An Improved Climatological Forecast Method for Projecting End-of-Season Water Requirement Satisfaction Index

William A. Turner aDepartment of Geography, University of California, Santa Barbara, Santa Barbara, California
bClimate Hazards Center, Department of Geography, University of California, Santa Barbara, Santa Barbara, California
cEarth Research Institute, Department of Geography, University of California, Santa Barbara, Santa Barbara, California

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Greg Husak aDepartment of Geography, University of California, Santa Barbara, Santa Barbara, California
bClimate Hazards Center, Department of Geography, University of California, Santa Barbara, Santa Barbara, California
cEarth Research Institute, Department of Geography, University of California, Santa Barbara, Santa Barbara, California

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Chris Funk aDepartment of Geography, University of California, Santa Barbara, Santa Barbara, California
bClimate Hazards Center, Department of Geography, University of California, Santa Barbara, Santa Barbara, California

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Dar A. Roberts aDepartment of Geography, University of California, Santa Barbara, Santa Barbara, California
cEarth Research Institute, Department of Geography, University of California, Santa Barbara, Santa Barbara, California

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Charles Jones aDepartment of Geography, University of California, Santa Barbara, Santa Barbara, California
cEarth Research Institute, Department of Geography, University of California, Santa Barbara, Santa Barbara, California

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Abstract

A simple—yet powerful—indicator for monitoring agricultural drought is the water requirement satisfaction index (WRSI). In data-sparse, food-insecure areas, the WRSI is used to guide billions of dollars of aid every year. The WRSI uses precipitation (PPT) and reference evapotranspiration (RefET) data to estimate water availability relative to water demand experienced over the course of a growing season. If the season is in progress, to-date conditions can be combined with climatological averages to provide insight into potential end-of-season (EOS) crop performance. However, if the average is misrepresented, these forecasts can hinder early warning and delay precious humanitarian aid. While many agencies use arithmetic average climatologies as proxies for “average conditions,” little published research evaluates their effectiveness in crop-water balance models. Here, we use WRSI hindcasts of three African regions’ growing seasons, from 1981 to 2019, to assess the adequacy of the arithmetic mean climatological forecast—the Extended WRSI. We find that the Extended WRSI is positively biased, overestimating the actual EOS WRSI by 2%–23% in East, West, and southern Africa. The presented alternative combines to-date conditions with data from previous seasons to produce a series of historically realistic conclusions to the current season. The mean of these scenarios is the WRSI Outlook. In comparison with the Extended WRSI, which creates a single forecast scenario using average inputs that are not covarying, the WRSI Outlook employs an ensemble of scenarios, which more adequately capture the historical distribution of distribution of rainfall events along with the covariability between climate variables. More specifically, the impact of dry spells in individual years is included in the WRSI Outlook in a way that is smoothed over in the Extended WRSI. We find that the WRSI Outlook has a near-zero bias score and generally has a lower RMSE. In total, this paper highlights the inadequacies of the arithmetic mean climatological forecast and presents a less biased and more accurate scenario-based approach. To this end, the WRSI Outlook can improve our ability to identify agricultural drought and the concomitant need for humanitarian aid.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: William A. Turner, wturner@ucsb.com

Abstract

A simple—yet powerful—indicator for monitoring agricultural drought is the water requirement satisfaction index (WRSI). In data-sparse, food-insecure areas, the WRSI is used to guide billions of dollars of aid every year. The WRSI uses precipitation (PPT) and reference evapotranspiration (RefET) data to estimate water availability relative to water demand experienced over the course of a growing season. If the season is in progress, to-date conditions can be combined with climatological averages to provide insight into potential end-of-season (EOS) crop performance. However, if the average is misrepresented, these forecasts can hinder early warning and delay precious humanitarian aid. While many agencies use arithmetic average climatologies as proxies for “average conditions,” little published research evaluates their effectiveness in crop-water balance models. Here, we use WRSI hindcasts of three African regions’ growing seasons, from 1981 to 2019, to assess the adequacy of the arithmetic mean climatological forecast—the Extended WRSI. We find that the Extended WRSI is positively biased, overestimating the actual EOS WRSI by 2%–23% in East, West, and southern Africa. The presented alternative combines to-date conditions with data from previous seasons to produce a series of historically realistic conclusions to the current season. The mean of these scenarios is the WRSI Outlook. In comparison with the Extended WRSI, which creates a single forecast scenario using average inputs that are not covarying, the WRSI Outlook employs an ensemble of scenarios, which more adequately capture the historical distribution of distribution of rainfall events along with the covariability between climate variables. More specifically, the impact of dry spells in individual years is included in the WRSI Outlook in a way that is smoothed over in the Extended WRSI. We find that the WRSI Outlook has a near-zero bias score and generally has a lower RMSE. In total, this paper highlights the inadequacies of the arithmetic mean climatological forecast and presents a less biased and more accurate scenario-based approach. To this end, the WRSI Outlook can improve our ability to identify agricultural drought and the concomitant need for humanitarian aid.

© 2022 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: William A. Turner, wturner@ucsb.com

1. Introduction

As the 5-year mark of the UN General Assembly 2030 Agenda for Sustainable Development looms on the horizon, hunger is on the rise globally (FAO et al. 2019). A 2020 Global Report on Food Crises by the Food Security Information Network (GRFC FSIN) estimates that 135 million people across 55 countries are, or will be, in need of urgent humanitarian food and nutrition assistance in 2021; of those, more than half are in Africa (FSIN 2020). Global food security can be categorized as a disruption to one or more of the following pillars: adequate food availability, food access, food utilization, stable prices, and incomes (Brown et al. 2015; Funk and Shukla 2020). The drivers that destabilize these pillars are often interlinked and mutually reinforcing, making it difficult to pinpoint the specific trigger or driver of each food crisis. (FSIN 2020). The GRFC takes a practical approach by estimating which drivers are the most salient for each population, with the three most common, broad categories being conflict and insecurity, climate and weather extremes, and economic shocks. While conflict and insecurity have been the predominant drivers of food insecurity (Anderson et al. 2021), weather extremes are increasingly impactful (FSIN 2020; Ray et al. 2015). Furthermore, when separated by key drivers, Africa had the largest numbers of acutely food-insecure people in need of assistance in countries predominantly affected by adverse weather events, particularly in East and southern Africa (FAO et al. 2019). In East Africa, for example, between 2015 and 2017, the number of food-insecure individuals increased from 45 to 70 million. Some of these increases have been linked to extreme droughts related to the 2015–17 El Niño–La Niña sequence (Funk et al. 2018b). There then followed an extreme positive Indian Ocean dipole event in 2019 (Nicholson et al. 2022), which contributed to a massive desert locust outbreak and widespread displacement in East Africa, and a historic La Niña–related three-season drought sequence (ICPAC et al. 2021). At present, the Famine Early Warning System Network (FEWS NET)1 anticipates that more than 20 million people in Ethiopia, Somalia, and Kenya will need urgent humanitarian food assistance in 2022 to prevent crisis (IPC Phase 3; IPC Global Partners 2021) or worse outcomes. The sharp increase in food assistance needs, which is over 70% higher than food crises in 2016 and 2017, is primarily driven by the impacts of severe drought across the eastern portion of the region, and by increased conflict in northern Ethiopia (FEWS NET 2021). While it is always difficult to untangle the causes of severe food insecurity, there is no doubt that climate extremes have a very strong impact in many parts of Africa.

