Evaluating Drought Indices for Alaska

Joshua M. Walston aDepartment of Geography, University of Nevada, Reno, Reno, Nevada

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Stephanie A. McAfee aDepartment of Geography, University of Nevada, Reno, Reno, Nevada

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Daniel J. McEvoy bWestern Regional Climate Center, Desert Research Institute, Reno, Nevada

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Abstract

Drought is a recurrent natural phenomenon, but there is concern that climate change may increase the frequency or severity of drought in Alaska. Because most common drought indices were designed for lower latitudes, it is unclear how effectively they characterize drought in Alaska’s diverse, high-latitude climates. Here, we compare three commonly used meteorological drought indices [the standardized precipitation index (SPI), the standardized precipitation evapotranspiration index (SPEI), and the self-calibrating Palmer drought severity index (scPDSI)] with each other and with streamflow across Alaska’s 13 climate divisions. All of the drought indices identify major droughts, but the severity of the drought varies depending on the index used. The SPI and the SPEI are more flexible and often better correlated with streamflow than the scPDSI, and we recommend using them. Although SPI and SPEI are very similar in energy-limited climates, the drought metrics do diverge in drier locations in recent years, and consideration of the impact of temperature on drought may grow more important in the coming decades. Hargreaves potential evapotranspiration (PET) estimates appeared more physically realistic than the more commonly used Thornthwaite equation and are equally easy to calculate, so we suggest using the Hargreaves equation when PET is estimated from temperature. This study, one of the first to evaluate drought indices for high-latitude regions, has the potential to improve drought monitoring and representation within the U.S. Drought Monitor, leading to more informed decision-making during drought in Alaska, and it improves our ability to track changes in drought driven by rising temperatures.

Significance Statement

Tracking drought at high latitudes is challenging because we have not adequately studied drought impacts in cold climates, and the primary meteorological drought indices were designed for lower latitudes and may not accurately estimate evaporative demand and the influence of snow. We investigate three common drought indices and recommend using the standardized precipitation index (SPI) or the standardized precipitation evapotranspiration index (SPEI) because they can track short and long droughts. The SPEI may be more useful because comparisons between the SPI and SPEI show that, in recent decades, temperature has made noticeable contributions to drought in drier parts of Alaska. If using the SPEI, we suggest the Hargreaves potential evapotranspiration rather than the Thornthwaite because it is more physically realistic.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Walston’s current affiliation: Alaska Pacific River Forecast Center, National Oceanographic and Atmospheric Administration, Anchorage, Alaska.

Corresponding author: Stephanie A. McAfee, smcafee@unr.edu

Abstract

Drought is a recurrent natural phenomenon, but there is concern that climate change may increase the frequency or severity of drought in Alaska. Because most common drought indices were designed for lower latitudes, it is unclear how effectively they characterize drought in Alaska’s diverse, high-latitude climates. Here, we compare three commonly used meteorological drought indices [the standardized precipitation index (SPI), the standardized precipitation evapotranspiration index (SPEI), and the self-calibrating Palmer drought severity index (scPDSI)] with each other and with streamflow across Alaska’s 13 climate divisions. All of the drought indices identify major droughts, but the severity of the drought varies depending on the index used. The SPI and the SPEI are more flexible and often better correlated with streamflow than the scPDSI, and we recommend using them. Although SPI and SPEI are very similar in energy-limited climates, the drought metrics do diverge in drier locations in recent years, and consideration of the impact of temperature on drought may grow more important in the coming decades. Hargreaves potential evapotranspiration (PET) estimates appeared more physically realistic than the more commonly used Thornthwaite equation and are equally easy to calculate, so we suggest using the Hargreaves equation when PET is estimated from temperature. This study, one of the first to evaluate drought indices for high-latitude regions, has the potential to improve drought monitoring and representation within the U.S. Drought Monitor, leading to more informed decision-making during drought in Alaska, and it improves our ability to track changes in drought driven by rising temperatures.

Significance Statement

Tracking drought at high latitudes is challenging because we have not adequately studied drought impacts in cold climates, and the primary meteorological drought indices were designed for lower latitudes and may not accurately estimate evaporative demand and the influence of snow. We investigate three common drought indices and recommend using the standardized precipitation index (SPI) or the standardized precipitation evapotranspiration index (SPEI) because they can track short and long droughts. The SPEI may be more useful because comparisons between the SPI and SPEI show that, in recent decades, temperature has made noticeable contributions to drought in drier parts of Alaska. If using the SPEI, we suggest the Hargreaves potential evapotranspiration rather than the Thornthwaite because it is more physically realistic.

© 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Walston’s current affiliation: Alaska Pacific River Forecast Center, National Oceanographic and Atmospheric Administration, Anchorage, Alaska.

Corresponding author: Stephanie A. McAfee, smcafee@unr.edu

1. Introduction

The Arctic and subarctic have been experiencing environmental change at an accelerated rate (Thoman and Walsh 2019). The changes include increases in average air temperature (e.g., Bieniek et al. 2014; Walsh and Brettschneider 2019; Overland et al. 2020); larger, more frequent wildfires (Box et al. 2019; Witze 2020; McCarty et al. 2021); greening and expansion of shrubs into tundra biomes (e.g., Sturm et al. 2001); and changes in precipitation (e.g., White et al. 2021; Box et al. 2019; Min et al. 2008) and snowpack (e.g., Mudryk et al. 2020; Jeong et al. 2017).

