An Analysis of the Lagged Relationship between Anomalies of Precipitation and Soil Moisture and Its Potential Role in Agricultural Drought Early Warning

C. Cammalleri aDipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Milan, Italy
bJoint Research Centre, European Commission, Ispra, Italy

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https://orcid.org/0000-0003-4834-7508
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N. McCormick bJoint Research Centre, European Commission, Ispra, Italy

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J. Spinoni cDipartimento di Ingegneria Gestionale, Politecnico di Milano, Milan, Italy
dResources for the Future–Euro Mediterranean Center on Climate Change, European Institute on Economics and the Environment, Milan, Italy

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J. W. Nielsen-Gammon eDepartment of Atmospheric Sciences, Texas A&M University, College Station, Texas

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Abstract

The standardized precipitation index (SPI) is the most commonly used index for detecting and characterizing meteorological droughts, and it is also extensively used as a proxy variable for soil moisture anomalies (SMA) for the purpose of monitoring agricultural drought in absence of long-term soil moisture observations. However, the potential capability of SPI to warn of the time-lagged soil water deficit—following the well-known “drought cascade” effect—is often overlooked in agricultural drought studies. In this research, a time-lagged correlation analysis is used to evaluate the relationship between the SMA dataset, generated as part of the Global Drought Observatory of the European Union’s Copernicus Emergency Management Service, and a set of SPIs derived from the ERA5 reanalysis produced by the European Centre for Medium-Range Weather Forecasts. The possibility to achieve an optimal agreement between SPI and SMA that also preserves the early warning skills of SPI is evaluated. The results suggest that if only the correlation between SPI and SMA is considered, the maximum agreement is usually obtained with a zero lead time (almost 80% of the cases), with SPI-3 representing the best option in about 40% of the grid cells at global scale. By also accounting for the benefits of a positive lead time, short accumulation periods tend to be favored, with SPI-1 being the optimal choice in about one-half of the cases, and 10–20 days of lead time in more than 90% of the grid cells is achieved without any significant reduction in either correlation or skill in drought extreme detection.

© 2024 American Meteorological Society. This published article is licensed under the terms of a Creative Commons Attribution 4.0 International (CC BY 4.0) License .

Corresponding author: C. Cammalleri, carmelo.cammalleri@polimi.it

Abstract

The standardized precipitation index (SPI) is the most commonly used index for detecting and characterizing meteorological droughts, and it is also extensively used as a proxy variable for soil moisture anomalies (SMA) for the purpose of monitoring agricultural drought in absence of long-term soil moisture observations. However, the potential capability of SPI to warn of the time-lagged soil water deficit—following the well-known “drought cascade” effect—is often overlooked in agricultural drought studies. In this research, a time-lagged correlation analysis is used to evaluate the relationship between the SMA dataset, generated as part of the Global Drought Observatory of the European Union’s Copernicus Emergency Management Service, and a set of SPIs derived from the ERA5 reanalysis produced by the European Centre for Medium-Range Weather Forecasts. The possibility to achieve an optimal agreement between SPI and SMA that also preserves the early warning skills of SPI is evaluated. The results suggest that if only the correlation between SPI and SMA is considered, the maximum agreement is usually obtained with a zero lead time (almost 80% of the cases), with SPI-3 representing the best option in about 40% of the grid cells at global scale. By also accounting for the benefits of a positive lead time, short accumulation periods tend to be favored, with SPI-1 being the optimal choice in about one-half of the cases, and 10–20 days of lead time in more than 90% of the grid cells is achieved without any significant reduction in either correlation or skill in drought extreme detection.

© 2024 American Meteorological Society. This published article is licensed under the terms of a Creative Commons Attribution 4.0 International (CC BY 4.0) License .

Corresponding author: C. Cammalleri, carmelo.cammalleri@polimi.it

1. Introduction

Drought is a natural disaster with a wide array of impacts on different socioeconomic sectors, as well as on ecosystems. The impacts of drought on agriculture are among the earliest drought impacts discussed by the scientific community (WMO 1975), mainly because drought effects in this sector are the most direct and easy to recognize (Mishra and Singh 2010). Many definitions of agricultural drought are found in the scientific literature, most of which are linked with the negative consequences for vegetated lands. This definition includes drought occurring also over natural vegetation areas, which are similarly affected by the lack of water. A common approach is to consider soil moisture availability dropping to a level that adversely affects the crop yield as the main driving force of agricultural drought (Panu and Sharma 2002), hence defining agricultural drought as a function of relative soil moisture conditions.

Following this definition, soil moisture anomaly (SMA) datasets are frequently applied in operational drought monitoring systems for the detection of agricultural drought events (which for this reason are also referred to as soil moisture droughts). Examples of operational SMA products used in large-scale drought monitoring systems are the ones included in the Global Drought Observatory of the European Union’s (EU) Copernicus Management Service (GDO; https://edo.jrc.ec.europa.eu/gdo), the U.S. Drought Monitor (https://droughtmonitor.unl.edu), and the Drought Service of the Australian Bureau of Meteorology (http://www.bom.gov.au/climate/drought).

In practice, because soil moisture observations are sparsely distributed and available over too short of a record to capture climate variability, the soil moisture values that are used in drought monitoring are often retrieved through indirect methods, including physically based hydrological or land surface models, and remote sensing data (Cammalleri et al. 2017). Additional tools for identifying soil moisture droughts, in the absence of specific information on soil moisture conditions, include indices that are based on a simplified water balance, such as the Palmer drought severity index (Dai et al. 2004), or meteorological drought indices that are computed at appropriated aggregation time scales, such as the standardized precipitation index (SPI; McKee et al. 1993) and the standardized precipitation evapotranspiration index (SPEI; Vicente-Serrano et al. 2010).

