa), ea is actual vapor pressure (kPa), Δ is the slope of the saturation vapor pressure curve (kPa °C−1), and γ is the psychrometric constant (kPa °C−1). The only required inputs for the FAO-56 PM equation are climatic variables.

For details on the calculation of each of the terms in Eq. (3), the reader is referred to Allen et al. (1998). Since the CFSv2 reforecast and forcing data of NLDAS-2 did not include dewpoint temperature (Tdew) or relative humidity (RH) that are required to calculate ea, we approximated Tdew using Tmin, which has been found to be suitable for humid regions (Allen et al. 1998).

Sensitivity coefficients (e.g., Gong et al. 2006) were used to evaluate variables that are most important for influencing ETo at different seasons over the SEUS. The forcing data of the NLDAS-2 were used in the estimation of the sensitivity coefficient. The sensitivity coefficient has a nondimensional form written as
e4
where is the sensitivity coefficient for Vijk, Vijk is the climatology of ith variable in the jth month at grid point k, ΔVijk is the difference between the maximum and minimum values of the ith variable in the jth month at grid point k throughout all years, ETojk is the reference evapotranspiration estimated by Eq. (3) with inputs of the climatology for each of the variables for the jth month at grid point k, and ΔETojk is the difference between the estimated ETo by Eq. (3) with inputs of the maximum and minimum values of each of the variables in the jth month at grid point k throughout all years. A greater sensitivity coefficient reflects a greater influence of a given variable on ETo in a given month, either negatively or positively.

b. Downscaling methods

The downscaled ETo seasonal forecasts were produced in two ways. The first was to calculate the coarse-scale ETo forecasts using the FAO-56 PM equation with the input of the CFSv2 forecasts of Tmean, Tmax, Tmin, Rs, and Wind and then downscale and bias correct the coarse-scale ETo (hereafter ETo1); the second was to downscale and bias correct the CFSv2 forecasts of Tmean, Tmax, Tmin, Rs, and Wind and then input those variables into the FAO-56 PM equation to calculate the downscaled ETo forecast (hereafter ETo2). Similarly, Yuan and Wood (2012a) conducted downscaling of the CFSv2 streamflow forecasts in two ways: 1) bias correcting streamflow predicted by the integrated land surface model in CFSv2 and 2) downscaling the meteorological seasonal forecast and using it as input to a well-calibrated hydrologic model. Two methods, SD and SDBC, were used to downscale each of those variables and ETo.

1) SD method

The SD method is an interpolation-based downscaling method that includes two steps. The first step is to spatially interpolate the anomalies of CFSv2 forecasts to a finer resolution (0.125° × 0.125°) using the inverse distance weighted (IDW) technique. The anomalies were defined as the departure of the reforecasts from the model climatology. The IDW technique estimates values at a point by weighting the influence of nearby data with the most distant data weighted the least. The IDW technique consists of two steps: 1) compute distances to all the points in the dataset and 2) compute the weight of each point. The weighting function is the inverse power of the distance:
e5
and
e6
where is the estimated value, Z is the value of the control points, di is the distance between the estimated value and the control points, p is the power to which the distance is raised (a power of 2 was used in this work), and (X, Y) represents the coordinates. The second step of the SD method is to produce the forecasts by adding the downscaled anomalies to the climatology of NLDAS-2 forcing data. The leave-one-out cross-validation procedure was conducted by leaving the target season (the season being forecasted) out when calculating the NLDAS-2 climatology.

2) SDBC method

Compared to the SD method, the SDBC method (Abatzoglou and Brown 2012) has three steps with an additional quantile-mapping bias-correction procedure. In the first step, the anomalies of the CFSv2 forecasts were interpolated to moderate resolution (0.125° × 0.125°) using the IDW technique. In the second step, the interpolated anomalies of the CFSv2 were bias corrected using the anomalies of the NLDAS-2 forcing data using the quantile mapping technique. In comparison to the SD method, the SDBC method corrects both mean and variance of the forecasts in probability space. This technique has three procedures: 1) creating cumulative density functions (CDFs) of the anomalies of NLDAS-2 forcing data for each grid point, 2) creating CDFs of the CFSv2 anomalies for each grid point and lead time, and 3) using the quantile mapping that preserves the probability of exceedence of the CFSv2 data but correcting the CFSv2 anomalies to the value that corresponds to the same probability of exceedence from the anomalies of NLDAS-2. Thus, bias-corrected data on time i at grid j were calculated as
e7
where F(x) and F−1(x) denote a CDF of the data and its inverse and subscripts sim and obs indicate downscaled CFSv2 anomalies and NLDAS-2 anomalies, respectively. The final step is to produce the forecasts by adding the bias-corrected downscaled anomalies to the climatology of NLDAS-2 forcing data. In steps 2 and 3, the cross-validation procedure was conducted by leaving the target season out when creating the CDFs of the NLDAS-2 anomalies and calculating the NLDAS-2 climatology.