Fortunately, international aid agencies, national disaster risk management systems, and nongovernmental organizations can often provide effective humanitarian relief by identifying and targeting the most food-insecure populations for assistance (Backer and Billing 2021; Braimoh et al. 2018; Choularton and Krishnamurthy 2019; FSIN 2020; Funk et al. 2019b). In particular, FEWS NET assists by providing timely and localized agroclimatic information to better inform governmental and humanitarian organizations’ responses to food insecurity (Backer and Billing 2021; Funk et al. 2019b). The ensuing food-security assessments employ a convergence of evidence method, using a wide range of socioeconomic and environmental indicators such as poverty, market prices, vegetative health, and weather conditions (Braimoh et al. 2018; Choularton and Krishnamurthy 2019). With early warning, appropriate interventions can be made (e.g., Becker-Reshef et al. 2020; DuBois et al. 2018; UNDP 2018). However, due to the exceptional financial cost of invoking such a response, decision-makers require clear, compelling evidence before making such commitments (Becker-Reshef et al. 2020). Natural uncertainty (variability) or, worse, inaccurate assumptions about these variables can result in misleading or contradictory indicators, which may obscure looming conditions and limit early warning (Headey and Barrett 2015; Choularton and Krishnamurthy 2019; Hillbruner and Moloney 2012). Here, we document the tendency of one commonly used indicator for seasonal crop-water monitoring, the extended water requirement satisfaction index (Extended WRSI), to systematically overestimate end-of-season (EOS) crop conditions when forecast with arithmetic average climatology inputs [precipitation (PPT) and reference evapotranspiration (RefET)]. In its place, we present a mean scenario-based approach, which corrects for these biases and provides an improved technique for projecting EOS crop conditions.

The timely and spatially focused monitoring products, seasonal outlooks, and agroclimatic alerts provided by FEWS NET and its partners guide humanitarian assistance, helping to save lives and secure livelihoods among some of the world’s most food-insecure populations. Given the increasing attribution of climate and weather-induced food insecurity (Archer et al. 2017; Funk et al. 2018a, 2019a; SADC 2016; Shukla et al. 2020), there is an increased effort to expand upon and improve the ability to monitor and forecast agroclimatic conditions. Some existing methods use remote sensing and in situ data, including precipitation (Funk et al. 2015a,b) and reference evapotranspiration (Hobbins et al. 2019a,b, 2020) products, and derived crop-water balance models (Shukla et al. 2014; Silva Fuzzo et al. 2020; Tarnavsky and Bonifacio 2020). One such water-balance model, the WRSI, was originally calculated with station rainfall and average dekadal2 reference evapotranspiration (Frére and Popov 1976, 1979), and has been shown to be directly related to crop-yield data in Senegal, Algeria, Bangladesh, Ethiopia, Togo, Argentina, and Tanzania using linear yield-reduction functions (Frére and Popov 1979, 1986). Lhomme and Katerji (1991) found similar successes when using daily rainfall and evapotranspiration data to calculate WRSI and corresponding yield-reduction predictions in France. Since then, a greater availability of operational gridded input data has allowed for geospatial calculation of the WRSI using time-varying meteorological inputs (Verdin and Klaver 2002). Subsequent evaluations of gridded WRSI against reported yield commonly report regression correlations exceeding 0.77 in Ethiopia, southern Africa, Zimbabwe, Tanzania, and Kenya, and of 0.52 in India (Patel et al. 2012; Senay and Verdin 2002, 2003; Tarnavsky et al. 2018; Verdin and Klaver 2002). In addition to its use as a proxy crop-yield index, satellite rainfall-based WRSI simulations have been used to determine loss exceedance probability curves, drought frequency maps, and agricultural drought risk for varying crops in Kenya, Malawi, Mozambique, Niger (Jayanthi et al. 2014), South Africa (Masupha and Moeletsi 2020; Moeletsi et al. 2016), and Brazil (Santos et al. 2012), and has been shown to be associated with child dietary diversity and malnutrition in Burkina Faso (Pinchoff et al. 2021). Clearly, the EOS WRSI can be a useful indicator for agroclimatic conditions and subsequent health impacts.

However, there has been considerably less cross validation of WRSI forecasts—specifically, how well does an early-season WRSI forecast capture the EOS WRSI? To our knowledge, no research has been undertaken to investigate the implications of using arithmetic mean climatological inputs, neither in regard to the original formulation using average RefET with time-specific PPT, nor in the case of the Extended WRSI, which uses average PPT and RefET to project EOS WRSI. The scenario-based forecast (WRSI Outlook) follows the same schema as that utilized in the Tropical Applications of Meteorology Using Satellite Data and Ground-Based Measurements-Agricultural Early Warning System (TAMSAT-ALERT) (Asfaw et al. 2018; Brown et al. 2017), which has been shown to be well correlated with observed WRSI (correlation coefficient r > 0.8) in Kenya (Boult et al. 2020). However, Boult et al. (2020) uses spatially averaged (county level) WRSI, confined to Kenya, for their analysis and did not compare the scenario method with other commonly used forecasts (e.g., the Extended WRSI). Furthermore, their primary skill metric (Pearson’s correlation coefficient) does not indicate accuracy or bias—two metrics that are essential to understanding the effectiveness of a forecast.

The following three sections are laid out as follows: section 2a details the data used in the calculation of the WRSI in this study; section 2b provides a brief documentation of the WRSI, describes the existing WRSI forecast methodology (Extended WRSI) and its shortcomings, presents an alternative approach to a climatological forecast (the WRSI Outlook), and details the methods and metrics used for testing the skill of both forecasts; and section 2c presents the regions and seasons of interest. Sections 3 and 4 describe the bias and accuracy scores of each forecast method and discuss the causes and implications of these results. Section 5 gives brief concluding remarks, including a summary of our findings, and a suggested way forward for WRSI forecasting.

2. Materials and methods

a. Data

1) Climate Hazards Infrared Precipitation with Stations

The Climate Hazards Infrared Precipitation with Stations (CHIRPS) dataset is a quasi-global rainfall dataset, with spatial coverage from 50°S to 50°N (over all longitudes) and a data record extending from 1981 to near present. CHIRPS blends a high-resolution climatology (Funk et al. 2015b) with station data and intercalibrated (Knapp et al. 2011) thermal infrared precipitation estimates to create a 0.05° native spatial resolution gridded rainfall time series appropriate for trend analysis and seasonal drought monitoring in data-sparse regions with complex terrain.

The creation of CHIRPS has supported drought monitoring efforts by numerous international stakeholders, including FEWS NET (Shukla et al. 2017) and GEOGLAM (Becker-Reshef et al. 2020; Verdin et al. 2013), and has proven to be one of the most accurate rainfall products for characterizing wet-season cycles (Dunning et al. 2016; Salerno et al. 2019), climate variability (Dinku et al. 2007, 2018), and agricultural drought in Africa (Agutu et al. 2017; Ayehu et al. 2018; Ndayisaba et al. 2017; Zhan et al. 2016), China (Gao et al. 2018), India (Sandeep et al. 2021), and Argentina (Rivera et al. 2019). Most relevantly, in a comprehensive analysis of WRSI’s sensitivity to rainfall inputs from three widely used precipitation datasets [Africa Rainfall Climatology 2.0 (ARC2), CHIRPS, and TAMSAT], CHIRPS-driven WRSI produced estimates that most closely correlated with reported yields in Kenya (Tarnavsky et al. 2018).