SPI datasets in particular have been widely used to simulate the dynamics of soil moisture droughts in absence of proper soil moisture datasets because of their minimal input data requirements and their overall ease of use. SPI datasets computed on short to medium aggregation times, such as 3 months (i.e., SPI-3) and 6 months (i.e., SPI-6), are often found to be the most suitable proxy variables for soil moisture drought. Ji and Peters (2003), for example, in a study over the U.S. Great Plains, showed that SPI-3 had the best correlation with vegetation growth on croplands and grasslands among those drought indices studied, especially during the middle of the growing season. Similarly, Halwatura et al. (2017) highlighted SPI-3 as the best proxy variable for soil moisture of fields simulated with the model Hydrus-1D over Australia, and Sims et al. (2002) found an analogous good correlation over North Carolina between short-term precipitation and soil moisture variation. Wang et al. (2015) tested, among other drought indicators, a range of SPIs as a proxy for soil moisture dynamics in China, and they found that the optimal time was of 1–3 months for the majority of stations, although they also observed some spatial variation in the results. Parsons et al. (2019) compared indices and periods to predict agricultural drought impacts in the United Kingdom, and they also highlighted regional variations in the optimal aggregation period, with SPEI-6 performing the best on average. However, despite its potential use as a proxy variable for soil moisture anomalies, SPI is a meteorological drought index, representing conceptually only an early warning signal of potentially upcoming soil moisture deficits.

According to the well-documented principle of the propagation of water deficits throughout the hydrological cycle (Changnon 1987), various degrees of temporal delay in soil moisture deficits are expected when compared with precipitation deficits, depending on local climate and catchment characteristics (Van Loon 2013, 2015). The propagation of drought from meteorological to hydrological quantities (either soil moisture or discharge) has been analyzed in the scientific literature to improve predictability of hydrological and agricultural drought conditions (e.g., Apurv et al. 2017; Barker et al. 2016; Zhang et al. 2021). The principle relating precipitation and soil moisture standardized anomalies has been evaluated in some studies by testing the time lag between agricultural and meteorological droughts (i.e., drought propagation). The analysis of Huang et al. (2015) in China and the study of Wu and Kinter (2009) over Illinois showed an asymmetric behavior in the correlation between soil moisture to SPI across a time lag of zero, due to how the dependence of soil moisture on precipitation is modeled. The combined drought indicator (CDI; Cammalleri et al. 2021; Sepulcre-Canto et al. 2012) is based on a similar principle, where an early warning of agricultural drought is associated with negative values in SPI-1 or SPI-3, but an actual warning for agricultural drought is only issued when SPI deficits are followed by negative effects on soil water availability and/or vegetation condition.

Despite these efforts, most of the studies on SPI and SMA time series focus solely on the overall agreement between the two quantities (quantified by the only criterion of the correlation metrics) (e.g., Afshar et al. 2022; Halwatura et al. 2017; Yuan et al. 2020), often neglecting the capability of SPI to warn of the occurrence of critical values of soil water deficits (hence an actual early warning capability). By selecting the SPI accumulation period to be used in a drought early warning system based only on this criterion (correlation), a key feature of SPI is severely overlooked, as the value of SPI to represent an early warning tool for agricultural drought is ignored in favor of its agreement with soil moisture deficits. The main research goal of this study is to investigate how the role of global SPI datasets may change in agricultural drought early warning systems if more emphasis on SPI forewarning capability is given. This is performed by investigating the possibility to simultaneous achieve (i) a good matching between global SPI and SMA time series at gridcell scale, with a special focus on agricultural drought extremes, and (ii) a reliable forewarning from SPI of upcoming soil moisture drought conditions suitable for an operational early warning system. To attain this goal, a time-lagged correlation analysis is used to investigate the temporal matching of the 20-yr datasets (2001–20) of global SMA and SPI available as part of the EU’s Copernicus Management Service.

2. Materials and methods

a. SMA and SPI datasets

The SMA global maps that are used in this study have been produced in near–real time as part of the GDO monitoring system, and cover a 20-yr period (2001–20) at a spatial resolution of 0.1° with dekadal updates (i.e., three updates per month, on the 10th and the 20th and at the end of the month) on a 3-dekad moving window (European and Global Drought Observatories 2021). This product was calculated following the procedure described in Cammalleri et al. (2017), which introduces a weighted ensemble of three independent datasets following a triple collocation analysis. The three base datasets are 1) standardized anomalies of root zone soil moisture simulated by the “Lisflood” hydrological model (De Roo et al. 2000) forced by ERA5 meteorological data, 2) standardized anomalies of land surface temperature from the Moderate-Resolution Imaging Spectroradiometer (MODIS) (MOD11C2, Collection 6; Wan and Li 1997), and 3) standardized anomalies of combined active/passive microwave surface soil moisture from the European Space Agency Climate Change Initiative (ESA CCI; Liu et al. 2012).

This merged dataset, covering only the overlapping period of the three base products (2001–20), is here used since numerous studies have highlighted how ensemble soil moisture products tend to outperform single datasets, especially for continental and global scale applications (e.g., Cammalleri et al. 2015; Crow et al. 2012; Srivastava et al. 2013; Xie et al. 2022).

For the computation of SPI at different aggregation time scales, precipitation data from the ECMWF ERA5 global atmospheric reanalysis model (https://www.ecmwf.int/en/forecasts/dataset/ecmwf-reanalysis-v5) were used. As part of GDO operational activities, ERA5 data were collected starting with 1979 through the EU’s Copernicus Climate Change Service (C3S; https://climate.copernicus.eu/). Hourly total precipitation at surface level were cumulated at dekadal time scale by simply summing up all the hourly values in a dekad (with no missing data detected in the analyzed period). The dekadal precipitation maps were then reprojected to the same regular latitude–longitude grid of 0.1° used for SMA with the bilinear method.