Alaska is rich in natural resources critical to subsistence users. The natural abundance of plants and wildlife is fundamental to Alaska Native peoples and their culture and provides a way of life for many rural non–Native Alaskans (Magdanz et al. 2016). Alaska’s diverse landscapes, variation in topography, and proximity to the North Pacific Ocean causes considerable geographic and interannual variation in climate (Shulski and Wendler 2007). Large-scale changes in climate may have a profound impact on the natural resources underlying subsistence (Markon et al. 2018), but drought impacts are diverse and may not be consistent across species or among places. For example, in a survey of southwest Alaska residents, more people agreed that a dry winter was bad for cloudberry than for crowberry, and residents from different communities had different perceptions of how a small snowpack impacted the blueberry harvest (Herman-Mercer et al. 2020).

In 2018, southeast Alaska, characterized by temperate rain forest, received less than half of the normal precipitation. These unusually dry conditions quickly led to the region’s first Extreme Drought (D3) classification declared by U.S. Drought Monitor and became the most significant drought in over 40 years. Communities across the region relied on diesel-generated power when hydropower reservoirs were too low (Winter 2019). Record-low reservoir levels and decreased precipitation reduced availability of municipal water and led to community-wide water restrictions (Leffler 2018; Jacobs and Thoman 2019). High temperatures led to increased fish mortality (Bellmore et al. 2019; Joling 2019).

Drier and warmer than normal conditions expanded northwest into southcentral Alaska during the summer of 2019, when the anomalously warm and dry conditions elevated fire danger. Indeed, 2019 was one of Alaska’s most active and destructive wildfire seasons (Bhatt et al. 2021; Herz 2019; Yu et al. 2021; Smith 2020).

This was far from the first drought to impact Alaska. Drought is a normal feature of the climate system and occurs in every geographical region (Sheffield and Wood 2007; Sheffield et al. 2009). However, climate change may increase the frequency or severity of drought. While most climate projections show significant increases in precipitation in all seasons in northerly parts of the state, southeastern Alaska may receive less summer rain in the future (IPCC 2013; Lader et al. 2020). Interannual variability will likely produce periods of low precipitation, and rising temperatures will enhance evaporative demand.

There have been considerable advances in understanding and monitoring drought through the use of indices tracking specific aspects of drought, increased reliance on local expertise, and a better assessment of impacts (Rippey et al. 2021). However, because droughts are less frequently reported in Alaska and other high-latitude regions (Leeper et al. 2022), their impacts are not always recognized. For example, during the 2019 drought in southeastern Alaska, local residents did not necessarily link impacts like an increased need to supplement hydropower to drought. This lack of detection, combined with indices that may not be suitable, challenges drought monitoring at higher latitudes (Bathke et al. 2019). Hence, there is a notable gap in the understanding of drought severity, extent, timing, and duration within Alaska. This research aims to address this gap by assessing three commonly used drought indices. The results presented here have the potential to aid drought monitoring and response and contribute to our understanding of climate change impacts on high-latitude drought.

Drought is a complex phenomenon that couples the atmosphere with hydrological and biological processes over a range of spatial and temporal scales (Redmond 2002). Lower precipitation can cause direct moisture stress. It can reduce snowpack storage capacity (e.g., snow drought; Harpold et al. 2017). Indirectly, lower than normal precipitation can change the surface energy balance by reducing the snowpack and, thus, the albedo. Changes in the partitioning between latent and sensible heating can also alter local near-surface temperatures. Higher temperatures can contribute to drought by increasing potential evaporation, but can also alter snowpack dynamics, and may influence the length of the growing season or rate of transpiration in ways that also influence the surface energy balance (Milly and Dunne 2020).

To better track drought, numerous indices have been developed (Heim 2002; Keyantash and Dracup 2002; Vicente-Serrano et al. 2012; Hobbins et al. 2016; McEvoy et al. 2016). Drought indices provide a quantitative assessment of drought by assimilating meteorological, hydrological, and/or ecological data. They are useful for climate and drought monitoring applications, such as the U.S. Drought Monitor (USDM; Svoboda et al. 2002) and for research on drought impacts. Three of the most commonly used drought indices are the Palmer drought severity index (PDSI; Palmer 1965), the standardized precipitation index (SPI; McKee et al. 1993), and the standardized precipitation evapotranspiration index (SPEI; Vicente-Serrano et al. 2010), and they are often assessed at the climate-division level. Coarse spatial metrics of drought, such as those provided by climate division data, are not appropriate for all applications. Microclimates and other fine-scale variability can alter the local severity of drought (Zang et al. 2020). Moreover, drought is often defined by its impacts, which depend not only on the length and severity of the dry period but also on the characteristics of the local and regional agriculture, hydrology, ecosystems, and infrastructure. Climate-based drought indicators may not be universally appropriate for all drought impacts but they are often the easiest and, therefore, the first line of information for those interested in drought monitoring (Bachmair et al. 2016).