The native time step for CHIRPS is the pentad, with all other time steps being either aggregates (e.g., dekadal; monthly) or disaggregates (e.g., daily); aggregated daily data are equal to pentadal amounts, and aggregated pentadal amounts are equal to dekadal amounts. This analysis uses dekadal CHIRPS resampled to 0.1° resolution, corresponding to the common temporal and spatial resolution of operational WRSI inputs/outputs (Verdin and Klaver 2002). The climatology CHIRPS used in this study is calculated as the mean dekadal CHIRPS value from 1981 to 2019.

2) Global Reference ET for the FEWS NET Science Community

The Global Reference Evapotranspiration for the FEWS NET Science Community (RefET) is produced by the National Oceanic and Atmospheric Administration’s Physical Sciences Division (NOAA/PSD) (Hobbins et al. 2018, 2019a,b, 2020). It is generated using atmospheric reanalysis data to calculate RefET using the American Society of Civil Engineers (ASCE) Penman–Monteith formulation on a daily basis (Allen 2005), which is used in many studies (e.g., McEvoy et al. 2016). RefET is driven by five Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA2; Gelaro et al. 2017) variables: 2-m air temperature (T2M), 2-m specific humidity (QV2M), surface downward shortwave radiation (SWGDN), 2-m wind speed at 2-m height (U2M and V2M), and surface atmospheric pressure (PS). The RefET is calculated for two different crop types, resulting in two separate products: (i) long-crop, or a 0.5-m alfalfa reference crop, and (ii) short-crop, or a 0.12-m short grass reference crop. Daily RefET surfaces are spatially downscaled to 0.125° × 0.125° using climatological monthly potential evaporation (PET) estimates from the International Water Management Institute (IWMI). The draft paper detailing this dataset is currently in progress. For more information, please visit the Global Reference ET for the FEWS NET Science Community website (NOAA PSL 2018).

For use in this analysis, the short-crop RefET is aggregated from daily to dekadal time steps and resampled to 0.1° resolution by the Climate Hazards Center, corresponding to the common temporal and spatial resolution of operational WRSI inputs/outputs (Verdin and Klaver 2002). The climatology RefET used in this study is calculated as the mean dekadal RefET value from 1981 to 2019.

b. Methodology

The computational procedure of the WRSI, Extended WRSI, and WRSI Outlook is described in detail, in part because descriptions of the WRSI are frequently glossed over in papers, and, in part, because the detail will help to illustrate some of the deficiencies in the Extended WRSI method, which have not been well documented. Furthermore, while the WRSI Outlook is akin to the TAMSAT-ALERT WRSI, it was developed and tested, and remains operational, by the Climate Hazards Center (CHC) independent of the TAMSAT-ALERT system. This paper serves to document the CHC product.

1) Water requirement satisfaction index

Our analysis revolves around the WRSI. Frère and Popov originally proposed this simplified crop-weather analysis model in 1976 to the U.N. Food and Agriculture Organization (FAO) as a proxy for crop performance, and an indicator of the satisfaction of the crop water requirements in areas of the world where water represents the main constraint for crops (Frére and Popov 1976, 1979). The components of this crop water balance model are depicted via a schematic diagram in Fig. 1 and described briefly in the text that follows. For a more robust, nuanced description of the model, see Turner (2020).

Fig. 1.
Fig. 1.

A schematic diagram showing the components of a crop water balance model. Terms and variables involved are described in more detail in the main text. This figure is modeled after a schematic diagram in Senay and Verdin (2003).

Citation: Journal of Hydrometeorology 23, 8; 10.1175/JHM-D-21-0184.1

The WRSI is determined by the water supply and water demand that a crop experiences during the growing season. As such, the EOS WRSI is calculated as the ratio of crop-adjusted actual evapotranspiration (AETc) to the crop water requirement, represented as the crop-adjusted reference evapotranspiration (RefETc):
WRSI=i=SOSEOSAETcii=SOSEOSRefETci×100.

The standard time step of the WRSI is the dekad, because a daily time step makes modeling data intensive and relatively noisy, without a proportional gain in information, and a monthly time step is too coarse to capture rainfall/RefET distribution during critical vegetation growth stages (Verdin and Klaver 2002). For a given season, the onset of rains [start of season (SOS)] is determined using a threshold amount and distribution of rainfall received in three consecutive dekads, as defined by the Centre Regional de Formation et d’Application en Agrométéorologie et Hydrologie Opérationnelle (AGRHYMET 1996). SOS is established when there is at least 25 mm of rainfall in an initial dekad, followed by a total of at least 20 mm of precipitation in the following two consecutive dekads. Once these rainfall metrics are met, the SOS is defined as the first dekad in that three-dekad series. Previous work has shown that rainfall-based SOS metrics such as this, while simple, are an effective means for estimating planting behavior in rainfed agricultural systems across Africa (Krell et al. 2022; Marteau et al. 2009; Sultan et al. 2005) and can be used as an early harbinger of drought (Shukla et al. 2021) and subsequent economic shocks (Davenport et al. 2021).

Antecedent soil moisture to be carried into the first dekad of the season is calculated using the preceding six dekads. The EOS is then calculated by adding the gridcell length of growing period (LGP) to the SOS dekad and subtracting 1. The LGP information for each region is provided as raster files in the GeoWRSI software package, at 0.1° spatial resolution.

While PET is the term most frequently used in literature, the newer and more precise term is reference crop ET (RefET), where Ref is referring to a 0.12-m-high, green-grass reference crop with defined characteristics (Allen et al. 1998). The WRSI further adjusts the RefET using crop-specific coefficients that vary based on the phenology of different cereals and grains:
RefETci=Kci×RefETi.

The Kc values define the water use pattern of a crop based on the growth stage at that point in the growing season. Published values (Allen et al. 1998) are available for critical points in a crop (or rangeland/grass) phenology (e.g., emerging, vegetative, flowering, and ripening), and intervening values are linearly interpolated for each time step (dekad) based on the LGP for that crop. For context, Kc values greater than 1.0 indicate periods of the phenological cycle in which the crop has a greater upper limit to its transpiration and evaporation than the reference green-grass crop used in the calculation of the RefET data. This heightened limit is representative of factors such as increased aerodynamic roughness (due to both height and foliage), which can increase the turbulent transfer of vapor from the plant and exposed soil surface. Our analyses use millet as the crop type for West Africa, and maize for East and southern Africa, as these are the primary crops for each region.

AETc, seen in the numerator of Eq. (1), represents the actual (as opposed to the potential) amount of water withdrawn from the soil water reservoir. In the context of the WRSI, which measures plant-water satisfaction as the ratio of AET:RefET, this relationship implies that when an area is experiencing water stress due to limited precipitation, AET will decrease due to lack of available soil moisture for evaporation, while RefET will increase due to an increase in the vapor pressure deficit, resulting from increased air temperature. As such, dry conditions, as measured by precipitation, can be exacerbated by increased atmospheric demand (RefET).