Five SPI datasets were computed for accumulation periods ranging from 1 to 12 months (SPI-1, SPI-3, SPI-6, SPI-9, and SPI-12) by fitting the gamma distribution over the 30-yr period of 1991–2020 (WMO 2017) with the generalized additive model in location, scale, and shape (GAMLSS) modeling framework (Stasinopoulos and Rigby 2007). All SPIs were computed on a dekadal moving window, resulting in a total of 36 SPI values per year for each accumulation period.

This set of SPIs are produced operationally as part of GDO, and ERA5 data were selected thanks to the relatively high spatial resolution and low temporal latency (5 days), which make the dataset suitable for near-real-time monitoring activities. Preliminary intercomparisons between SPI derived from different global precipitation datasets showed an overall good consistency among products over most of the regions included in this analysis (see the online supplemental material).

b. Time-lagged correlation analysis

The Pearson correlation coefficient r is used as the main statistical metric to evaluate the overall agreement between the SPI and SMA datasets over the full 20-yr overlapping period (2001–20). Given the relatively short time span of the period under investigation, no major effect of nonstationarity is expected on the computation of the standardized quantities. Under this assumption, focusing on the capability of SPI to warn of SMA, a set of time-lagged correlation analyses was performed for 36 lead time values ranging from 0 (i.e., no time lag) to 35 dekads (i.e., 1-yr lead for SPI before SMA). For each grid cell, five different correlograms were obtained (one for each SPI aggregation), returning a large set of r values that can be analyzed to extract key information.

If the focus of the analysis is only on the capability of SPI to reproduce the SMA dynamic at local scale (i.e., being a proxy of soil moisture drought), the most common solution is to select the SPI that returns the highest correlation value with SMA (i.e., rmax) out of the 36 × 5 (lead time × aggregation times) r values, independently from the corresponding SPI accumulation period SPImax and lead time Lmax. However, it is possible to maximize the SPI early warning capability by relaxing this constrain on the maximum correlation, and by selecting as “optimized” solution the case characterized by the maximum lead time Lopt among all the cases with rrp, where rp is a cutoff value close to rmax such as to ensure correlation nearly as accurate as the “max” index. This cutoff value can be derived from either a simple constant difference (viz., Δd) or as a function of a fixed ratio (viz., Δr). Reasonable values of these constant thresholds can be more easily expressed in terms of variance explained r2 under the assumption that correlations are mostly positive in all the observed cases. In case of multiple SPIs with equal Lopt values, the one with the highest r values is selected as optimal. The flowchart in Fig. 1, which shows the correlograms for an example case for a grid cell in Spain, summarizes the key steps of this optimization procedure.

Fig. 1.
Fig. 1.

Illustration of the optimization procedure for SPI selection vs the maximum correlation selection, and example of time-lagged correlograms for a grid cell in central Spain (central panel). The left side of the figure shows the retrieval of the maximum correlation values (rmax, SPImax, and Lmax), whereas the right side of the figure shows a schematic of the estimation procedure for the constant-difference Δd optimization approach (ropt, SPIopt, and Lopt).

Citation: Journal of Applied Meteorology and Climatology 63, 2; 10.1175/JAMC-D-23-0077.1

For the example shown in Fig. 1, the analysis starts from a total of 180 correlation analyses (i.e., 36 lag times in SMA × 5 SPI accumulation) performed for each grid cell to produce a set of correlograms (and example is shown in the central panel). The SPI and lag time (SPImax and Lmax) corresponding to the maximum correlation (rmax, small circle in the central panel) are reported on the left-hand side in Fig. 1. The values corresponding to the optimization procedure (SPIopt and Lopt) are shown on the left-hand side in Fig. 1, for the correlation value (ropt, small triangle in the central panel) corresponding to the constant-difference Δd approach.

In the case of two r values derived from two independent samples, Fisher (1925) suggests a methodology to transform the r values into z scores and to evaluate the statistical significance of their difference. While the Fisher approach cannot be directly applied to our data, since they are not independent samples (hence overestimating the statistical significance of the difference), this method is here used to obtain some rule of thumb values for rp, as follows:
rp=tanh[tanh1(rmax)2n3erf1(1p)],
where n is the sample size, erf−1 represents the inverse of the cdf standard Gaussian, and p is the two-tailed statistical significance level.

c. Evaluation strategy

Since the proposed optimization strategy focuses on the overall correlation and lead time, the introduction of a cutoff value does not guarantee the preservation of the capability to correctly identify negative extreme values, which is a key feature of any drought monitoring system. For this reason, we performed a confusion matrix analysis for each grid cell on the occurrence of SMA < −1 (as a typical threshold to detect droughts) to evaluate the difference between the “maximum” and the “optimized” estimates in term of skill, as quantified according to the Heidke skill score (HSS; Heidke 1926). In the confusion matrix, true positives are considered the cases where both SMA and SPI are lower than −1. HSS summarizes in a single quantity two key features of a detection systems, such as the probability of detection (capability to correctly identify droughts) and the false alarm ratio (number of false alarms released).

In addition, to better understand the spatial variability of the optimized solutions, the spatial patterns of the most frequent SPI–lead time combinations are investigated as a function of three essential climate variables—the average annual precipitation and the average temperature from ERA5 (for the period 1991–2020), and annual average satellite-derived fraction of absorbed photosynthetically active radiation (fAPAR) from the MODIS sensor (for the period 2001–20) (Myneni 2015). These quantities are used as concise descriptors of the key features that may control the temporal relationship between precipitation and soil moisture, with the aim of proving evidence of nonrandom patterns.

3. Results

a. Evaluate maximum agreement

The main tool of this analysis is the set of time-lagged correlograms, an example of which is shown at the center of Fig. 1 for a grid cell in central Spain. This example shows some typical behaviors observed across the whole domain, and in particular, the fact that a lagged peak is present only for short-term SPIs (i.e., SPI-1 and SPI-3), whereas time-lag zero correlograms are available for the long-term SPIs (i.e., monotonic decreasing function). The representativeness of this example of most of the conditions observed in this study is well indicated by the percentages reported in Table 1 for the full global domain.