c. Evaluation statistics

Seasonal skill for both deterministic and probabilistic forecasts were evaluated for each NLDAS-2 grid point from lead 0 to 9 and summarized by season. The deterministic forecasts were determined by the ensemble mean of the 24 members. The mean squared error skill score (MSESS) was computed for each grid point, each season, and each lead. MSESS is a relative skill measure that compares the downscaled forecasts with the climatology forecast, which was calculated from NLDAS-2 seasonal values at the same time as the forecast season. The mean squared error of the forecasted values (MSEf) and the mean squared error of the climatology (MSEc) were calculated for each grid point for each season and lead. MSESS is calculated by
e8
MSESS ranges from −∞ to 1.0, with values of 0 indicating the forecast has equivalent skill as climatology, negative values indicating the forecast has less skill than climatology, and a value of 1.0 indicating a perfect forecast.
The ensemble forecast of CFSv2 can be used as a probabilistic forecast by counting the number of ensemble members falling into three equal categories or terciles. The Brier skill score (BSS) was employed to evaluate the skill of probabilistic forecasts in terciles (above normal, near normal, and below normal) for each grid point, each season, and each lead. The terciles of the NLDAS-2 data were used to divide the forecast into three categories. The climatological forecast was, by definition, 33.3% for all three categories. The BSS is written as (Wilks 2011)
e9
where BSf is the Brier score of the forecast and BSc is the Brier score of climatology, which was computed from NLDAS-2 seasonal values at the same time as the forecast season. The BSf and BSc were calculated as
e10
and
e11
where n is the number of forecasts and observations of a dichotomous event; and are the forecasted probability of the event using the forecasts and climatology, respectively; and = 1 if the event occurred and = 0 if the event did not occur. The BSS ranges between −∞ to 1.0, and values of 1 indicate perfect skill and values of 0 indicate that the skill of the forecast is equivalent to climatology.

4. Results

Tables 1 and 2 show the overall mean MSESS and BSS for downscaled CFSv2 variables and ETo by the SD and SDBC methods in 0-month lead for all seasons. In Table 1, in terms of the overall mean skill scores for the CFSv2 variables, Tmax had the highest skill for both deterministic and probabilistic forecasts and was followed by Tmean, Tmin, Rs, and Wind. The skill scores for the SDBC method were slightly higher than the SD method. The probabilistic forecasts in the above-normal and below-normal categories had positive skill, while the forecast skill in the near-normal category was all negative. Failure of the near-normal forecast has been found in many previous studies (e.g., van den Dool and Toth 1991; Barnston et al. 2003). This failure is related to two facts: 1) narrowing of the forecast probability distribution increases the probability in the near-normal category and decreases the probability in the outer two categories, but the change is usually not sizeable, and 2) overall shifts in the forecast probability distribution can reduce the probability in the near-normal category, but changes the probabilities in below- and above-normal categories far more substantially (van den Dool and Toth 1991). In general, for the overall mean predictive skill of the two ETo methods, ETo2 showed slightly higher skill than ETo1, and the SDBC showed slightly higher skill than the SD method (Table 2).

Table 1.

The overall average MSESS and BSS for different downscaled CFSv2 variables in 0-month lead by SD and SDBC methods. The MSESS and BSS evaluate the overall skill and tercile skill, respectively.

Table 1.
Table 2.

As in Table 1, but for the downscaled ETo with ETo1 calculated using the CFSv2 variables before downscaling, and ETo2 calculated with the downscaled CFSv2 variables. The higher positive scores between ETo1 and ETo2 are highlighted in bold.