In theory, a situation of “no deficit” (i.e., EOS WRSI = 100) corresponds to normal crop yields, whereas a value of less than 100 is associated with reduced crop yields. In actuality, the range of WRSI values and correlation to above/below-average yields varies depending on the region. As such, the most common form of the WRSI used as a monitoring tool is the percent of average, which normalizes the EOS WRSI by dividing by the historical median EOS WRSI. Quasi-global gridded datasets, such as CHIRPS and the reference evapotranspiration dataset used in this paper, allowed this process to be adapted and extended from a single-station location to a gridcell-based, geospatial application (GeoWRSI) (Verdin and Klaver 2002), in which each grid cell is treated like a station from the classic FAO (Frére and Popov 1976) method. Although there are many more robust and data-intensive, physically based, crop models available, FEWS NET adapted the FAO WRSI model for implementation in 2002 because of its limited data requirements, its simplicity in operational use, and its ability to capture spatially varying crop-water satisfaction in data-sparse areas around the world (Senay and Verdin 2002, 2003; Tarnavsky et al. 2018). Most recently, the Climate Hazards Center implemented the GeoWRSI model in Interactive Data Language (IDL) to facilitate simulations using varying precipitation and evapotranspiration inputs, including forecast data for use in current-season monitoring. To ensure consistency, this IDL implementation of the WRSI model is used for all WRSI runs and comparisons in this study.

2) USGS/EROS Extended WRSI

The Extended WRSI (Melesse et al. 2007) is provided by the USGS FEWS NET Project, which is part of the Early Warning Focus Area at the USGS Earth Resources Observation and Science (EROS). The Extended WRSI is a forecast estimate of what the WRSI would be at the end of the growing season, assuming the dekadal precipitation and evapotranspiration for the remainder of the season matches the historical average (also known as an arithmetic mean climatological forecast). At a given point in a monitored growing season, long-term average climatological data are used to fill in the missing data between the current dekad and the end of the season. Once that is done, the calculation principles are the same as the standard WRSI (ratio of the season total crop evapotranspiration to the crop water requirement). As the season progresses and actual PPT and RefET data become available, the climatology data previously used for those dekads are replaced so that, at the end of the growing season, only current-year PPT and RefET are used as inputs. It is important to note here that this methodology is not meant to be a forecast that is responsive to existing or prevailing climate conditions but rather a baseline estimate of what the EOS WRSI would be if the remainder of the season resembled the average of years past. The Extended WRSI is useful in cases, for example, in which seasonal rainfall has a historically consistent end date but rainfall for a given year starts exceptionally late. In this case, although water requirements for planting are met, if a normal conclusion to the season is experienced, rainfall will end in the middle of the crop’s growth cycle—when crop-water demand is highest. In this case, the Extended WRSI would likely accurately predict an EOS crop-water deficit (below-average WRSI), despite the early season conditions being satisfactory. The problem arises when the methodology systematically misrepresents “average” conditions.

The motivation for this research stems from an observed tendency of this Extended WRSI method to be overly optimistic (i.e., producing above-average projected anomalies), particularly early in the monitoring season. The source of this erroneous reporting is due to two significant shortcomings. First, several studies have shown that precipitation and evapotranspiration covary. More specifically, there tends to be a nonlinear inverse relationship; evapotranspiration tends to be lower during rainy days, primarily as a result of decreased solar radiation and increased relative humidity, and conversely evapotranspiration tends to be higher during dry days, primarily as a result of increased solar radiation and decreased relative humidity (Collischonn and Collischonn 2016). Furthermore, there exists a complementary relationship between actual evapotranspiration and reference evapotranspiration (Bouchet 1963; Morton 1965). This is especially important and apparent when monitoring drought years, as below-average rainfall conditions are exacerbated by above-average evapotranspiration, resulting in twofold water stresses (Funk et al. 2021a,b). Long-term averages of precipitation and evapotranspiration fail to capture these finer-time-scale interplays between PPT, AET, and RefET, and, as such, the historical WRSI calculated with average dekadal evapotranspiration has considerably lower variability than does WRSI calculated with time-specific data (Fig. 2). The second, and perhaps more profound, shortcoming of using climatology inputs to predict EOS WRSI, is that using average precipitation results in heavily biased EOS WRSI projections, especially when used early in the season. This is primarily due to consistently wet days (>0 mm), which are inherent in any historical average calculation. More to this point, using an arithmetic mean inherently results in a failure to capture the proper distribution of historical rain events, including the probability of zero-rainfall days. On the other side of the coin, marginal cropping zones with short rainy seasons rely on above-average rainfall events to recharge soil moisture and satisfy crop-water demands, and thus, average inputs in these areas result in consistently below-average projected WRSI (dry bias). Regardless of the directionality of the bias, any reduction in variability resulting from a failure to use time-specific data (as opposed to averaged data) limits our ability to place current events in context with historical precedents—a practice that is integral to early warning systems and consequent resource allocation (food and humanitarian assistance). This study aims to reduce the biases associated with using climatology inputs by introducing more historically relevant hydroclimatic data, thereby improving EOS projections, and subsequent monitoring efforts to timely and adequately allocate food and humanitarian assistance.

Fig. 2.
Fig. 2.

Change in the standard deviation of historical (1981–2019) EOS WRSI when using time-specific evapotranspiration, instead of average (climatology) values, in West, East, and southern Africa growing seasons. Blue and red hues indicate areas where the variability of EOS WRSI increases and decreases, respectively, with the addition of time-specific RefET in place of climatology RefET.

Citation: Journal of Hydrometeorology 23, 8; 10.1175/JHM-D-21-0184.1

3) WRSI Outlook

The presented alternative, the WRSI Outlook, is a scenario-based approach akin to the TAMSAT-ALERT methodology (Asfaw et al. 2018; Brown et al. 2017), which uses historical precipitation and evapotranspiration seasons from 1981 to 2019 to produce historically relevant EOS WRSI scenarios. Whereas the Extended WRSI method uses average PPT and RefET to fill in the gap from the current dekad and the end of the season, the WRSI Outlook fills in the missing series of dekads with historical (e.g., 1981, 1982, 1983, …, 2019) PPT and RefET data for the same period, with each set of year-specific data resulting in one potential EOS scenario; what would the EOS WRSI be if the remainder of the growing season looked exactly like that period in 1981, or 1982, or 1983, and so on? The average (mean) of these potential scenarios is calculated to produce the WRSI Outlook. Figure 3 shows this process at the gridcell level and is described in more detail as follows.

Fig. 3.
Fig. 3.