Table 1.

Percentage of grid cells with peak correlation rmax in a specific lead time for each SPI accumulation period relative to SMA.

Table 1.

The data in Table 1 show that the majority of the grid cells have a peak correlation for SPI-1 at a lead time of 1 dekad (i.e., monthly SMA correlates best with a 10-day delay to monthly precipitation), but also that this percentage decreases significantly for longer accumulation periods. For SPI-6 or longer, almost all the grid cells (about 95% or more) have the correlogram peaking at time lag of zero. The percentage of grid cells with a maximum correlation at lead time of 3 dekads (i.e., 1 month) or more is negligible for all the SPIs (<1% in all cases). It is noticeable that the few grid cells with large lead times (≥2 dekads; see Fig. 2c) are generally characterized by an overall low correlation between SPI and SMA (rmax < 0.4, see Fig. 2a). These are cases where all the r values in the correlograms are small and often statistically not significant, even ignoring the multiplicity of testing, hence the location of the maximum is often not meaningful. All of the grid cells with rmax < 0.4 were masked out in the subsequent analyses, amounting to less than 1% of the entire domain.

Fig. 2.
Fig. 2.

Output of the maximum correlation analysis on the time-lag correlograms between SPIs and SMA: (a) spatial distribution of the maximum correlation rmax values, (b) SPI index returning the rmax values, or SPImax, (c) the corresponding lead time Lmax, and (d) a mask of the grid cells with enough correlation (rmax > 0.4) as used in the successive analyses. Areas in white in (a)–(c) include grid cells with less than 50% of reliable SPI or SMA data available for a correlation analysis.

Citation: Journal of Applied Meteorology and Climatology 63, 2; 10.1175/JAMC-D-23-0077.1

Focusing on the overall maximum correlation, the map in Fig. 2a depicts the global spatial distribution of rmax. This map shows a generally good correlation between SMA and the local best SPI, with most of the rmax values between 0.4 and 0.7 (rmax = 0.56 ± 0.12). Some notable areas with spatially consistent high rmax values are Australia, Europe, southern Africa, eastern and southern South America, and central United States. In contrast, most of the low rmax values (i.e., rmax < 0.4, Fig. 2d) are located around the regions where the SMA dataset is characterized by several missing data, due to low quality in the ensemble inputs or discordance between products [described in Cammalleri et al. (2017)], namely, central Africa, and the Amazon forest.

The map in Fig. 2b shows that SPI-3 is most frequently the dataset with the highest correlation, in just over one-third of the grid cells (38.3%), most notably over eastern Australia, western Europe and central United States, whereas SPI-1 seems to be the selected option (according to r only) in most of the dry areas of the world. Long-term SPIs cover the remaining one-third of the world (29.3%), with some notable high concentration of SPI-9 in some of the northernmost lands (i.e., across Russia and Canada). The fact that SPI-3 is optimal over both very spatial heterogenous areas (western Europe) and relatively uniform regions (western Australia), may also suggest that this result is not particularly sensitive to spatial resolution.

In terms of lead time, the map in Fig. 2c clearly shows how the overwhelming majority of rmax values are obtained from time lag of zero analyses (79%), with a few notable exceptions over some of the regions where SPI-1 is the best option (but often with low r values, such as in the southern Sahara).

b. Optimizing approach

Following the outcomes of the previous analysis on the maximum correlation, we applied the optimization strategy only to the grid cells mapped in Fig. 2d, removing from the next tests the regions where the correlation was proved to be already weak overall. In these areas, we observed a sample size ranging between 650 and 720 values (i.e., maximum 10% of missing values) and an rmax value between 0.4 and 0.75 (from medium to high correlation). By assuming p values equal to 0.05 and 0.1, we obtained Δd values from the rp in Eq. (1) and rmax ranging between 0.03 and 0.08. An undesirable feature of using Eq. (1) is to obtain larger Δd values for small rmax, meaning that a larger deterioration of the correlation is allowed for those grid cells where the correlation is already low. To avoid this issue, a fixed value of Δd = 0.04 is used for all the grid cells, representing a relatively small reduction in correlation across the expected range of variability of r. A similar range of variability in degradation can be obtained with the fixed ratio by assuming a reduction in the explained variance of 20% (Δr=rp2/rmax2=0.8). Using Δr = 0.8, values of Δd roughly ranging between 0.08 (for high rmax) and 0.04 for (low rmax) are obtained, representing a generally weaker constraint on r relative to the fixed-difference method.

The differences between the obtained ropt values and rmax are directly constrained by these Δd and Δr values, hence they are not worth analyzing since the overall spatial distribution of both ropt-d and ropt-r values (not shown) are practically indistinguishable from the one in Fig. 2a. Instead, the main difference from the maximum correlation lies in both the optimal SPI (SPIopt) and the lead time (Lopt) spatial distribution, as shown in Fig. 3 for both Δd and Δr. These maps depict rather different results from the ones in Fig. 2, with a clear increase in the frequency of grid cells where SPI-1 is the optimal choice (Figs. 3a,c), and an increase of the lead time to values of 1 dekad or longer almost everywhere (more than 90% in both cases, see Figs. 3b,d).

Fig. 3.
Fig. 3.

Spatial distribution of (left) the optimized SPI, or SPIopt, and (right) the corresponding lead time Lopt for (a),(b) the fixed-difference method Δd (subscript -d) and (c),(d) the fixed-ratio method Δr (subscript -r). Areas in white correspond to the mask reported in Fig. 2d.

Citation: Journal of Applied Meteorology and Climatology 63, 2; 10.1175/JAMC-D-23-0077.1

Overall, the results reported in both Figs. 3a and 3c show limited changes relative to Fig. 2b over some regions, such as the eastern United States, central Europe, and western Australia and a general tendency to shorter accumulation periods in the rest of the grid cells. In contrast, the map of Lopt (Figs. 3b,d) shows an extended increase of the lead times for both optimization methods, with values between 1 and 2 dekads covering most of the investigated areas (>90%).