Table 2.

a. Evaluation of forecast skill in different seasons

This section compared the mean forecast skill in different seasons averaged over the entire region in 0-month lead. Figure 2 shows the forecast skill of the deterministic and tercile probabilistic forecasts in different seasons for the five downscaled CFSv2 variables for the SD and SDBC methods in 0-month lead. In terms of the MSESS and BSS in below- and above-normal categories, Tmean and Tmax had the highest skill over all seasons, Tmin and Rs were skillful only during the cold seasons, and Wind showed minor skill in warm seasons. Figure 3 shows a comparison of skill scores of downscaled ETo for the SD and SDBC methods in different seasons at 0-month lead. Both ETo1 and ETo2 showed skill in cold seasons while the skill dropped below 0 during warm seasons; the two methods for downscaling ETo did not show much difference in terms of the forecast skill, particularly in cool seasons when the skill was positive. Both Figs. 2 and 3 show there is no sizeable difference between the SD and SDBC methods.

Fig. 2.
Fig. 2.

Comparison of skill scores of five CFSv2 downscaled variables—Tmean, Tmax, Tmin, Rs, and Wind— by (a)–(d) the SD and (e)–(h) the SDBC methods as a function of consecutive three-month periods (January–March to December–February) for 0-month lead time: (a) MSESS for SD; BSS for SD (b) below, (c) near, and (d) above normal; (e) MSESS for SDBC; and BSS for SDBC (f) below, (g) near, and (h) above normal.

Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-087.1

Fig. 3.
Fig. 3.

Comparison of skill scores of downscaled ETo by the SD and SDBC methods as a function of consecutive three-month periods (January–March to December–February) for 0-month lead time: (a) MSESS and BSS (b) below, (c) near, and (d) above normal.

Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-087.1

Since ETo estimation is governed by Tmean, Tmax, Tmin, Rs, and Wind, it would be useful to look at the influence of each variable on ETo. In terms of the sensitivity coefficients in Table 3, Tmax and Rs had the greatest influence on ETo, followed by Tmin and Tmean, and Wind showed only slight influence, particularly in warmer seasons. All variables had positive influence on ETo except Tmin, which had negative influence. While the influence of Tmax is relatively constant for all seasons, Tmean, Tmin, and Rs have greater influence in warmer seasons than in cooler seasons. During warm seasons, because of the influence of Tmin and Rs on ETo, the poor forecasts of these two variables by CFSv2 would cause the negative skill of the ETo forecast in these seasons. While during cold seasons when Tmax, Tmean, Tmin, and Rs forecasts had relatively good performance, ETo showed positive forecast skill.

Table 3.

Spatial average of monthly sensitivity coefficients for Tmean, Tmax, Tmin, Rs, and Wind over the SEUS.

Table 3.

b. Evaluation of forecast skill over space

The forecast skill in this section was the skill scores averaged over all seasons in different grid points in 0-month lead. Figures 4 and 5 show the spatial distribution of the deterministic and probabilistic forecast skill of the downscaled CFSv2 variables (Tmean, Tmax, Tmin, Rs, and Wind) for the SD and SDBC methods for all seasons in 0-month lead, respectively. For both the SD and SDBC methods, Tmean and Tmax had the highest skill over the region, followed by Tmin, Rs, and Wind (Figs. 4, 5). Figure 4 shows, for the SD method, both deterministic and probabilistic forecasts for Tmean and Tmax were skillful in most of the region. The MSESS and BSS for Tmin were highest in southern Florida, northern Georgia, northern Alabama, and coastal areas for the below- and above-normal categories. For deterministic forecasts and above-normal forecasts of Rs, there was skill in northern Florida, while for the below- and near-normal forecasts, there were no skill in most of the area. The forecasts of Wind did not show skill anywhere in the region, with western Florida and Alabama showing the most negative skill. Compared to the other variables, Wind is the most influenced variable by land surface conditions. The failure of the Wind forecasts was likely due to several reasons. First, the boundary layer changes diurnally and seasonally, which makes it difficult to model; second, the turbulent fluxes in the boundary layer (drag force due to land surface friction) in CFSv2 may not be resolved, likely because of the coarse spatial resolution of the model configuration. Figure 5 shows that for the SDBC method, although the skill showed a similar spatial pattern with the SD method, there were improvements of skill over the whole area.