The scenario WRSI process for a single grid cell in southern Africa (Zimbabwe), shown for three separate hindcast opportunities of the 2006/07 growing season. This particular grid cell has an LGP of 12 dekads. (a)–(c) Plots showing how to-date (2006) PPT (solid thick blue line) and RefET (solid thick red line) are combined with historical data (1981–2019, without 2006) to create a series of scenarios. The historical PPT is indicated by thin light-blue lines; historical RefET is indicated by thin light-red lines. The dotted blue and red lines represent the long-term PPT and RefET climatologies (1981–2019 dekadal averages), respectively. (d)–(f) Plots showing each of the associated potential WRSI scenarios, calculated using the PPT and RefET scenarios from (a)–(c). The thin green lines are potential WRSI scenarios calculated using the historical PPT and RefET scenarios [light-blue and light-red lines from (a)–(c)]. The dotted green line indicates the mean of these scenarios, with the solid green triangle indicating the EOS WRSI Outlook. The dotted blue line indicates the calculated WRSI using climatology inputs [the dotted blue and red lines from (a)–(c)], with the solid blue triangle indicating the EOS Extended WRSI. The dotted black line indicates the actual WRSI for the 2006/07 season, with the solid black triangle indicating the true EOS WRSI for this gridcell season.

Citation: Journal of Hydrometeorology 23, 8; 10.1175/JHM-D-21-0184.1

For a given monitoring season, the first opportunity for a WRSI Outlook is the first dekad after an SOS is confirmed (the start of the fourth dekad of a grid cell’s growing period). Each potential scenario uses these first three dekads of to-date PPT and RefET, combined with PPT and RefET data from each year in the historical record (1981–2019). For example, if the monitoring year is 2020, and the SOS for a given grid cell is dekad 10 (1 April 2020), with dekads 11 and 12 confirming that start, those three dekads of PPT and RefET data are coupled with 1981 data from dekad 13 (1 May) to dekad 33 (30 November). This composite scenario, combining 2020 and 1981 data, is used to calculate one potential EOS WRSI for the 2020 monitoring season for that grid cell. The same process is performed for each of the remaining years in the historical record, for each grid cell in the region that has recorded an SOS in 2020. In testing, we found that historical scenarios that did not record enough PPT to meet the SOS thresholds (25 mm in one dekad, followed by two consecutive dekads summing to 20 mm) in their own year resulted in a significant underestimation of the projected EOS WRSI (dry bias). As such, these no-start scenarios are removed from the mean-scenario calculation; for example, when projecting the 2020 season for a specific grid cell, if that grid cell did not actually record an SOS in 1981, then 1981 data would not be used in the collection of potential 2020 scenarios. The arithmetic mean of the remaining potential scenarios is used as the WRSI Outlook.

For our study, this process is performed at each hindcast opportunity of the growing period, for every year (1981–2019) to compare the bias and accuracy of both the Extended WRSI and WRSI Outlook. The hindcast error testing procedure will be described in more detail in the following section. In section 3, we show the results of this testing, but a few observations can be made from Fig. 3: 1) the observed covariability between PPT and RefET is lost when simply using long-term averages (climatologies) and 2) average dekadal PPT, when calculated for a known wet season, results in dekadal precipitation values that are consistently well above zero, a phenomenon that is unlike the natural intraseasonal variability of precipitation (well-above-average dekads interspersed with near-zero dekads). In contrast, the WRSI Outlook uses historical, coupled precipitation and evapotranspiration data to create scenarios that are inherently more realistic potential conditions for the remainder of the season. This results in an estimate much closer to the initial intention of the Extended WRSI: what would the EOS WRSI of the forecast season be if the remainder of the season resembled the average of years past?

4) Hindcast error testing

To compare the two WRSI forecast methods, we performed hindcasts, using both methods, at every time step in the historical record (1981–2019). For West and East Africa, whose growing seasons are contained within the calendar year (April–November for West Africa and February–November for East Africa), the maximum number of hindcast seasons is 39; the southern Africa growing season (September–May) crosses the calendar year, and as such, the maximum is 38 (1981/82–2018/19). There can be no hindcast for a season that does not have an SOS, and so a given grid cell may have fewer hindcast seasons depending on its no-start frequency. Within a single hindcast season, a given grid cell, with, say, a length of growing period of 12 dekads, has eight forecasting opportunities per season; one at the point the SOS has been confirmed (dekad 4 of the season), and once per dekad of the season up until one dekad before the end of the season (i.e., dekad 11). At each point, the performance of the hindcast was measured by comparing each method’s projected WRSI with the actual EOS WRSI for that historical season. The two forecast performance metrics used in this study are multiplicative percent bias (herein simply referred to as bias) and root-mean-square error (RMSE). These metrics are routinely used in accuracy assessments of satellite-derived products and climate forecasts to determine the difference between satellite estimates and reference data (e.g., Shen et al. 2014; Carvalho et al. 2014; Jolliffe and Stephenson 2012). The same principles are applied to the present study, in which the WRSI forecasts (e.g., Extended WRSI, WRSI Outlook) are treated as the estimates, and the actual EOS WRSI are the ground truth.

The bias of the forecast method for a given grid cell is calculated as
bias=1Ni=1NFi1Ni=1NOi×100100,
where N is the total number of predicted WRSI seasons (described above), F is the predicted EOS WRSI (either the Extended WRSI or the WRSI Outlook), and O is the observed (true) EOS WRSI for that season. The formula shown here multiplies the traditional bias formula by 100 to convert the bias to a percentage of the mean historical WRSI and then subtracts by 100 for ease of dry/wet bias interpretation. As such, the bias values shown here range from −∞ to +∞, with a value of 0% indicating the forecast method has no bias.
The accuracy of the forecast method for a given grid cell is calculated using RMSE:
RMSE=1Ni=1N(FiOi)2.
Simply put, the RMSE measures average error, weighted according to the square of the error. The RMSE does not indicate the direction of the deviations but does put greater influence on larger errors than on smaller errors. Because the WRSI ranges from 0 to 100, the corresponding RMSE range is also 0 to 100, with 0 constituting a perfect score (i.e., the forecast method’s average prediction is equal to the true event). In reality, the RMSE of either method rarely exceeds 25.

The results discussed below focus on the forecast bias and accuracy at the first forecast opportunity (dekad 4 of the season) because this is when the disparity between the two methods is most apparent. As the season progresses, there is less remaining season to forecast and so the two methods’ projections converge on the actual EOS result. The RMSE is reported for all hindcast years (as described above), as well as for three subsets of the hindcast years. The subsets are divided based on the true EOS percent-of-average WRSI for each of the historical years, with cutoffs at below 90% of average and above 110% of average. These designations are based on the standard color bars used in percent-of-average WRSI graphics popular for in-season monitoring (USGS/EROS 2021); <90% is the first color indicating below-average conditions, and conversely, >110% is the first color cutoff indicating above-average conditions. The purpose of these subsets is to identify whether one of the forecast methods performs better or worse during dry, average, or wet years. For a given grid cell, the dry-season RMSE is calculated using only the hindcasts of seasons in which the true outcome was less than 90% of the historical average WRSI. The average-season RMSE is calculated using only the hindcasts of seasons in which the true outcome was between 90% and 110% of the historical average WRSI. The wet-season RMSE is calculated using only the hindcasts of seasons in which the true outcome was greater than 110% of the historical average WRSI. For example, the dry-season RMSE indicates the expected forecast error when forecasting an event with a known outcome of less than 90% of average. Because the WRSI variability ranges considerably spatially, the number N of dry, average, and wet seasons will vary for each grid cell.

c. Regions of interest

This study focuses on the primary growing season for three subSaharan regions of interest in West Africa (WA), East Africa (EA), and southern Africa (SA) (Fig. 4). Approximately 52% of the global number of individuals predicted to be acutely food insecure in 2020 reside in these three regions (FAO et al. 2019; FSIN 2020). Weather extremes are anticipated to be the predominant driver of 13%, 48%, and 37% of those affected in WA, EA, and SA, respectively (FSIN 2020).