These results are summarized in the plots in Fig. 4, where the average frequencies for the two optimizing approaches are reported alongside the one for the maximum correlation. The histogram in Fig. 4a confirms a reduction in the frequency of all the SPI datasets with an accumulation period of three months or longer when either optimizing approach is adopted, with SPI-1 chosen by the optimizing approach for slightly less than half of the grid cells (46.4%) for the Δd method and slightly more than half (55.8%) for the Δr method.

Fig. 4.
Fig. 4.

Frequency distribution of (a) selected SPI accumulation period and (b) lead time for the maximum correlation method (black bars), the Δd optimizing approach (dark-gray bars), and the Δr optimizing approach (light-gray bars). Only the gray-shaded grid cells in Fig. 2d are included.

Citation: Journal of Applied Meteorology and Climatology 63, 2; 10.1175/JAMC-D-23-0077.1

In terms of lead time (Fig. 4b), while the maximum correlation had a zero lag in about 80% of the grid cells, the Δd optimizing approach have a 1-dekad lead time in almost 80% of the domain, with a significant percentage of the grid cells (10%) having a 2-dekad lead time or more. The fraction of cells with a lead time ≥ 2 dekads is even larger (30%) in the case of the Δr method. This result, combined with the increasing frequency of short-term SPIs in Fig. 4a, summarizes the improved early warning capability that can be achieved using SPI-1.

A more in-depth analysis of the changes observed in the selected SPI between the maximum correlation and the two optimization approaches is summarized in Table 2. Here, it is possible to see that between 60% and 70% of the grid cells do not experience a change in the selected SPI (depending on the optimization method), with almost all the changes occurring in SPI-3 or longer accumulations. Indeed, most of the changes occur for SPI-3, and this is where the major difference between the two optimization strategies can be also observed. In the case of the fixed difference (columns d in Table 2), only about one-third of the SPI-3 grid cells move to SPI-1 for optimal accumulation period, whereas this percentage goes up to almost two-thirds for the fixed-ratio method (column r in Table 2). Of all the observed changes, almost all occurred to a shorter accumulation period (SPImax > SPIopt in about 98% of the grid cells with SPImax ≠ SPIopt). In addition, it can be seen that most of these reductions in the accumulation period occur as a single SPI down (i.e., SPI-6 becomes SPI-3, SPI-9 becomes SPI-6, etc.).

Table 2.

Summary of how the selected SPI changes from the maximum correlation to the two proposed optimizing approaches (columns d and r, respectively). Numbers represent percentage of all grid cells with rmax ≥ 0.4 and the specified characteristics. Columns “=” correspond to the grid cells with no changes in SPI; columns “≠” correspond to the grid cells where the SPI changes; columns “<” correspond to the cases in which the accumulation period for the maximum correlation method is smaller than for the optimizing approach; columns “>” correspond to the cases in which the accumulation period for the maximum correlation method is larger than for the optimizing approach; and columns “one SPI down” represent the case “>” for which the change in accumulation period is of just one category (e.g., from SPI-9 to SPI-6). The bottom line summarizes the results for all of the accumulation periods.

Table 2.

It is worth emphasizing that even if about two-thirds of the grid cells did not experience a change in the selected accumulation period, this does not imply that the lead time remains the same (e.g., see the example in Fig. 1, in which the selected SPI-3 remains the same but the lead time increases by 2 dekads). This result is highlighted by the data reported in Table 3, where it is reported that only for SPI-1 a significant fraction of grid cells with no change in optimal SPI (columns SPImax = SPIopt in Table 2) also do not experience any change in lead time (about 70% and 60% for method d and r, respectively), while changes between +1 and +2 are the most commons for the other accumulation periods.

Table 3.

Summary of how the lead time changes for the grid cells where no SPI aggregation period change is observed between optimization approaches and the maximum correlation method (see columns SPImax = SPIopt in Table 2). Columns d and r correspond to the fixed-difference and fixed-ratio approaches, respectively.

Table 3.

The criterion adopted to maximize the lead time, based on a defined minimal degradation in the overall correlation (by setting either Δd or Δr), does not guarantee a similarly small variation in the capability of the selected SPI to detect soil moisture drought events.

The performance of the two optimized SPI datasets (based on Δr and Δd) in term of detecting negative extremes in soil moisture anomalies (SMA < −1) is summarized by the HSS values reported in Figs. 5a and 5c. Both optimized approaches prove to be skillful (HSS > 0) over practically the entirety of the domain (>99%), with an average value of HSSopt-d = 0.30 ± 0.10 and HSSopt-r = 0.29 ± 0.10, both values are only slightly lower than the one for the maximum correlation approach (HSSmax = 0.31 ± 0.11). The differences in skill between the two approaches (HSSmax − HSSopt) depicted in Figs. 5b and 5d show mostly small values (<0.05 in absolute values in about 80% of the grid cells), and only a slight tendency toward positive values (i.e., reduced skill for the optimized approaches). Some regions with negative differences (i.e., better skill for the optimized approach) can be observed in both maps, most notably over Brazil and India, but with differences that are mostly negligible. Slightly larger differences are obtained for the fixed-ratio optimization method, mainly because larger differences in correlation are allowed for this method for high rmax values in comparison with the fixed difference.

Fig. 5.
Fig. 5.

Analysis of the model skill in detecting soil moisture drought extremes (SMA < −1) for the (a),(b) fixed-difference and (c),(d) fixed-ratio methods; the maps report (left) the spatial distribution of the Heidke skill score HSSopt for the optimizing approaches (subscripts -d and -r, respectively) and (right) the difference between the skill of the maximum correlation approach HSSmax and the two optimizing approaches. The inserts in (b) and (d) show the frequency distribution of the observed differences in skill as reported in the maps.