Fig. 4.
Fig. 4.

The average skill scores of the downscaled CFSv2 variables—(top to bottom) Tmean, Tmax, Tmin, Rs, and Wind— by the SD method for the deterministic and tercile forecasts across the SEUS: (left to right) MSESS and BSS below, near, and above normal.

Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-087.1

Fig. 5.
Fig. 5.

As in Fig. 4, but for the SDBC method.

Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-087.1

Figure 6 shows the average skill scores of the deterministic and probabilistic forecasts of the downscaled ETo1 and ETo2 for the SD and SDBC methods for 0-month lead. For the SD method, both ETo1 and ETo2 showed skillful deterministic forecasts for most of the area except southern Florida. The forecast skill for ETo1 and ETo2 was very similar. For the SDBC method, in terms of the MSESS and above-normal BSS, there were larger areas showing higher skill for ETo2 than for ETo1. There were greater areas showing high skill for the SDBC method than the SD method. The greatest improvement of skill occurred in the near-normal forecasts, though the skill was still negative in most of the area. The skill improvement for the SDBC was due to the additional procedure to bias correct the overall shape of the forecast distribution. In terms of the monthly average of the absolute sensitivity coefficients for each variable in Fig. 7, Tmax and Rs had the greatest influence on ETo, followed by Tmin, Tmean, and Wind. The absolute sensitivity coefficient for each variable was relatively homogeneous over space. Given the influence of Rs on ETo, the low skill of ETo in southern Florida is likely caused by the low skill of Rs in the area.

Fig. 6.
Fig. 6.

The average skill scores of the downscaled CFSv2 ETo by the SD and SDBC methods—(top to bottom) SD ETo1, SD ETo2, SDBC ETo1, and SDBC ETo2 variables—for the deterministic and tercile forecasts across the SEUS: (left to right) MESS, BSS below, BSS near, and BSS above normal.

Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-087.1

Fig. 7.
Fig. 7.

The average of absolute sensitivity coefficients for (left to right) Tmean, Tmax, Tmin, Rs, and Wind over all consecutive three-month periods (January–March to December–February) in the SEUS.

Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-087.1

c. Evaluation of forecast skill for different leads

The skill scores in this section were the spatial average over all the grid points for different months and leads. All the contours in Figs. 710 were smoothed for display purposes. Figures 7 and 8 demonstrate the predictive skill of the deterministic and probabilistic forecasts of the CFSv2 variables (Tmean, Tmax, Tmin, Rs, and Wind) for all seasons and leads over the entire area for the SD and SDBC method, respectively. In general, both figures indicate Tmean and Tmax had longer skillful leads than Tmin, Rs, and Wind, with Tmin and Rs having skillful leads out to approximately 3 months during the cold seasons. Figure 8 shows the MSESS of Tmean and Tmax were skillful at long leads for most seasons of the year. The BSS for Tmean and Tmax indicates that the below- and above-normal forecasts were skillful at near leads. Tmin only showed skill at near leads for cold seasons and no skill for warm seasons in terms of MSESS and BSS in the outer two categories. The deterministic forecasts for Rs were skillful at long leads for cool seasons, while the probablistic forecasts were skillful at near leads during the cold seasons. The deterministic forecasts for Wind showed some skill out to month 3 lead for warm seasons, while there was no skill for other seasons and tercile forecasts. Figure 9 shows the SDBC method improved skill for longer leads for below-normal and above-normal forecasts of Tmax and Rs and deterministic forecasts of Wind. The greatest improvement occurred for near-normal forecasts of Tmax even though the skill was still negative. There were no obvious improvements for the other forecasts.

Fig. 8.
Fig. 8.

As in Fig. 4, but as a function of consecutive three-month periods (January–March to December–February) and lead times of 0–9 months. The thick contour denotes 0 skill.

Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-087.1

Fig. 9.
Fig. 9.

As in Fig. 8, but for the SDBC method.

Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-087.1

Fig. 10.
Fig. 10.

The average skill scores of (top) ETo1 and (bottom) ETo2 by the SD method as a function of consecutive three-month periods (January–March to December–February) and lead times of 0–9 months for the deterministic and tercile forecasts across the SEUS: (left to right) MSESS and BSS below, near, and above normal. The thick contour denotes 0 skill.

Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-087.1

Figures 10 and 11 show the predictive skill of ETo1 and ETo2 as a function of seasons and leads for the SD and SDBC methods, respectively. In general, ETo1 showed similar skill to ETo2, and skillful forecasts at long leads occurred in cold seasons (Figs. 10, 11). In Fig. 10, for the SD method, the predictive skill of the deterministic forecasts of ETo1 and ETo2 had skill at all leads for cold seasons, while there was no skill for warm seasons. Both ETo1 and ETo2 had skill for below-normal forecasts at long leads for cold seasons. For above-normal forecasts, both ETo1 and ETo2 show skill at long leads out to month 5 in cold seasons. Figure 11 shows the SDBC method indicates a slight improvement of skill at longer forecast lead in terms of the above- and below-normal BSS and a great improvement of skill at longer leads for the near-normal BSS even though the skill was still negative. The Student’s t test was conducted to compare the skill of SDBC and SD. For ETo1, the improvements were significant (p < 0.05) for the below-normal BSS from month 6 to month 9 leads, for the near-normal BSS at all leads, and for the above-normal BSS from month 6 to month 9 leads; for ETo2, only the near-normal BSS from month 6 to month 9 leads and the above-normal BSS from month 6 to month 8 leads showed significant improvement (p < 0.05). There were no improvements for any other forecasts.

Fig. 11.
Fig. 11.

As in Fig. 10, but for the SDBC method.

Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-087.1

d. Evaluation of forecast skill during ENSO events

Since CFSv2 has been shown to accurately predict the phase of ENSO (Kim et al. 2012), ETo might be better predicted during ENSO events. To evaluate this, we summarized the skill scores of ETo forecasts where the forecast initial seasons (Figs. 12, 13) and target seasons (Fig. 14) were classified as either El Niño [Oceanic Niño Index (ONI) exceeds +0.5°C for at least five consecutive overlapping seasons] or La Niña events (ONI is below −0.5°C for at least five consecutive overlapping seasons) according to the historical ENSO episodes issued by NOAA’s Climate Prediction Center. Figure 12 shows the predictive skill of downscaled ETo by the SDBC method in different seasons at 0-month lead during ENSO events. While the ETo forecast skill was still negative in warm seasons, it was positive in cold seasons and higher than the forecast skill for the entire period (Fig. 3). Figure 13 shows the predictive skill of the downscaled ETo by the SDBC method as a function of seasons and leads where forecast initial seasons were during ENSO events. It shows the forecast skill was higher than during the entire period at long leads (Fig. 11). Figure 14 shows the predictive skill of the downscaled ETo by the SDBC method as a function of seasons and leads where the forecast target seasons were during ENSO events. It shows the skill was negative at long leads even though it showed high skill at 0-month lead. These results indicate that the CFSv2 model can predict ETo with good skill only when the forecast initial seasons were in either the El Niño or La Niña phase of ENSO. The ETo forecasts were not skillful when the forecast target months were during an ENSO event but the forecast initial months were not.

Fig. 12.
Fig. 12.

The skill scores of downscaled ETo1 (black) and ETo2 (gray) by the SDBC method as a function of consecutive three-month periods (January–March to December–February) for 0-month lead during ENSO events: (a) MSESS and BSS (b) below, (c) near, and (d) above normal.

Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-087.1

Fig. 13.
Fig. 13.

As in Fig. 10, but by the SDBC method. The forecast initial season is during ENSO events.

Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-087.1

Fig. 14.
Fig. 14.

As in Fig. 13, but the forecast target season is during ENSO events.

Citation: Journal of Hydrometeorology 15, 3; 10.1175/JHM-D-13-087.1

5. Concluding remarks

ETo is an important hydroclimatic factor for regional water resources planning and management. Based on the seasonal forecasts of Tmean, Tmax, Tmin, Rs, and Wind from the NCEP CFSv2, this study evaluated the deterministic and probabilistic forecasts of seasonal ETo and the predictability of the five relevant variables over the SEUS. The ETo was estimated by two methods. The first method (ETo1) calculated the coarse-scale ETo using the FAO-56 PM equation with the input from the seasonal forecasts of Tmean, Tmax, Tmin, Rs, and Wind from the CFSv2 and then downscaled the coarse-scale ETo to a regional 12-km grid. The second method (ETo2) downscaled each of the five CFSv2 variables to the 12-km grid and then calculated ETo using the FAO-56 PM equation with those downscaled variables. Two methods of statistical downscaling were tested for all seasons and all leads, spatial disaggregation (SD), and spatial disaggregation with bias correction (SDBC).