Fig. 4.
Fig. 4.

The three regions of interest: West Africa (green), East Africa (purple), and southern Africa (orange). The countries that reside in these WRSI-defined growing areas are labeled numerically and are indicated as follows: for West Africa there are 1) Mauritania, 2) Senegal, 3) The Gambia, 4) Guinea-Bissau, 5) Guinea, 6) Mali, 7) Côte d’Ivoire, 8) Burkina Faso, 9) Ghana, 10) Togo, 11) Benin, 12) Niger, 13) Nigeria, 14) Cameroon, 15) Chad, and 16) Central African Republic; for East Africa there are 17) Sudan, 18) South Sudan, 19) Eritrea, 20) Ethiopia, 21) Somalia, 22) Kenya, 23) Uganda, 24) Rwanda, and 25) Burundi; for southern Africa there are 26) Tanzania, 27) Democratic Republic of the Congo, 28) Republic of the Congo, 29) Gabon, 30) Angola, 31) Zambia, 32) Malawi, 33) Mozambique, 34) Zimbabwe, 35) Botswana, 36) Namibia, 37) South Africa, 38) Lesotho, 39) Eswatini, and 40) Madagascar.

Citation: Journal of Hydrometeorology 23, 8; 10.1175/JHM-D-21-0184.1

The monitoring period for WA begins on the 10th dekad of the year (1 April) and concludes on the 33rd dekad of the year (30 November). While East Africa has a bimodal rainfall pattern, and correspondingly has two distinct growing seasons, this study focuses on the primary, or long rains, growing season simply because we anticipate the longer season (LGP) will make the differences between the two forecast methods most apparent (larger number of dekads filled with forecast data). The monitoring period for the long rains growing season begins on the 4th dekad of the year (1 February) and concludes on the 33rd dekad of the year (30 November). In southern Africa, the monitoring period begins on the 25th dekad of the year (1 September) and concludes on the 15th dekad of the following calendar year (31 May).

These monitoring windows are designed to confine the time frame during which an SOS can occur to best correspond with likely planting dates. Once the SOS for a given season has been identified, the WRSI is calculated based on the PPT and RefET during the designated LGP for that grid cell, initialized by a 6-dekad preseason window used to calculate antecedent soil moisture. All three regions have default land masks, produced by the FAO, incorporated in the GeoWRSI to focus monitoring on rainfed agricultural zones. We further refined the regions of interest by masking out areas that failed to start more than 33% of the historical record (one-in-three event, since 1981). The reasoning for this is that these areas are more likely to either 1) not be cropped areas or 2) practice rangeland subsistence farming, which uses adaptive cropping strategies that differ from the standard parameters built into the WRSI model (greater crop-row spacing, irrigation, etc.) (Allen et al. 1998). As such, the standard WRSI model is not ideal for monitoring cropping conditions in those areas.

3. Results

The results presented here first address the significant biases associated with the Extended WRSI method, relative to the proposed WRSI Outlook technique. Next, we investigate the accuracy of the two methods, as measured by the RMSE for all hindcasts, as well as for dry-season, average-season, and wet-season subsets. For both metrics, the results below are for the first forecast opportunity (dekad 4 of the season), as this is when the outlooks will be most impactful, in terms of lead time, and the disparity between the two methods is most apparent. As the season progresses, forecast data are replaced with prevailing conditions for the season in question; there is less remaining season to forecast, and so the two methods’ projections converge on the actual EOS result. Our results find that the WRSI Outlook method considerably reduces the magnitude of the biases of the Extended WRSI method in areas of all three regions (e.g., West, East, and southern Africa). Correspondingly, the conservative (unbiased) nature of the WRSI Outlook lends itself to having higher (or equivalent) overall accuracy in all three regions. In particular, the absence of a wet bias in the WRSI Outlook results in markedly reduced error in projecting below-average WRSI. Overall, the results of the WRSI Outlook are highly encouraging and are a marked improvement to the existing Extended WRSI method, particularly in regard to the reduction in bias.

a. Bias

The primary initiative for this study is to detail the presumed bias associated with the Extended WRSI, which uses climatology (average) precipitation and reference evapotranspiration inputs. Systematic biases in EOS projections, whether they are underestimating or overestimating, can have serious implications in regard to monitoring and subsequent humanitarian aid efforts. Overly optimistic outlooks may result in certain areas systematically being excluded from more fine-detail monitoring reports, thereby inhibiting timely responses. Systematic underestimations (pessimistic outlooks) can also result in attention being directed to the wrong areas, as well as “alert fatigue.” In either case, precious attention and resources may be delayed, miscalculated, or allocated in the wrong locations, and thus, inhibit timely and necessary aid. The less ambiguous an early warning can be, the more likely it will elicit early response (Becker-Reshef et al. 2020).

In taking the average Extended WRSI at the first opportunity of a forecast (dekad 4) in the forecast season and comparing it with the actual average historical EOS WRSI, we find that the Extended WRSI has a substantial wet bias (average forecast WRSI is greater than the average true WRSI) in all three regions (Fig. 5a). In West Africa, the average Extended WRSI has a 2%–10% wet bias throughout the northern half of the region (e.g., Senegal, southern Mali, northern Burkina Faso, southern Niger, northern Nigeria, and southern Chad). In East Africa, the average Extended WRSI has at least a 2%–5% wet bias throughout much of the region and has a 5%–10% wet bias in eastern Sudan, southeastern South Sudan, central Ethiopia, eastern Uganda, southwestern Kenya, Rwanda, and northern Tanzania. The Extended WRSI also has a 2%–10% dry bias in central Sudan, southern Somalia, and central Kenya. The biases associated with the Extended WRSI are most severe in southern Africa, where the wet bias is greater than 5% throughout the central and eastern half of the region, and ranges from 10% to 23% in southeastern Angola, southern Zambia, Zimbabwe, Mozambique, eastern Malawi, eastern South Africa, and southern Madagascar. Additionally, the Extended WRSI has a considerable dry bias (2%–10%) in northern Namibia and central South Africa and exceeds 15% in central Botswana. In contrast, the WRSI Outlook has a near-zero bias throughout the three regions, with biases only exceeding ±5% in parts of northcentral Ethiopia, southern Somalia, northern Namibia, southern Botswana, and southern Zimbabwe (Fig. 5b). With the exception of the five aforementioned locations, the magnitude of the WRSI Outlook bias is smaller than that of the Extended WRSI bias in all areas. There are no areas in which the WRSI Outlook bias exceeds 10%.

Fig. 5.
Fig. 5.