Citation: Journal of Applied Meteorology and Climatology 63, 2; 10.1175/JAMC-D-23-0077.1

c. Analysis of the main SPI and lead time combinations

With a minimal degradation in modeling skill for both the optimized approaches relative to the maximum correlation confirmed, we finally analyze the frequency in which each possible combination of SPIopt and Lopt occurs across the full domain. Given the similarities between the two optimization methods, and the larger differences from the maximum correlation observed for the fixed-ratio approach, we focused this analysis on the results obtained with this method only. Overall, some of the SPIopt–Lopt combination are characterized by a very low frequency of occurrence, hence frequencies lower than about 10% are grouped to the closest pair to synthesize further the data. Following this grouping strategy, six main sets of combinations are obtained as reported in Table 4.

Table 4.

Frequency for the main combinations of SPIopt-r and Lopt-r values.

Table 4.

The frequency of each of these six combinations is analyzed as a function of three essential climate variables at annual scale (total precipitation, average temperature, and average fAPAR), as reported in Fig. 6. These variables are selected to capture both the main climatological drivers of soil moisture, as well as the main target of drought studies, which are regions with vegetation dynamics (either agricultural or natural).

Fig. 6.
Fig. 6.

Frequency distribution for each set of pairs (SPIopt-r and Lopt-r) in Table 3 as a function of (a) annual total precipitation, (b) annual average temperature, and (c) annual average fAPAR. See Table 4 for an explanation of each ID (from A to F).

Citation: Journal of Applied Meteorology and Climatology 63, 2; 10.1175/JAMC-D-23-0077.1

The relationship with annual precipitation (Fig. 6a) shows a predominance (up to 70%) of short lead time and SPI-1 [set identifier (ID) = A] for low precipitation values (<600 mm), while SPI-1 with longer lead time (ID = B) has an above average frequency for annual precipitation between 2000 and 3000 mm. The highest frequency for longer accumulation periods (SPI-6 or longer, ID = E and F) are mostly located in the intermediate precipitation values.

In terms of annual average temperature (Fig. 6b), the long term SPIs (i.e., SPI-9 and SPI-12; ID = F), have higher-than-average frequency only for regions with temperatures below zero (which have, however, a very limited spatial extent, see Figs. 3a,c), while a spike for both SPI-1 classes (ID = A and B) for the highest temperature values (>25°C) is observed. Frequencies for both SPI-3 and SPI-6 have a concave-downward shape, with peak frequencies at around 15° and 5°C, respectively.

Last, the relationship with annual average fAPAR (Fig. 6c) shows an opposite behavior for SPI-1 short lead times (ID = A) and long lead times (ID = B), with the former having a peak value (around 70%) for average fAPAR of 0.1 (sparsely vegetated areas) and the latter for fAPAR values around 0.75 (highly vegetated areas). A similar, even if less marked, behavior can be seen for SPI-3 for short (ID = C) and long (ID = D) lead times. The frequency values for SPI-6 (ID = E) and SPI-9 and SPI-12 (ID = F) have a “bump” for intermediate fAPAR values, at around 0.5 and 0.6, respectively.

4. Discussion

The results of the lagged correlation analysis and of the optimization strategy are discussed separately below.

a. Lagged correlation analysis

The large set of results from the time-lag correlations between SPI and SMA datasets makes it possible to discover some general features. One main difference between short-term SPIs (1 and 3 months) and long-term SPIs (6 months or longer) is the virtual absence of any lead time in the latter. This lagged response in SPI-1 and SPI-3 may be explained by the fact that soil moisture responses to an abrupt change in precipitation, usually captured by short-term SPIs, with a temporal delay due to the persistence (or “memory” effect) of soil moisture (Song et al. 2019). On the case of long-term SPIs, this effect is blurred by the average process, causing a loss of a clear lagged signal.

Wu and Kinter (2009) found zero time lag between SPI-3 and soil moisture using monthly updates, and even soil moisture leads on SPI-9 and -24 over some regions (conditions not analyzed in this study). The results of our study are in agreement with their finding, confirming that early warning capability (e.g., SPI lead over SMA) are unlikely to be achieved with long accumulation periods. Recently, Odongo et al. (2023) studies drought propagation from precipitation to soil moisture in the Horn of Africa, observing maximum correlation for short accumulation periods (1–4 months) for arable lands and longer accumulation (5–7 months) for shrubs, and a key role of soil properties.

Overall, one clear result is the discovery that, given the option to select the locally best SPI dataset based only on correlation, it is possible to reproduce consistently the dynamics of soil moisture drought over most of the regions investigated. This suggests that SPI datasets are well suited for use as a reliable proxy variable for the SMA dataset at global scale in absence of a proper soil moisture dataset (rmax is statistically significant in 99.8% of the grid cells at p ≤ 0.01 and greater than 0.4 in more than 93% of the domain). The observed range of SPI aggregation scales that return the best agreement with SMA is in line with the available literature on the topic, which is indeed mostly based only on maximizing correlation. Previous studies have shown how is it not possible to reliable capture SMA dynamics at global scale with a single SPI accumulation period, with spatial variations primarily related to differences in local hydrological and climatic characteristics, as well as depth of the root zone and vegetation strategies to cope with deficits (Chaves et al. 2003).

The predominance of SPI-3 (over about one-third of the domain) corresponds to the common assumption that SPI-3 is a good proxy variable for agricultural drought, and the observed patterns match well the results reported in some previous studies. Wang et al. (2015) observed good performances of SPI-3 at the majority of stations in China. Over Europe, Bachmair et al. (2018) found that SPI-3 performs generally well in reproducing vegetation stress, but also highlighted large regional differences in correlations, which can be largely explained by climatic variables (i.e., temperature and precipitation). Wang et al. (2015) also observed longer time scales over northeastern China, suggesting an effect of root zone depth on the results. Feng et al. (2019) successfully used SPEI-3 as proxy for agricultural drought in southeastern Australia.