While research has shown that all drought indices can be useful, none is inherently superior, and each has strengths and limitations (Keyantash and Dracup 2002; Heim 2002; Hayes et al. 2011; Vicente-Serrano et al. 2012). However, drought indices were predominately developed for low- and midlatitude locations, so it is not clear how effective they are at higher latitudes. Moreover, drought index data for Alaska are limited and have been less thoroughly vetted than at lower latitude. Many studies have investigated the impacts of drought on Alaska ecosystems (e.g., Barber et al. 2000) and hydrology (e.g., Kane et al. 2008), but most relied on temperature and precipitation rather than defined metrics. Studies that have used standard meteorological drought indices (e.g., Cahoon et al. 2018; Lange et al. 2020) often used SPEI with the standard Thornthwaite calculation because that was assumed to be the best choice or because it is the default. Because there has been very little assessment of how well standard drought indices perform at high latitudes, participants at an Alaska drought workshop recommended that relevant drought indices and indicators be identified to improve drought monitoring across Alaska (Bathke et al. 2019). Very few studies have evaluated how well drought indices and indicators track drought in Alaska or other high-latitude areas. We have found no direct evaluation or comparison of drought indices and indicators for Alaska, although Ziel et al. (2020) did test two drought indices, SPEI and the evaporative demand drought index, for use as wildfire predictors.

Here, we compare three meteorological drought indices with each other and compare them with streamflow, a commonly used drought indicator, across Alaska’s 13 climate divisions to improve the understanding of drought characteristics across Alaska. We assume that all three primary meteorological drought indices accurately classify moisture availability across various regions, but we also hypothesize that the SPEI is a more robust drought index throughout Alaska’s 13 climate divisions owing to its incorporation of evaporative demand and its ability to characterize drought over multiple time scales.

2. Data and methods

a. Data

Monthly meteorological variables, including total precipitation and maximum, minimum, and average temperatures, were obtained from the National Centers for Environmental Information (NCEI 2020) Climate Division Database. Alaska climate divisions (Fig. 1) are defined by latitude, elevation, proximity to the ocean, and regional homogeneity in climatic variation, and were previously identified through a cluster analysis performed by Bieniek et al. (2012). Official NCEI divisional data for Alaska are similar to those developed by Bieniek et al. (2012) but incorporate some inhomogeneity correction and use the Parameter Regression on Independent Slopes Model (PRISM; Daly et al. 1994) climatological averages to provide temperature and precipitation values as well as anomalies (Vose et al. 2017). Divisional precipitation and temperature were used to calculate each drought index from 1925 to 2019 for all 13 climate divisions of Alaska.

Fig. 1.
Fig. 1.

Map of the study region. Alaska climate divisions are indicated by dark gray lines and labeled with the division name and number. The U.S. Geological Survey streamflow gauges used in the analysis and listed in Table 1 are shown. The HUC8 basins associated with those gauges are shown with blue (primary gauges) or green (secondary gauges) shading.

Citation: Earth Interactions 27, 1; 10.1175/EI-D-22-0025.1

Streamflow has previously been shown to be good indicator of drought (Garen 1993) with a robust relationship with multivariate drought indices (McEvoy et al. 2012) in the western United States. Although there could be differences in hydrological response to drought at higher latitudes due to contributions from glaciers or permafrost, there are some similarities related to the varying elevational importance of snowmelt to streamflow. To evaluate the relationship between derived drought indices and streamflow across Alaska, 24 U.S. Geological Survey streamflow gauges were selected for analysis based on record length and completeness. Each has a minimum of 20 years of daily observations ending in 2019 (Table 1, Fig. 1). We attempted to find two gauges in each division but were not able to find long (ideally, ≥20 years) complete streamflow records in all locations. All divisions are represented by one primary gauge, and 10 of the divisions also have a secondary with a shorter and/or less complete record. Monthly values were computed if daily data were complete or missing fewer than three days, except for missing values in late 2019. Monthly streamflow values are summed daily discharge measurements standardized to z scores by subtracting the mean flow and dividing by the standard deviation for comparison with drought indices.

Table 1

Information about U.S. Geological Survey stream gauges used in the evaluation of drought indices. In divisions with two gauges listed, the first gauge is the primary gauge because it has a longer and/or more complete record, and the second is the secondary gauge, with a shorter and/or less complete record. Primary and secondary gauges are shown in Fig. 1. Here, R is River, NR is near, BL is below, and C is Creek.

Table 1

When possible, we also provided qualitative comparison of PET with seasonal evapotranspiration patterns described in the published literature. In most cases, direct quantitative comparisons between locally measured evapotranspiration (ET) and divisional PET are not practical because of differences in scale, the influence of vegetation type (e.g., Yuan et al. 2010), and inherent differences between PET and ET even in wet environments, due to physiological impediments to water transfer (e.g., Liljehdal et al. 2011).

b. Potential evapotranspiration calculation

Both self-calibrating PDSI (scPDSI) and SPEI are based on a climatic water balance model that compares precipitation with PET. The Food and Agricultural Organization (FAO) recommends calculating PET with the Penman–Monteith equation (Allen et al. 1998). However, this method requires variables, including incoming solar radiation, relative humidity, and vapor pressure, that are not available from the divisional data. Opinions about the importance of PET calculation are mixed. Hobbins et al. (2008), McAfee (2013), and Albano et al. (2022) suggest that sophisticated PET calculations that account for all drivers of evapotranspiration are more representative and reduce uncertainties at regional scales. Mavromatis (2007) showed that in drought indices, simple PET estimation methods are adequate, but Beguería et al. (2014) found that the choice of PET calculation can influence the SPEI in arid climates.