The CFSv2 showed potential to make deterministic and probabilistic forecasts of seasonal ETo and the five relevant variables in the SEUS. The skill for forecasting seasonal ETo varied with different seasons and across three states of the SEUS. Overall, the deterministic and probabilistic forecasts for both ETo methods were skillful at longer leads during the cold seasons but showed no skill at any leads during the warm seasons. The ETo2 had slightly higher skill than ETo1 over space; however, there was little difference in terms of the forecast skill in different seasons or at different leads. In terms of the computational time, the SD method is more efficient than the SDBC method since it does not include the quantile mapping bias correction procedure. However, the SDBC method slightly improved the probabilistic forecast skill for most of the area except part of southern Florida; the skill for probabilistic forecasts was significantly enhanced over all seasons with longer skillful leads during the cold seasons, but the skill for all leads was still negative during the warm seasons. For downscaling of the forecasts of the five variables, the SDBC method improved the skill mostly in warm seasons when the SD method showed minor or negative skill. The improvement of the skill was over most of the study area, especially over the areas showing minor or negative skill, and the enhancements of the skillful forecast leads were mostly in warm seasons.

Considering the similarity of forecast skill and the efficiency of computational time, ETo1 is the preferred method to ETo2 because it downscaled only one variable (ETo) instead of five. However, ETo2 is helpful to identify the skillful or unskillful variables and, accordingly, to determine the ETo calculation method. Based on this information, other approximate ETo calculation methods such as the Hargreaves method (Hargreaves and Samani 1985), Turc method (Turc 1961), or Priestley–Taylor method (Priestley and Taylor 1972) that require fewer variables might be as skillful as the PM method to produce ETo forecasts in the region (Droogers and Allen 2002; Martinez and Thepadia 2010; Sperna Weiland et al. 2012; Thepadia and Martinez 2012; Todorovic et al. 2013). In addition, the replacement of unskillful variables with the climatology from reanalysis datasets has been shown to improve forecast skill (Tian and Martinez 2012a,b). The improvement of skill for the SDBC method over the SD method implies the additional quantile mapping procedure is effective to correct the systematic errors of the CFSv2 forecast since the SDBC method corrects for bias in the entire shape of the distribution.

ETo was found to be better predicted by the CFSv2 model when the forecast initial seasons were in either the El Niño or La Niña phase of ENSO. However, the ETo forecasts were not skillful when the forecast target months were during an ENSO event but the forecast initial months were not. This result is consistent with the findings from the CFSv1 model, which was found to be able to capture the impact of ENSO on precipitation when the initial conditions already contained the ENSO signal (Yoon et al. 2012).

The variability of the ensemble of the forecasted variables was not evaluated in this work. Such variability of the ensemble is most likely different among different variables. However, downscaling and bias-correction procedures could reduce the forecast uncertainty (e.g., Wilks and Hamill 2007). There are different methods to evaluate the uncertainty of ensemble forecasts (e.g., Wang 2014). Such a study was beyond the scope of this paper. Future work could be conducted to evaluate the uncertainties associated with each of the forecasted variables and how much the downscaling and bias correction could reduce such uncertainty.

The CFSv2-based seasonal prediction of ETo showed moderate skill in cold seasons but no skill in warm seasons. The low performance of ETo prediction in summer was caused by the skill drops of Rs and Tmin. Our explanation is that more convective heating occurs in summer than in winter. Such convection could generate different weather conditions (e.g., clouds) at a small scale that are not captured by the CFSv2 because of its coarse resolution. When the forecast target is in summer, most of the forecasts except Tmean and Tmax showed no skill. These variables, including ETo, Tmin, Rs, and Wind, may not be ready for applications in planning and decision making in summer in the SEUS. Since Rs had no skill during summer and was found to be one of the most important influential variables for ETo estimation in the SEUS, efforts such as running the CFSv2 at a high grid spacing could be done in order to improve the Rs forecasts in the summer. When the forecast target is in winter, using the forecast product could potentially bring benefits for planning or decision making for different sectors even though the skill is moderate. For the application of ETo forecasts in agricultural water management, summer is not the only growing season for many crops in the SEUS because of the warmer climate; the forecast information in other seasons could be useful for farmers. The evaluation of the economic value for using the seasonal forecasts could be conducted in future work.