However, the absence of lead time of SPI over SMA for the maximum correlation suggests that such solution is not optimal for an early detection of soil moisture droughts, since a warning based on SPI anomalies will be issued without any warning of on actual soil moisture deficits (given that the lead time in these cases is null almost everywhere). It follows that simply maximizing the correlation returns an optimal agreement solution but at the expense of the SPI’s ability to act as an early warning tool for soil moisture drought. While this may not be an issue if the SPI is used just as a replacement for the SMA index in absence of soil moisture data, it also highlights how a selection approach that takes into account also the lead time may carry on some additional benefits in understanding the temporal evolution of a drought event in a near-real-time system, especially when multiple indicators can be simultaneously analyzed to reproduce the cascading process of the drought from meteorological to agricultural drought.

b. Optimization of the SPI early warning capability

The methodology proposed in this study highlights the fact that, with a minimum compromise in term of correlation, it is possible to increase the lead time with which SPI warns of the soil moisture anomalies. The two optimization strategies tested in this study cover two complementary ways to derive a cutoff value in correlation, one based on a fixed difference and the other on a fixed ratio. Independent of the adopted method, a general move toward shorter accumulation periods is observed. Given the lagged peaks observed in SPI-1 and SPI-3, it comes as no surprise that the optimal approach tends to favor short-term SPIs over long-term SPIs.

While the common assumption—often based only on considerations on the correlation—that SPI-3 and SPI-6 are of the optimal time scales in the framework of soil moisture drought (WMO 2012), still holds true in many cases, it seems that shorter accumulation periods can deliver similar performances in term of correlation, with the added value of a noticeable increase in lead time. In this regard, commonly neglected accumulation periods (i.e., 2 months), may attract a new interest as a compromise between the best solution in term of maximum correlation (SPI-3) and the optimal effectiveness for early warning capability (SPI-1). This result, besides the specific local-optimal accumulation period and derived lead time, seems to be of general validity and independent from the specific datasets used in this study. Of course, different results may be achieved with different datasets or higher/lower update frequency, but the key message seems supported by the consistency of the outcomes at global scale.

The spatial patterns in the optimal SPI agree with some general considerations recently reported by Zhu et al. (2021) on the propagation of meteorological drought to soil moisture. In this study, based on a multivariate analysis, the likelihood of soil moisture drought conditioned by 1-month meteorological drought was higher in the Amazon and China, and better explained by 3-month accumulation over Europe and the United States.

Evidence of a lagged response of soil moisture to meteorological factors has been suggested by Tian et al. (2022) using a cross-wavelet transform method in north and south China, and to a more limited extent by Zeri et al. (2022) over Brazil. These studies, similarly to our results, suggest that the search for the optimal SPI dataset to be used in a drought monitoring system in combination with SMA data (hence aiming at a drought early warning) needs to go beyond the simple goal to optimize the correlation (which is a suitable approach only if SPI is used as a proxy variable of SMA) in order to properly maximize the overall information content and usefulness of each indicator, as well as the ability to capture different aspects of the drought propagation. While the acceptable level of reduction in correlation may vary for different stakeholders, based on their willingness to sacrifice accuracy in favor of early warning, the overall message of the results reported in this study remain valid independently from the chosen cutoff value. In general, the fixed-ratio approach seems to return larger lead time and differences for grid cells with high correlation values when compared with a fixed-difference value, since the former is characterized by a more relaxed constraint on the high r values (i.e., larger correlation differences are allowed for high r values).

The implementation of such optimizing strategies may appear too time consuming for operational monitoring systems, since it requires performing multiple correlation analyses on different aggregation time scales. However, in support to the transferability of the obtained results, it is encouraging that the spatial patterns in the observed optimized results are well explained by simple climatic and vegetation information, a result in line with Gevaert et al. (2018), where a connection between drought propagation and climate types is inferred. The results highlight the tendency of SPI-1 with short lead time (0–1 dekad) to be the best option in areas with low precipitation, high temperature, and low vegetation greenness. This result is in line with the expected behavior for such areas, which have a quick response to precipitation deficit, as shown in Sehler et al. (2019), where drier, less vegetated climates show a highly linear relationship between soil moisture and rainfall. Longer lead times (i.e., ≥2 dekads) are instead found to be obtained for areas with high precipitation and greenness, where a delayed hydrological response of the soil is expected. The frequency values for long-term SPIs (accumulation periods of 6 months or longer) are generally low, but with relatively high values observed for areas with intermediate precipitation and fAPAR, or with below zero temperatures (albeit these latter are of limited spatial extent). The introduction of the proposed optimization methods does not seem to alter these overall considerations, allowing to infer some recurring feature that can be exploited even in absence of a proper local search for an optimal SPI dataset. The observed patterns in the relationship between the “optimized” SPI and the climate and vegetation variables suggest an effect of climate conditions on the SPI-SMA lagged correlation, even if the analyses are performed on standardized quantities. In this regard, further tests on subseasonal data (i.e., warm and cold seasons, separately) may be valuable to identify differences among seasons.

The observed improvements in lead time (on the order of 10–20 days over most of the studied grid cells) relative to the zero-lead of the maximum correlation may be a worthwhile trade off in many operational applications, given that the requirements for drought early warning range from a few weeks to several months (United Nations Secretariat of the International Strategy for Disaster Reduction 2009). It is worth highlighting that among the key factors limiting the integration of climate services in agriculture systems there is the credibility of climate service outputs, especially in the case of forecast data (Warner et al. 2022). The possibility to improve the early warning capability of a climate service without compromising the accuracy can be seen as a valuable advancement fostering the interest of decision-makers.