We evaluated two simple PET algorithms, those of Thornthwaite [1948; Eq. (1)] and Hargreaves [1994; Eq. (2)], that can be calculated with the available climate division data. Both methods are temperature and latitude based but vary slightly in execution. Thornthwaite PET is the simpler method. As implemented in the SPEI package for R (Beguería and Vicente-Serrano 2017), it requires monthly mean temperature and a central latitude of a given location, which are used to determine a specific heat index based on an empirically derived solar angle (Thornthwaite 1948). The Hargreaves method also uses a central latitude but includes monthly maximum and minimum temperatures to capture radiative balance near the surface (Hargreaves and Samani 1985; Hargreaves 1994). A central latitude for each Alaska climate division was found using a standard centroid method. Climatologies of the two PET methods were then compared with each other to describe differences and determine which method seemed more physically realistic for each climate division based on expected seasonality in the water balance and measured evapotranspiration, when available.

Thornthwaite potential evapotranspiration (Vicente-Serrano et al. 2010) is given by
PETTH=16K(10Ta/I)mifTa>0°C,elsePETTH=0,
where
I=i=112(T/5)1.514,
m=6.75×107I37.71×105I2+1.79×102I+0.492,
K is a correction factor related to latitude’s effect on insolation, and Ta is monthly average temperature (°C). Hargreaves’s equation is
PETH=0.0023R(Ta+17.8)(TmaxTmin)0.5,
where R is extraterrestrial radiation estimated from latitude and month and Tmax and Tmin are monthly average maximum and minimum temperatures (°C).

c. Drought index calculation

Three widely used drought indices were included in this study: scPDSI, SPI, and SPEI. Each index was computed from 1925 to 2019 for all 13 climate divisions using existing algorithms. The scPDSI was computed at monthly time steps, while SPI and SPEI were calculated at 1-, 3-, 6-, 12-, 24-, 36-, 48-, and 60-month time scales.

The PDSI is arguably the most widely used drought index. It is based on a two-layer soil moisture model that tracks the standardized difference between atmospheric moisture supply and surface moisture demand. While the PDSI is effective at depicting drought conditions for large areas of uniform topography, particularly in low and midlatitudes (Dai et al. 2004; Dai 2011), it preferentially identifies droughts of different durations and severities in different places and can, but does not always, change markedly in response to precipitation in a specific month (Karl 1983; Alley 1984; Guttman et al. 1992). Wells et al. (2004) improved the spatial limitations of the PDSI with the addition of dynamically adjusted constants based on historical climate data for a given location. This form of the PDSI is now referred to as the scPDSI and has been shown to be more suitable for drought quantification at global scales (Vicente-Serrano et al. 2012). However, the scPDSI does not explicitly specify the time scale of drought (e.g., 1, 3, or 12 months) in the way that SPI and SPEI do—an important feature required to address various impacts affecting natural and human environments.

The scPDSI was calculated using the standard method outlined by Wells et al. (2004) and the R algorithm developed by Zhong et al. (2018). Monthly standardized moisture supply is estimated using monthly observed precipitation, derived PET, and dynamically adjusted coefficients based on the distinct climatic conditions of individual Alaska climate divisions. scPDSI values range from −10 (dry) to +10 (wet), with values below −4 representing severe to extreme drought conditions.

The SPI determines the departure of observed precipitation relative to historical probabilities estimated from a gamma or Pearson III distribution over various accumulation periods (e.g., 1, 3, 6, or 12 months; McKee et al. 1993; Guttman 1999). The SPI can be used across vastly different regions with distinct climatic variations. For these reasons, the World Meteorological Organization has adopted the SPI to be used by national meteorological and hydrological services worldwide to characterize drought (Hayes et al. 2011). However, SPI is not without limitations. First, SPI is limited by the quantity of observations; sufficient data are required to properly fit a statistical distribution. Second, SPI does not account for the evaporative demand of the atmosphere (i.e., evapotranspiration). To resolve this limitation, Vicente-Serrano et al. (2010) designed the SPEI after the SPI algorithm and accounted for both moisture supply (i.e., precipitation) and evaporative demand (i.e., potential evapotranspiration), and also found the best fit distribution to be the log-logistic.

The SPI was computed using the methods outlined by McKee et al. (1993) and the R statistical software package developed by Beguería and Vicente-Serrano (2017). The algorithm fits monthly observed precipitation to a gamma probability distribution. The data series is then transformed into standardized values. Values of SPI are essentially standard deviations from the defined 95-yr climatology. Positive values indicate greater than normal precipitation, negative values indicate less than normal precipitation. SPI values greater than +2 or less than −2 indicate extremely wet or extremely dry conditions, respectively.

The SPEI was computed using the methods proposed by Vicente-Serrano et al. (2010) and implemented in the R statistical software package developed by Beguería and Vicente-Serrano (2017). The SPEI algorithm is similar to SPI but uses the difference between observed monthly precipitation and PET (P-PET) as the parameter input. The SPEI algorithm quantifies monthly P-PET as the standardized departure from a normally transformed three parameter log-logistic distribution. Values of SPEI are interpretated in this research as the standard deviations from the 95-yr climatology. Similar to SPI, SPEI quantifies drought conditions from +2 to −2, where +2 is “extremely wet” and −2 is “extremely dry”.