The ETo forecasts produced in this work were bias corrected using the NLDAS-2 fields that were based on interpolation of the NARR. While the NLDAS-2 data were used as a surrogate for observations, they may contain biases compared to station-based observations. Therefore, the downscaled and bias-corrected CFSv2 predictions produced by this work are still affected by the biases in the NLDAS-2 data. Nevertheless, the methods for ETo estimation and forecasts used in this work are ready to be extended to other regions. The evaluation of the forecast skill can provide valuable information for users who want to use the seasonal forecast product. The downscaled seasonal ETo forecast product could potentially be used to drive hydrological models, urban water supply and demand models, and crop models; inform irrigation schedules; guide water resources planning; assess the risk of climate variability, etc.; and thus improve the reliability of decision-making and reduce risk in different societal sectors such as water management, resource management, and agricultural production management.

Acknowledgments

This research was supported by the NOAA/Climate Program Office SARP and RISA program Grants NA10OAR4310171 and NA12OAR4310130. 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).

APPENDIX

Derivation of the FAO Penman–Monteith Equation for the Hypothetical Grass Reference Crop

For the original PM equation, the aerodynamic resistance is estimated using Eq. (A1):
ea1
where ra is aerodynamic resistance (s m−1); zm is height of wind measurements (m); zh is height of humidity measurements (m); d is zero plane displacement height (m), zom is roughness length governing momentum transfer (m); zoh is roughness length governing transfer of heat and vapor (m); k is von Kármán’s constant, 0.41 (–); and uz is wind speed at height z (m s−1).
For a wide range of crops, the zero plane displacement height d (m) and the roughness length governing momentum transfer zom (m) can be estimated from the crop height h (m) by the following equations:
eq1
eq2
The roughness length governing transfer of heat and vapor zoh (m) can be approximated by
eq3
Assuming a grass reference crop surface with constant crop height of 0.12 m and standardized height for wind speed, temperature, and humidity measurements at 2 m (zm = zh = 2 m), Eq. (A1) becomes
ea2
For the original PM equation, the surface resistance is estimated using Eq. (A3):
ea3
where rs is surface resistance (s m−1), r1 is bulk stomatal resistance of the well-illuminated leaf (s m−1), and LAIactive is active (sunlit) leaf area index [m2 (leaf area) m−2 (soil surface)]. Assuming the same grass reference crop surface, a general equation for LAIactive is
eq4
which takes into consideration the fact that generally only the upper half of dense clipped grass is actively contributing the surface heat and vapor transfer. A general equation for LAI is
eq5
where h is the crop height (m).
The stomatal resistance n of a single leaf has a value of about 100 s m−1 under well-watered conditions. Thus, Eq. (A3) becomes
ea4
Then, Eq. (5) is derived based on Eqs. (A2) and (A4):
ea5
In Eq. (2), Rn and G are energy available per unit area and expressed in MJ m−2 day−1. The conversion from energy values to equivalent depths of water or vice versa is given by
ea6
The specific heat at constant pressure is given by
eq6
and considering the ideal gas law for ρa:
eq7
where , the virtual temperature, can be substituted by
eq8
which results in
eq9
where cp is specific heat at constant pressure (MJ kg−1 °C−1), ρa is mean air density at constant pressure (kg m−3), ra is aerodynamic resistance (s m−1), γ is psychrometric constant (kPa °C−1), ε is ratio molecular weight of water vapor/dry air (=0.622), λ is latent heat of vaporization (MJ kg−1), R is specific gas constant (=0.287 kJ kg−1 K−1), T is air temperature (°C), and P is atmospheric pressure (kPa):
ea7
When divided by λ (=2.45), Eq. (A7) becomes
ea8
The FAO-56 PM equation [Eq. (3)] is then derived by plugging Eqs. (A5), (A6), and (A8) into Eq. (2).

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