The observed SPI lead times are in line with the results in Sepulcre-Canto et al. (2012) for a few stations in Europe. An improved early warning capability of short-term SPIs over long-term SPIs was also observed by Meroni et al. (2017) over the Sahel, where vegetation productivity anomalies are well predicted by SPI-1 and SPI-3, especially early in the growing season. Regarding the predictability of negative extremes, the skill scores suggest a skillful performance for both optimization strategies, with results that are comparable to the maximum correlation. Even if the skill is only moderate in most of the cases (between 0.2 and 0.4), this result does not seem to be driven by the optimization strategy, but it is likely intrinsically connected to the capability to predict SMA starting from SPI.

The large lead time obtained for grid cells with abundant vegetation (i.e., fAPAR > 0.7) are interesting to analyze in the frame of the consideration that SMA usually precede actual effects on vegetation. In this regard, Crow et al. (2012) show how soil moisture precedes effects on vegetation indices, such as NDVI, of about one month on a global scale. Li et al. (2022) found a lagged response of vegetation from soil moisture, ranging between 9 and 35 days depending on the vegetation type in southern China. Na et al. (2021), in the arid and semiarid Mongolian Plateau, show lags between 0.5 and 3 months between soil moisture and NDVI depending on vegetation stage, and a similar lagged repose of vegetation to water availability, up to 3 months, was reported by Papagiannopoulou et al. (2017) at global scale. Since vegetated areas (both agricultural and natural) are the main focus of agricultural drought studies, it follows that the obtained results suggest that a valuable early warning signal can be inferred for these regions by a combined use of the proper SPI and SMA information.

5. Summary and conclusions

In this study, the results of a time-lagged correlation analysis between five datasets of SPI (at different accumulation periods) and SMA, have demonstrated that taking the SPI lead time into consideration, in addition to the correlation coefficient, can significantly affect the choice of the “optimal” SPI dataset for the purpose of agricultural drought monitoring.

In general, on the one hand, only considering the maximum correlation tends to favor SPI-3 as the ideal solution, a result that is in line with most of the scientific literature on the topic, as well as the preferred choice of many operational drought early warning systems. On the other hand, if the lead time is also taken into account, SPI-1 is preferred over a much higher proportion of grid cells. This strategy leads to a negligible reduction in the overall correlation between SPI and SMA, as well as in the skill of detecting drought extremes, but it results in a noticeable improvement in the effectiveness in warning upcoming agricultural droughts, with lead times ranging between 10 and 20 days over almost all the analyzed grid cells (>90%). This increased early warning capability can be exploited in the context of climate service-driven decision-making in the agriculture sectors, where a few weeks’ early warning can be valuable for preemptive actions.

The results of our analysis suggest that to fully exploit the early warning capability of SPI in the case of soil moisture drought shorter accumulation periods should be favored in the design of a system, as a general rule of thumb. SPI-1 seems to perform particularly well over regions with low (<500 mm) and high (2000–3000 mm) total precipitation values, with a longer lead time in the high-precipitation regions than in the low-precipitation areas.

The increase in lead time of 10–20 days comes at a “free cost” simply because it is based on a better exploitation of how drought propagates through the hydrological cycle, independently of any additional forecast capability. The possibility of issuing a warning for agricultural drought with a slight lead time in warning relative to the commonly used SPI accumulation periods can have a significant effect on how water managers and stakeholders can react in case of an emergency.

Data availability statement.

All of the data used in this study can be access through the Global Drought Observatory (GDO) web portal (https://edo.jrc.ec.europa.eu/gdo/php/index.php?id=2112).

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  • Zhu, Y., Y. Liu, W. Wang, V. P. Singh, and L. Rn, 2021: A global perspective on the probability of propagation of drought: From meteorological to soil moisture. J. Hydrol., 603, 126907, https://doi.org/10.1016/j.jhydrol.2021.126907.

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  • Fig. 1.

    Illustration of the optimization procedure for SPI selection vs the maximum correlation selection, and example of time-lagged correlograms for a grid cell in central Spain (central panel). The left side of the figure shows the retrieval of the maximum correlation values (rmax, SPImax, and Lmax), whereas the right side of the figure shows a schematic of the estimation procedure for the constant-difference Δd optimization approach (ropt, SPIopt, and Lopt).

  • Fig. 2.

    Output of the maximum correlation analysis on the time-lag correlograms between SPIs and SMA: (a) spatial distribution of the maximum correlation rmax values, (b) SPI index returning the rmax values, or SPImax, (c) the corresponding lead time Lmax, and (d) a mask of the grid cells with enough correlation (rmax > 0.4) as used in the successive analyses. Areas in white in (a)–(c) include grid cells with less than 50% of reliable SPI or SMA data available for a correlation analysis.

  • Fig. 3.

    Spatial distribution of (left) the optimized SPI, or SPIopt, and (right) the corresponding lead time Lopt for (a),(b) the fixed-difference method Δd (subscript -d) and (c),(d) the fixed-ratio method Δr (subscript -r). Areas in white correspond to the mask reported in Fig. 2d.

  • Fig. 4.

    Frequency distribution of (a) selected SPI accumulation period and (b) lead time for the maximum correlation method (black bars), the Δd optimizing approach (dark-gray bars), and the Δr optimizing approach (light-gray bars). Only the gray-shaded grid cells in Fig. 2d are included.

  • Fig. 5.

    Analysis of the model skill in detecting soil moisture drought extremes (SMA < −1) for the (a),(b) fixed-difference and (c),(d) fixed-ratio methods; the maps report (left) the spatial distribution of the Heidke skill score HSSopt for the optimizing approaches (subscripts -d and -r, respectively) and (right) the difference between the skill of the maximum correlation approach HSSmax and the two optimizing approaches. The inserts in (b) and (d) show the frequency distribution of the observed differences in skill as reported in the maps.

  • Fig. 6.

    Frequency distribution for each set of pairs (SPIopt-r and Lopt-r) in Table 3 as a function of (a) annual total precipitation, (b) annual average temperature, and (c) annual average fAPAR. See Table 4 for an explanation of each ID (from A to F).

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