d. Comparing drought indices

Drought indices were first compared with each other across all 13 Alaska climate divisions using the Pearson correlation across all months and for each month individually. The scPDSI was correlated against SPI and SPEI indices at each time step. SPI and SPEI were compared with each other at comparable time steps only (e.g., the 1-month SPI was correlated with the 1-month SPEI, the 3-month SPI with the 3-month SPEI). We then compared the frequency, timing, and duration of drought events indicated by the scPDSI, the SPEI, and SPI. A month was considered in drought if it met the criterion for D1 Moderate Drought used by the U.S. Drought Monitor (scPDSI ≤ −2.0, SPI/SPEI ≤ −0.8; USDM 2021). One-month excursions above the D1 criterion were not considered a break in drought. For example, if the SPI in three consecutive months was −0.85, −0.78, and −0.9, all months would be considered in drought. Drought events were identified as 3 or more months in drought broken by at least 2 months when the drought index was above the D1 criterion. Guttman (1999) notes that the scPDSI typically represents antecedent climate conditions for about the past year, and correlations between the scPDSI and the SPI and SPEI typically peaked around 12 months (see Fig. 5), so the drought event analysis was performed using scPDSI and the 12-month SPI and SPEI only.

Correlation was also used to evaluate the relationship between drought indices and standardized streamflow. The Pearson correlation coefficient was calculated for a range of aggregated time scales from 1 to 60 months for SPI and SPEI to reflect the response of streamflow to drought observed across different watersheds. A monthly one-to-one correlation was also computed between standardized streamflow and scPDSI. The drought indices were recalculated for the period of record for each stream gauge listed in Table 1 to avoid potential mismatches in mean related to streamflow standardization.

3. Results and discussion

a. Comparison of PET methods and implications for the climatic water balance

Long-term monthly average precipitation, Thornthwaite PET, and Hargreaves PET for each climate division are presented in Fig. 2. Precipitation varies greatly across Alaska climate divisions, with a sharp decrease from south to north. This is largely a result of synoptic-scale flow and orographic controls on the distribution of precipitation (Shulski and Wendler 2007). The timing of annual maximum precipitation also varies from south to north. Southern divisions receive peak precipitation during the autumn and winter months, while there is a summer maximum in western, interior, and northern climate divisions. In general, across all climate divisions, PET displayed a pronounced annual cycle that peaks during the warm season. PET in each division followed the expected annual cycle of near-surface air temperature in high-latitude regions (Bieniek et al. 2012). Divisions with the lowest PET were found along the southern coastal regions of Alaska. The most extreme range of PET occurred in the northeast interior and along the North Slope, likely a function of their long summer day lengths.

Fig. 2.
Fig. 2.

Monthly climatological pattern of potential evapotranspiration (PET) estimated by the Thornthwaite PET equation (solid red line), and the Hargreaves PET equation (dashed black line) compared with monthly climatological pattern of total precipitation (gray bars) across all 13 Alaska climate divisions from 1925 to 2019. Climate division numbers are marked on the map. Note that the y axes differ in scale among panels to best compare PET and precipitation in each climate division.

Citation: Earth Interactions 27, 1; 10.1175/EI-D-22-0025.1

Noticeable differences between PET estimates were found between the two methods (Fig. 2). Across all climate divisions, the Thornthwaite method estimated lower PET during winter months [December–February (DJF)] and much greater PET during summer months [June–August (JJA)] relative to the Hargreaves method. The largest difference between methods was seen in the North Slope climate division, where maximum PET estimated by the Thornthwaite method was greater than ∼1.5 times that of the Hargreaves PET. The springtime increase in Thornthwaite PET lagged Hargreaves PET by 1–2 months in all climate divisions, but Thornthwaite PET remained higher than Hargreaves PET through September or October in southern parts of the state. The Thornthwaite method assumes zero PET if the monthly average temperature is ≤ 0°C (Thornthwaite 1948), which explains the delayed onset of PET in the North Slope division where monthly average temperatures are below freezing until June in most years.

The difference between precipitation and PET (P-PET) was positive in the winter when PET was low in all divisions. The wettest divisions, in southern and southeastern Alaska, typically maintained a positive P-PET throughout the year, while drier northern and interior divisions experienced summer conditions where PET exceeded precipitation P (Fig. 3). The seasonality and magnitude of negative P-PET were dependent on the specific PET method selected (Fig. 3). While both PET methods yielded similar annual cycles of P-PET, the Thornthwaite PET method produced deeper moisture deficits than the Hargreaves method. The differences were especially notable in northerly climate divisions.

Fig. 3.
Fig. 3.

Comparison of the monthly averaged precipitation − potential evapotranspiration (P-PET) estimated with the Thornthwaite PET equation (solid red line), and the Hargreaves PET equation (dashed black line) across all 13 Alaska climate divisions from 1925 to 2019. Climate divisions are denoted by name and number, and their locations are given on the map. Note that the y axes differ in scale among panels to best compare PET and precipitation in each climate division.

Citation: Earth Interactions 27, 1; 10.1175/EI-D-22-0025.1

Despite these differences, a strong linear association (R2 > 0.80) remained between short-term SPEI estimated with the two PET methods over all months (Fig. 4). However, correlations decreased as aggregated time scales of SPEI increased beyond the 3-month time scale, particularly in the North Slope division. There was some seasonal variability in the strength of the correlation between SPEI estimated with Hargreaves versus Thornthwaite PET, particularly at short aggregations in division 1 North Slope and division 4 Northeast Interior. Correlations at 1 month are weakest, on average, in the spring (March–May), when Thornthwaite PET remains near or at 0 (Fig. S1 in the online supplemental material). In several climate divisions (2, 3, 6, and 7), correlations between the 3-month SPEI indices calculated with different PET formulations were slightly weaker in the summer than in other seasons.

