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How do multiscalar drought indices relate to soil moisture in the semi-arid Southwest?

Vegetation productivity in the semi-arid Southwestern United States (‘Southwest’) is adapted to the seasonal timing and magnitude of precipitation for soil water recharge (Hadley & Szarek, 1981; Neilson et al., 1992; Wilcox et al., 2003). To monitor vegetation health and drought development throughout the year, many land managers use multiscalar meteorological drought indices, like the Standardized Precipitation Index (SPI) and Standardized Precipitation-Evapotranspiration Index (SPEI), as proxies for soil water availability (McKee et al., 1993, Vicente-Serrano et al., 2010). However, the lack of long-term and reliable in-situ soil moisture datasets has created unique drought monitoring challenges for land managers, as objectively identifying the index and timescale that best represents soil water availability remains ambiguous. This has left land managers with a significant gap for applying available climate information to land management action. A recent study published in the Journal of Geophysical Research (link) evaluates this issue by conducting a regional analysis of the Southwestern United States to define the relationship between SPI and SPEI timescale length and water availability at different depths within a soil profile. 

The SPI and SPEI are popular drought indices used by land managers, climate experts, and government officials for early drought detection. Crossing certain drought thresholds often triggers key actions within a state or regional agencies drought plan and are used by managers to make management decisions – like managing stocking rates for livestock or assessing wildfire risk (Svoboda & Fuchs, 2016). The Standardized Precipitation Index (SPI) is a time series of index values that convey the frequency and magnitude of monthly precipitation compared to the historical record (McKee et al., 1993). The Standardized Precipitation-Evapotranspiration Index (SPEI) is a time series of monthly water balance values that represent the difference between precipitation and potential evapotranspiration (PET) (Vicente-Serrano et al., 2010). An advantage of the SPEI compared to the SPI is this inclusion of PET, allowing temperature to be incorporated into index values. However, this comes at the expense of needing additional data and the choice of PET estimation method – each of which carry their own issues, such as a limited period of record or estimation problems in arid/semi-arid environments (Beguería et al., 2014; Stagge et al., 2015). Both the SPI and SPEI are multiscalar, where values over a selected monthly duration (or timescale) are summed and compared with other instances in the historical record (for example, comparing this year’s May-June-July precipitation totals with all other May-June-July’s on record). This key feature allows index users to quickly identify how recent month(s) or seasons are performing compared to climatic norms. 

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Map of study sites in southern CA, AZ, NM and West TX for assessing the relationship between soil moisture and drought indices
Figure 1: Subsurface soil texture class for each study location (n=240) acquired using the ‘soilDB’ R-package (Beaudette et al. 2021). Subsurface texture classes were selected based on their regional popularity and control over dryland vegetation productivity (Shepard et al. 2015). A total of 10 of each texture class were selected from each MLRA. 

To evaluate how the SPI and SPEI compares to soil moisture, a new soil water dataset needed to be created due to the lack of extensive soil moisture datasets throughout the Southwest. By coupling site-specific meteorological data and soils information with HYDRUS-1D, a deterministic modeling software designed for simulating water movement in a one-dimensional variably saturated porous media (Simunek et al., 2005), daily soil matric potential time series were simulated at 5 cm intervals from 0-200 cm for 240 locations throughout the Southwest (figure 1). Soil matric potential, or the amount of energy plants must exert to extract water molecules from a soil matrix, is another way to measure soil water content and was chosen as it better communicates vegetation response to changing drought conditions. The modeled time series were converted into a Matric Potential Index (MPI) using similar methodology to the SPI and SPEI derivations. To identify the best index-timescale combination for each depth, MPI time series at increasing depth intervals were correlated with SPI and SPEI time series at different timescale lengths. Conceptually, this study aligns the linear timescales of the SPI and SPEI with the non-linear movement of water through a soil profile, as shown in the top and bottom contour plots of figure 2. At shallow depths, the MPI should correlate highly with shorter index timescales in a more linear fashion. At deeper depths, the MPI should align with longer timescales but with lower correlation as the linear index timescales struggle to match the non-linearity of water movement in the soil profile.