Multiplicative percent bias, represented as the percent deviation from the mean historical WRSI, of the two EOS WRSI forecast methods, taken at the first opportunity of a forecast (i.e., dekad 4 of the season) for West, East, and southern Africa growing seasons (1981–2019). Brown hues indicate areas where the forecast method has a dry bias, meaning the average forecast is less than the true event outcome. Blue hues indicate areas where the forecast method has a wet bias, meaning the average forecast is greater than the true event outcome. White indicates areas where the forecast method is relatively unbiased (i.e., the average forecast is within ±2% of the true outcome). Shown are multiplicative percent bias of the (a) Extended WRSI method, which uses climatology (average) inputs to predict EOS WRSI, and (b) WRSI Outlook, which predicts the EOS WRSI by calculating the mean of a series of scenarios based on year-specific historical data.

Citation: Journal of Hydrometeorology 23, 8; 10.1175/JHM-D-21-0184.1

b. Accuracy

While assessing the bias of the two forecast methods is the primary focus, there is an implicit interest in the accuracies of the two. The desired expectation is that the results will provide sufficient empirical evidence of 1) the shortcomings and inaccuracies of the existing Extended WRSI and 2) the improved methodology provided by the WRSI Outlook for unbiased and accurate prediction of EOS crop water requirements.

Figure 6 shows the difference in RMSE between the two methods in dry (Fig. 6a), average (Fig. 6b), wet (Fig. 6c), and all (Fig. 6d) seasons. The results correspond well to the expectations outlined previously. In areas where the biases of the two products are nearly equal, their RMSE values are also nearly equal.

Fig. 6.
Fig. 6.

Difference of average RMSE between the two EOS WRSI forecast methods, taken at the first opportunity of a forecast (i.e., dekad 4 of the season) for West, East, and southern Africa growing seasons (1981–2019). Pink or green hues indicate areas where the Extended WRSI using climatology inputs has a smaller or greater RMSE, respectively, than does the WRSI Outlook using the mean scenario method. White indicates areas where the average RMSE of the two forecast methods is within 2 WRSI units of each other (i.e., the two methods have equivalent accuracy). Shown is the average difference in RMSE between the two methods for (a) years in which the true EOS WRSI is < 90% of average (dry years), (b) years in which the true EOS WRSI is 90%–110% of average (average years), (c) years in which the true EOS WRSI is > 110% of average (wet years), and (d) all years.

Citation: Journal of Hydrometeorology 23, 8; 10.1175/JHM-D-21-0184.1

For dry seasons (Fig. 6a), in areas where the Extended WRSI has a considerable wet bias, the WRSI Outlook has a notably smaller RMSE. In East Africa, the WRSI Outlook has an RMSE that is 2–10 WRSI units less than that of the Extended WRSI in South Sudan, central Ethiopia, Uganda, southern Kenya, and northern Tanzania. In southern Africa, the WRSI Outlook has an RMSE that is 2–10 WRSI units less than that of the Extended WRSI in Tanzania, Malia, southern Angola, Zambia, South Africa, and Madagascar, and 10–15 WRSI units less than the Extended WRSI RMSE in central Zimbabwe and central and southern Mozambique. In northern Namibia, Botswana, and western South Africa, where the Extended WRSI has a considerable dry bias, the WRSI Outlook’s RMSE is 2–5 WRSI units larger than the Extended WRSI’s RMSE.

For near-average seasons (Fig. 6b) the RMSE of the two methods are comparable in west and east Africa. In southern Africa, where the Extended WRSI bias exceeds 10%, the RMSE of the WRSI Outlook is 2–14 WRSI units smaller than that of the Extended WRSI in southern Angola, central Zimbabwe, and southern Mozambique. In southern Zambia and northern Zimbabwe, where the Extended WRSI has a 5%–10% wet bias and the WRSI Outlook bias is near zero, the Extended WRSI RMSE is 2–7 WRSI units less than that of the WRSI Outlook. This implies that the natural distribution of the historical (true) WRSI has a long tail of low values that pulls down the mean WRSI more than the median WRSI (left skew), which would lend itself to a method with a wet bias having a lower RMSE than one with no bias.

During wet seasons (Fig. 6c), as previously stated, the systematic wet bias of the Extended WRSI lends itself to having a lower RMSE during above-average (wet) seasons. In West Africa, the RMSE of the Extended WRSI is 2–5 WRSI units lower than that of the WRSI Outlook in the northern most parts of the region, including northern Senegal, central Mali, northern Burkina Faso, southern Niger, and central Chad. In East Africa, the RMSE of the Extended WRSI is 2–10 WRSI units lower than that of the WRSI Outlook in southern Sudan, southeastern South Sudan, central Ethiopia, southern Uganda, southwestern Ethiopia, and northern Tanzania. The differences in RMSE are more substantial in southern Africa, where the Extended WRSI has the largest wet bias (exceeding 10%), and correspondingly, has a RMSE that is more than 5 WRSI units less than the WRSI Outlook in southern Angola, central Zimbabwe, central and southern Mozambique, and southern Madagascar.

When averaged over all years (Fig. 6d), the RMSE is comparable between the two methods. The increase in accuracy when using the WRSI Outlook in dry seasons (Fig. 6a) is largely offset by the decrease in accuracy in wet seasons (Fig. 6c). The RMSE of the WRSI Outlook is 2–5 WRSI smaller than that of the Extended WRSI in Tanzania, Malawi, southern Namibia, southern Zambia, northern Zimbabwe, central and southern Mozambique, and southern Madagascar. These areas indicate where the variability of the historical WRSI is the greatest, and correspondingly, the conservative estimate provided by the WRSI Outlook has fewer large errors than does the heavily biased Extended WRSI (the calculation of the RMSE naturally punishes larger errors more so than smaller errors, and thus tends to favor more conservative estimates). This is particularly evident early in the season, when the disparities between the two forecast methods are largest.

While the accuracy results detailed here are predominantly artifacts of the systematic biases of the Extended WRSI method, they illustrate how these biases could result in a failure to identify drought conditions (or worse, falsely project above-average conditions).

4. Discussion

There are two fundamental reasons for the expected bias in the Extended WRSI, which are described in more detail in section 2b(1). First, using average precipitation inherently results in a roughly bell-shaped curve—to describe the amount of rainfall over time—with an increase to peak rainy season, then a decline into the dry season, and consistently wet (i.e., nonzero) dekads in between. In reality, a given rainy season will have intraseasonal variability, in which wet dekads may be interspersed with abatement or absence of rain. The greater the intraseasonal variability in a given season (e.g., more frequent dry dekads, or variable length of the rainy season), the larger the expected impact using average inputs would have on the water satisfaction calculation. Second, there exists a tendency for precipitation and evapotranspiration to be inversely correlated; evapotranspiration tends to be relatively higher when precipitation is lower, primarily as a result of higher solar radiation and lower relative humidity. Likewise, evapotranspiration tends to be relatively lower when precipitation is higher, primarily as a result of lower solar radiation and higher relative humidity. A complementary relationship between AET and RefET provides a further nuanced relationship in the ratio of water supply and atmospheric demand, which is particularly important in characterizing drought conditions, as the elevated potential evapotranspiration exacerbates the water stress experienced in times of insufficient precipitation. Because using a long-term average inherently results in a loss of these finer-time-scale relationships, the expectation was that the current practice of using climatology inputs is inadequate for accurately predicting EOS crop-water satisfaction. More specifically, we anticipated the Extended WRSI would overestimate water satisfaction when monitoring dry and average years, be closer to the true water satisfaction in wet years, and, overall, have an average predicted WRSI that was consistently larger than the true historical average (wet bias).