Fig. 4.
Fig. 4.

Correlation between SPEI calculated using Thornthwaite PET and SPEI calculated using Hargreaves aggregated time scales ranging from 1 to 60 months across all climate divisions of Alaska from 1925 to 2019.

Citation: Earth Interactions 27, 1; 10.1175/EI-D-22-0025.1

Differences between the two estimates of PET, P-PET, and SPEI calculated using different PET estimates suggest that it is important to identify the most appropriate PET formulation for the available data. Previous studies have suggested that the Hargreaves formulation may be more realistic (Allen et al. 1998; McAfee 2013; Beguería et al. 2014) owing to inclusion of the diurnal temperature range (maximum–minimum temperature), which proxies the surface energy balance.

Our divisional estimates of PET are not directly comparable to observations of ET that are limited by precipitation and other aspects of water availability (Liljehdal et al. 2011) and vary with vegetation type (Brümmer et al. 2012) and disturbance history (Liu and Randerson 2008). However, observations do provide a qualitative point of comparison. Flux-tower measurements from Alaska and boreal Canada provide another piece of evidence for using the Hargreaves equation rather than that of Thornthwaite. Brümmer et al. (2012) describe annual total ET between 200 and 500 mm at a number of sites across Canada with latitudes between 42° and 56°N. At higher latitudes, annual ET is typically between 150 and 400 mm and the water balance is generally positive (P > ET; Bring et al. 2016). Annual average PET calculated by the Hargreaves equation varied between 302 mm in division 1 North Slope and 487 mm in division 12 South Panhandle. Thornthwaite PET estimates were higher, from 423 to 510 mm per year. Correspondingly, water balances were more positive when PET was estimated with the Hargreaves equation, although the same three climate divisions (1: North Slope; 3: Central Interior; and 4: Northeast Interior) had negative water balances with both PET estimates.

The Hargreaves equation also appeared to produce more seasonally realistic patterns in PET. The timing of spring ET onset in Thunberg et al. (2021) was more consistent with that estimated by Hargreaves’s PET than Thornthwaite’s [compare our Fig. 2 with Fig. 3 in Thunberg et al. (2021)]. The seasonal water balance in Thunberg et al. (2021) (P-ET) was more similar to P-PET estimated using the Hargreaves equation, with the lowest values earlier in the summer and a more rapid recovery in the late summer. Although Raz-Yaseef et al. (2017) indicated no ET during the spring near Utqiaġvik, their measurements started in May, raising the possibility that they missed small amounts of winter or early spring ET. In other studies, mostly from boreal sites, winter ET was typically low, but not zero (Liu and Randerson 2008; Yuan et al. 2010; Nakai et al. 2013; Brümmer et al. 2012; Kasurinen et al. 2014), more consistent with the Hargreaves PET than the Thornthwaite PET. Because the Hargreaves equation uses an arguably more physically realistic formulation and produces results that better match observations, we used Hargreaves’s PET in calculating the scPDSI and SPEI for the remainder of the analysis.

b. Comparison of drought indices

The three drought indices were strongly correlated at most aggregation time scales (Fig. 5). The correlation between SPI and SPEI was high (R > 0.80) across all aggregated time scales and climate divisions. In southeastern Alaska and the Aleutians (divisions 8–13), the correlations between SPI and SPEI were near 1 at all aggregations. This suggests that, in these regions, precipitation was the dominant control on drought at time scales up to 60 months. Physically, this seems plausible because these climate divisions are very wet, with moderate temperatures and frequent cloud cover that limit atmospheric demand. In other climate divisions, the strength of the relationship between SPI and SPEI peaked at time scales between 1 and 6 months and decreased at longer aggregations (Fig. 5), suggesting that interior and northern climate divisions are likely moisture-limited environments, where temperature can play a larger role in drought development (Budyko 1974; Eagleson 1978; Hobbins et al. 2008). This conclusion is also supported by negative summer values of P-PET in northern and interior climate divisions (Fig. 3).

Fig. 5.
Fig. 5.

Pearson’s correlation coefficient between various time scales of SPI and SPEI ranging from 1 to 60 months, and scPDSI for each Alaska climate division from 1925 to 2019. The horizontal axis represents SPI and SPEI time scales. Correlations are for all months.

Citation: Earth Interactions 27, 1; 10.1175/EI-D-22-0025.1

The scPDSI and SPI were most strongly correlated at the 12–24-month time scales in most climate divisions (Fig. 5). Similar correlations were observed between scPDSI and SPEI across all climate divisions, implying that, across Alaska, scPDSI is better at capturing longer-term drought than it is at representing shorter droughts. In the wettest divisions (divisions 6–13), correlations between scPDSI and SPEI were essentially identical to those between the scPDSI and the SPI, consistent with the very strong correlations between SPI and SPEI. In the North Slope and Northeast Interior divisions, scPDSI was, as expected, better correlated with SPEI than the SPI, particularly at shorter time scales. In the West Coast, Central, and Southeast Interior divisions, scPDSI was more strongly correlated with SPI than SPEI at aggregations of 24 months and longer.