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Conceptual figure showing how linear standard precipitation index timescales (top) compare with non-linear depths of the Matric Potential Index (bottom) for a loam soil
Figure 2: Conceptual figure demonstrating the alignment of linear SPI timescales (top) with non-linear depths of the MPI (bottom) for a loam soil (example from model run 121 of 240; MLRA 30). The monthly precipitation anomaly (center) is provided to show when wet and dry spells occur.  

The highest Pearson correlation value between an SPI and SPEI time series at each MPI depth interval was identified, and a line was plotted to evaluate the relationship between timescale and depth. Average correlations for all 240 study sites for each depth-timescale combinate are shown in figure 3. Results indicate the general relationship between the highest correlating index-timescale pairing at each MPI-depth operates roughly on a 1-month:5 cm step progression at shallow depths (<80 cm). Below 80 cm, the relationship between timescale and depth becomes less linear and has a shallower slope. Analysis by soil texture class (figure 4) shows that soils with higher clay content produced shallower sloped relationships (>1-month:5 cm) and higher correlations than sandy soils (<1-month:5 cm). Overall, the SPI produced higher correlations and less error with the MPI compared to the SPEI across all texture classes and depths. 

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two dimensional correlation maps that shoe the relationship of the standardized precipitation index (SPI: left) and the standardized evaporation-precipitation index (SPEI: right) with the Matric Potential Index. Red colored cells show where the correlation is highest. The SPI map shows the most red.
Figure 3: General timescale-depth relationship between the SPI – MPI (left) and SPEI – MPI (right). Each grid cell represents the mean Pearson correlation value between the time series of the X-timescale SPI or SPEI and time series of the Y-depth MPI of all 240 study locations. Grayed-out grid cells represent instances when the resulting p-value from the Pearson correlation between the multiscalar index timescale and MPI was not statistically significant (p>0.05). 

Findings of this study demonstrated that the SPI better matched MPI temporal variability compared to the SPEI. Furthermore, it is clear that the inclusion of temperature through the PET component in the SPEI calculation did not improve the ability to approximate soil water availability in the semi-arid Southwest compared to using just monthly precipitation totals. This was attributed to the SPEI using potential instead of actual ET. The SPI, which excludes PET from its calculation, produced higher correlations and less error with the MPI due to the MPI incorporating AET through the HYDRUS modeling and annual precipitation being closer to annual AET compared to PET. Thus, this study recommends the SPI for soil drought monitoring on Southwestern drylands, as it is a good indicator of soil water availability at shallow depths (<80 cm). However, land managers should consult local soils information, if available, given the impacts of texture class on timescale-depth relationships. 

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Correlation lines on two graphs (SPI on the left, SPEI on the right), show that SPI more closely correlates with the Matric Potential Index than SPEI. Highest correlations are found at shorter timescales.
Figure 4: The highest correlation line (HCL) for sand (dotted) and clay loam (solid) variants of the MPI and the SPI (4a) and SPEI (4b). The HCL for loamy sand, sandy loam, loam, and sandy clay loam are not plotted for simplification, as they plot between the sand and clay loam HCL. Each depth-timescale point along the HCL is the mean correlation value (n=40) between the soil texture variant MPI (circle = sand; square = clay loam) and SPI (4a) or SPEI (4b). 

More information on this study can be found in the source article, published in the Journal of Geophysical Research titled Defining the Multiscalar Index Timescale – Soil Water Depth Continuum for the Southwestern United States, which has been made available free with open access at: https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2023JD039348. For any comments of questions, please email Dr. Trevor McKellar at tmckella@arizona.edu.

Citation: McKellar, T. T., Crimmins, M. A., Schaap, M. G., & Rasmussen, C. (2023). Defining the multiscalar index timescale—Soil water depth continuum for the southwestern United States. Journal of Geophysical Research: Atmospheres, 128(23), e2023JD039348.

References

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McKellar, T. T., Crimmins, M. A., Schaap, M. G., & Rasmussen, C. (2023). Defining the

multiscalar index timescale—Soil water depth continuum for the southwestern United States. Journal of Geophysical Research: Atmospheres, 128(23), e2023JD039348.

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Stagge, J. H., Tallaksen, L. M., Xu, C. Y., & Van Lanen, H. A. (2014). Standardized precipitation-evapotranspiration index (SPEI): Sensitivity to potential evapotranspiration model and parameters. In Hydrology in a changing world (Vol. 363, pp. 367-373).

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