The removal of the systematic biases associated with the existing WRSI projection methodology is critical for the effectiveness of the WRSI as a monitoring tool for early and accurate agricultural drought identification. The Extended WRSI method does indeed have a tendency to significantly overestimate crop-water satisfaction in large portions of all three regions (West, East, and southern Africa), as well as significantly underestimate the average crop-water satisfaction in portions of southwestern Africa. In contrast, it is shown that the WRSI Outlook method of taking the mean of a series of historically based scenarios provides a relatively unbiased alternative to the Extended WRSI. As such, the WRSI Outlook is much closer to the initial intention of the Extended WRSI: what would the EOS WRSI of the forecast season be if the remainder of the season resembled that of years past?

While increased accuracy is a welcome by-product, note again that the primary initiative of this research is to provide an alternative, unbiased methodology for projecting EOS WRSI. Furthermore, because of the significant biases of the Extended WRSI documented in section 3a, and the fact that both forecasts are based solely upon the climatological statistics for a region rather than the dynamical implications of the current conditions, note that any changes in the accuracy of the two methods are more due to the change in mean value of the projections, and less due to their actual prediction capabilities. For example, the significant wet bias of the Extended WRSI naturally results in projections that resemble above-average (wet) seasons, and thus, the RMSE during wet seasons is comparatively low. Furthermore, the Extended WRSI RMSE is doubly high during below-average (dry) seasons. In contrast, the WRSI Outlook is a conservative estimate, and therefore, it slightly overestimates dry seasons, slightly underestimates wet seasons, and is fairly accurate during average seasons. As mentioned previously, these traits are most noticeable early in the season, when forecast data make up a majority of the climatological inputs of the WRSI projection. As the season progresses, and forecast data are replaced with prevailing conditions for the season in question, the two methods’ projections converge on the actual EOS result.

The results presented here were for crop types of millet in West Africa and maize in East and southern Africa. However, while the Kc values do vary based on crop type, they are simply scalar values and are applied in the same way in both forecast methods (Extended WRSI and WRSI Outlook). Therefore, we would expect the results of this study to remain comparable regardless of the crop-type selection.

Not presented in this paper were various attempts to identify methods of selecting analog years (as opposed to using all historical scenarios). One such method involves to-date precipitation ranking to group historical seasons into more-likely relevant analog years. While this is an interesting avenue for further research, the results were inconsistent, and where improved accuracy was seen, the improvements were not substantial enough (<5 WRSI accuracy improvement) to warrant the significant increase in computations required. Other analog approaches, such as selecting years on the basis of similarities in large-scale climate conditions, could result in better performance. Most recently, an operational, stochastic approach has been implemented, which uses all scenarios calculated in the WRSI Outlook method to calculate a WRSI Outlook probability, based on the number of scenarios that fall within historical terciles. The preliminary results from this extension of the WRSI Outlook are promising.

5. Concluding remarks

Agroclimatic monitoring, and, in particular, drought early warning and forecasting, is a rapidly advancing science. Dozens of organizations, including FEWS NET, USGS/EROS, NASA, and the CHC, are working tirelessly to expand the tools available for predicting and identifying hydroclimatic conditions that contribute to food insecurity. Their collection of indicators is employed using a convergence of evidence method to identify hazards and to classify the severity and magnitude of concomitant acute food insecurity. Confidence in and agreement between indicators can provide the compelling evidence required to guide decision-makers and humanitarian organizations to partition vital aid to countries around the world in a timely and precise manner. However, methodological differences between systems and associated discrepancies in reported conditions can cause ambiguity and reduce decision-makers’ confidence to mount a response.

Although the WRSI is a relatively simple model, it is used widely because of its proven accuracy as a proxy for crop yield and drought risk, and for its relatively few input requirements. However, the common method of using arithmetic mean climatology inputs to forecast EOS conditions (i.e., Extended WRSI) was observed to frequently produce overly optimistic outlooks. Given this, we sought to investigate the adequacy of this method for forecasting EOS WRSI. In general, the results presented here confirm a significant wet bias in the projected EOS WRSI when using arithmetic mean climatological inputs, which, among other shortcomings, significantly hinders the model’s ability to capture drought events. As an alternative, we implemented a mean scenario-based approach, which uses historical precipitation and evapotranspiration data to run out a series of historically realistic WRSI scenarios, of which the mean is selected as the WRSI Outlook. This method proves to be relatively unbiased, and, correspondingly, it has a considerably lower RMSE in both dry (below-average) and average seasons, relative to the commonly used method. When comparing the average accuracy of these models, the differences may seem trivial. However, the reduction in wet bias and improved accuracy during drought years is a significant step toward a more accurate and useful model. This tool is one of many in a suite of indices that are used to identify environmental stresses that may lead to increased food insecurity in rainfed agricultural areas around the world. Systematic biases, such as the wet bias seen early in the season when using the Extended WRSI, are particularly detrimental to the effectiveness of in-season monitoring, as one indicator’s overly optimistic end-of-season outlook for a given area may fail to highlight impending poor conditions, and result in that area not getting the monitoring attention it deserves until later in the season, thereby shortening the delicate timeline for timely humanitarian assistance. It is our hope that this mean scenario-based approach will replace the existing arithmetic mean Extended WRSI method currently used by FEWS NET partners, so as to provide a more accurate approach for predicting crop water requirements and, more generally, to continue to improve the suite of tools used to identify climate and weather-related shocks to food-insecure regions.

Future research could utilize forecasts tuned to existing climate conditions to either create stochastic probabilistic forecasts, selection criteria for relevant analog years (as opposed to running out with all years of historical data), or, if skilled downscaled dynamic climate forecasts are available, replace the scenarios entirely. In either case, the scenario-based climatological forecast presented here is essential, as it serves as an unbiased baseline to be improved upon.

1

FEWS NET partners and implementers include the U.S. Agency for International Development’s Bureau for Humanitarian Assistance (USAID BHA), U.S. Geological Survey Earth Resource Observation and Science Center (USGS/EROS Center), National Aeronautics and Space Administration (NASA), National Oceanic and Atmospheric Administration (NOAA), Chemonics International, the Group on Earth Observations Global Agricultural Monitoring initiative (GEOGLAM), Crop Monitor for Early Warning (CM4EW), and the Climate Hazards Center (CHC).

2

Dekadal time steps split the months into three parts; the first two dekads of a given month are 10 days long, and the third dekad completes the month (8–11 days) (WMO 1992). Similarly, the pentad splits the month into six parts; the first five pentads of a given month are 5 days long, and the sixth pentad completes the month (3–6 days).

Acknowledgments.

The authors thank the Climate Hazards Center’s technical editor Juliet Way-Henthorne for providing professional editing. This research was funded by the U.S. Geological Survey Drivers of Drought, the U.S. Geological Survey (USGS) (Cooperative Agreement G14AC00042), U.S. Agency for International Development (USAID) (Cooperative Agreement 72DFFP19CA00001), and National Aeronautics and Space Administration (NASA) Harvest Consortium (Award 80NSSC18M0039).

Data availability statement.

The original contributions presented in the study are included in the article. Further inquiries can be directed to the corresponding author.

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