There was some seasonal variability in the strength of the correlations among drought indices (Figs. S2–S4 in the online supplemental material). In most, but not all, climate divisions, correlations between scPDSI and SPEI or SPI were strongest in the autumn (September–November) and weakest in the summer (June–August) or spring (March–May), particularly at longer time scales. Seasonal variation in the strength of the correlation between SPI and SPEI was most notable in climate divisions 1–4 at subannual time scales. Correlations were typically strongest in the winter when PET is minimal and weakest in the spring or summer.

c. Number, timing, and duration of droughts

Here, we focus on meteorological droughts meeting the U.S. Drought Monitor’s D1 criterion in scPDSI, the 12-month SPI, or the 12-month SPEI, as described in section 2d, which necessarily means that this portion of our analysis is focused on longer-term droughts. All of the drought indices generally track wet and dry periods. However, scPDSI sometimes indicated different drought occurrence or character than did SPI and SPEI, and drought indices that include temperature indicate more drought in some climate divisions in recent decades.

Drought indices that include temperature characterized more months in meteorological drought than SPI, which is based on precipitation alone, although there were a few exceptions. In eight of the 13 divisions, SPEI characterized more months as in drought than any other drought index, and the SPEI always indicates more months of drought than SPI (Fig. 6, top panel). In four divisions, both northerly and southerly, SPI indicates more months in D1 or more significant drought than does scPDSI. In all but one climate divisions, scPDSI also indicated fewer meteorological droughts overall than the other indices (Fig. 6, middle panel). In some cases, like in climate division 4 Northeast Interior, this is because the scPDSI, while slightly negative, did not meet the D1 criterion, “missing” droughts in the 1970s, that the other indices did flag (Fig. 7). In other cases, such as in division 12 South Panhandle, the scPDSI was not as responsive to wetter intervals, leading it to characterize much of the late 1970s and early 1980s as drought, while the other two indices indicated more frequent but shorter droughts. The scPDSI also did not show the recovery during the latter half of 2019 indicated by the other two indices (Fig. 7). The persistence of meteorological droughts in scPDSI is also apparent when looking at the length of the longest drought (Fig. 6, bottom panel). The longest droughts defined by the scPDSI were often a year or two longer than droughts identified by other indices, suggesting that the time scale of drought expressed by the scPDSI increases at higher latitudes.

Fig. 6.
Fig. 6.

Drought characteristics for the scPDSI, SPEI-12, and SPI-12: (a) the total number of months in drought as defined in section 2d, (b) the number of droughts lasting at least 3 months, (c) the duration of the longest drought (months).

Citation: Earth Interactions 27, 1; 10.1175/EI-D-22-0025.1

Fig. 7.
Fig. 7.

Time series of 12-month SPEI, SPI, and monthly scPDSI for climate divisions 4 and 12 [(a)–(c) Northeast Interior; (d)–(f) South Panhandle]. Droughts lasting at least 3 months are shaded. Plots for all climate divisions are shown in Figs. S5–S17 in the online supplemental material.

Citation: Earth Interactions 27, 1; 10.1175/EI-D-22-0025.1

d. Drought evolution across Alaska climate divisions

Across the southwestern United States, higher temperatures and evaporative demand have clearly exacerbated droughts (e.g., Williams et al. 2020; McEvoy et al. 2020; Albano et al. 2022). While the rapid warming in high latitudes is well documented (e.g., Bieniek et al. 2014), it is not yet clear whether anthropogenic warming is influencing drought in Alaska. One way to begin assessing this is to evaluate differences between SPI and SPEI, although this simplistic approach cannot fully elucidate the impact of increasing temperatures on drought development.

Differences between SPI and SPEI were most pronounced at longer time scales (12 to 48 months) and in northern and interior climate divisions. They have also become more apparent in recent years (Fig. 8; Fig. S18 in the online supplemental material). Early in the record, SPI generally indicated conditions similar to or drier than SPEI. For example, known dry periods in the observational record across Alaska, such as the late 1970s (Stewart et al. 2022), were captured by SPI and SPEI; however, SPI estimated a deeper moisture deficit in northern and interior climate divisions, particularly at >12-month time scales. One notable exception is during the late 1930s and early 1940s, a known warm period, when SPEI was less than SPI in northern and interior divisions. Recently, SPEI has indicated drier conditions than SPI in divisions 1–5, 7, and (possibly) 13. The timing of divergence between SPI and SPEI varied by division. It occurred earliest in division 1 North Slope, beginning in the 1980s. In the rest of the state, SPEI and SPI have indicated different degrees of moisture availability beginning in the 2000s.

Fig. 8.
Fig. 8.

Difference between the SPEI and SPI for climate divisions (a) 1 (North Slope), (b) 5 (Southeast Interior), (c) 6 (Cook Inlet), and (d) 10 (North Panhandle). From lightest to darkest, the lines indicate integrations at 3, 6, 12, 36, and 60 months.

Citation: Earth Interactions 27, 1; 10.1175/EI-D-22-0025.1

Because SPEI includes the effect of temperature, these findings suggest that warming is influencing moisture conditions at 12- to 60-month time scales in parts of Alaska. The increasing influence of temperature in northern and interior Alaska is consistent with higher rates of warming in those locations (Bieniek et al. 2014), as well as the moisture-limited environment. The lack of discernable temperature influence on drought in southeast Alaska is consistent with expectations for a relatively cool, energy-limited environment.

One notable caveat to our finding that temperature has had a limited effect on drought conditions in southern and southeast Alaska is that none of these drought indices account for precipitation phase. Recent work on snow droughts indicates that precipitation phase can influence drought and drought impacts directly (e.g., snowpack water storage; Harpold et al. 2017) and indirectly (e.g., by mediating evapotranspiration; Milly and Dunne 2020). Although several studies have indicated that it is important to better characterize snowpack dynamics in drought indices (Qiu 2013; Weiner et al. 2016), operational versions of the indices do not distinguish between snow and rain.

e. Correlations between drought indices and streamflow

Shanley et al. (2015) group Alaska watersheds into three general categories: 1) rain-dominated, where annual patterns of streamflow follow precipitation; 2) snowmelt-dominated, characterized by peak streamflow during spring snowmelt, a summer minimum, and a second peak when precipitation increases during autumn; and 3) glacial melt–dominated, where streamflow peaks during late spring through early autumn and streamflow significantly drops during winter and early spring. We used streamflow gauges displaying a variety of hydrographs from each category. Owing to the paucity of long, high-quality streamflow records, the gauges used here represent basins that vary widely in size (from 50 to more than 500 000 km2) as well as in hydrologic regime. There are also challenges in comparing streamflow in a basin with divisional drought indices because they do not cover the same spatial regions and, in some cases, the HUC8 (HUC is hydrologic unit code) basin associated with the gauge falls partly outside the climate division (Fig. 1). Unfortunately, the small number of high-quality ≥20-yr-long streamflow records in Alaska places practical limits on this analysis. Consequently, our comparison of drought indices and streamflow is not comprehensive and, rather, acts as a common-sense check.

Across all months, monthly standardized streamflow was positively and weakly to moderately correlated (0 < r < 0.5 in most basins) with all three of the drought indices evaluated here (Tables 2 and 3). Correlations between streamflow and scPDSI were weaker than the strongest correlations between streamflow and SPI or SPEI, except in divisions 1 North Slope and 4 Northeast Interior. In the wettest and warmest divisions (climate divisions 8–13), streamflow was more strongly correlated with shorter aggregations of SPI and SPEI (1 or 3 months) than with longer-duration drought indices. Correlations between streamflow and SPEI were very similar to correlations between streamflow and SPI, consistent with the very strong correlations between SPEI and SPE in those divisions (Tables 2 and 3). The relatively low fraction of precipitation that falls as snow at lower elevations in these divisions (Littell et al. 2018) may explain higher correlations at shorter aggregations. However, these gauges also tended to measure discharge from smaller drainage areas, which could also contribute to the high correlations at shorter aggregations. In other divisions, streamflow was usually most strongly correlated with 6-, 12-, or 24-month aggregations of SPEI. In these primarily drier divisions, SPEI appears to be a better predictor of streamflow. Peak correlations at 6-month to 2-yr aggregations are consistent with both a greater contribution from snow and also the generally larger drainage areas.

Table 2

Pearson correlations between streamflow at primary gauges across all months and the corresponding drought indices. Boldface font indicates the value of the strongest correlation. Information about the gauges and drainage basin areas is provided in Table 1.

Table 2
Table 3

Pearson correlations between streamflow at secondary gauges across all months and the corresponding drought indices. Boldface font indicates the value of the strongest correlation. Correlations are shown only for divisions with secondary gauges. Information about the gauges and drainage basin areas is provided in Table 1.

Table 3

4. Conclusions

The 2019 drought in southeastern Alaska underscored the need for effective operational drought monitoring in Alaska. Drought indices are a key component of drought monitoring, but their skill in tracking drought in high-latitude areas for which they were not developed has not been thoroughly investigated.

We evaluated two ways of estimating temperature-based PET for use in divisional scPDSI and SPEI. The Hargreaves and Thornthwaite PET estimates were different, introducing significant differences into the annual potential water deficit. In most climate divisions, drought indices were not particularly sensitive to the PET estimate used. Longer-time-scale drought indices at higher latitudes displayed the largest differences related to how PET was calculated. Given the potential for differences in the most northerly divisions and more realistic water balance results from the Hargreaves equation, we recommend using that over the more commonly used Thornthwaite equation.

The three drought indices we evaluated identified similar drought periods and were reasonably well correlated to each other, but there were some differences. The scPDSI was less likely to identify short-term improvements within a drought than the 12- and 24-month SPI and SPEI indices with which it was most strongly correlated, more closely tracking the 48-month SPI and SPEI during significant droughts. In moisture-limited climate divisions, SPEI is increasingly more negative than SPI, indicating a stronger temperature contribution to drought in recent years, even at high latitudes, a consideration that is likely to grow more important in the coming decades. Although this was not observed in all climate divisions, it underscores the importance of evaluating temperature influences on drought in all environments. In almost all cases, SPI or SPEI was a better predictor of streamflow, and thus hydrological drought, than scPDSI.

There are still unexplored questions about the utility of drought indices at high latitudes, for example, about relationships between different drought indices and terrestrial ecosystem responses or the best way to account for snow in drought indices. However, evaluations presented here indicate that both the SPI and the SPEI calculated with the Hargreaves PET equation are reasonable drought indices to use for regional drought assessment and tracking and are likely more appropriate than the scPDSI. Although SPI and SPEI are very similar in energy-limited climates, the two drought metrics do diverge in drier locations in recent years, and consideration of the impact of temperature on drought may grow more important in the coming decades.

Acknowledgments.

Funding was provided by the Alaska Climate Adaptation Center.

Data availability statement.

Data and production code are available from the Alaska Climate Adaptation Center through the USGS Science Base. Data and production code are available online (https://doi.org/10.21429/93m7-w557).

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