Drought Indicators and Indices

Summary

Drought Type	Definition & Focus	Key Indices	Primary Indicators	Typical Applications
Meteorological	Precipitation deficit relative to regional norms over specific periods	- Standardized Precipitation Index (SPI) - Percentage of Normal Precipitation - Rainfall Anomaly Index (RAI)	- Precipitation data - Climate norms	Early drought detection, regional dry spell analysis
Agricultural	Soil moisture deficits impacting crops/livestock	- Palmer Drought Severity Index (PDSI) - Vegetation Condition Index (VCI) - Soil Moisture Index - Standardized Precipitation Index (SPI) - Standardized Precipitation-Evapotranspiration Index (SPEI)	- Soil moisture - NDVI - Evapotranspiration data	Crop stress monitoring, irrigation planning
Hydrological	Surface/subsurface water shortages (rivers, lakes, groundwater)	- Surface Water Supply Index (SWSI) - Streamflow Index - Reservoir Levels	- River discharge - Snowpack - Groundwater levels	Water supply management, drought impact assessment
Socioeconomic	Water scarcity affecting human activities & economic systems	- No single index - Economic impact assessments	- Water prices - Crop yield data - Employment stats	Resource allocation, policy development

1. Introduction

1.1. Definition of Drought

Drought is a prolonged period of abnormally low rainfall, leading to a shortage of water. Its precise definition can vary depending on the region, the specific needs for water, and the perspective being considered.

• From a meteorological standpoint, drought is defined based on the degree of dryness and the duration of the dry period.
• Agricultural drought links meteorological drought to agricultural impacts, focusing on soil moisture deficits and their effect on crop production and livestock.
• Hydrological drought refers to deficiencies in surface and subsurface water resources, such as rivers, lakes, reservoirs, and groundwater.
• Socioeconomic drought occurs when the supply of water fails to meet the demand of human activities, leading to social and economic consequences.

1.2. Importance of Drought Monitoring

Accurate and timely drought monitoring is essential for effective water resource management and disaster preparedness.

Drought indicators and indices provide crucial information for:

• Early Warning Systems: Identifying the onset and progression of drought to allow for timely interventions.
• Impact Assessment: Quantifying the severity and spatial extent of drought on various sectors.
• Policy Development: Informing the creation of drought management plans and mitigation strategies.
• Resource Allocation: Guiding decisions on water distribution and conservation efforts.
• Risk Management: Helping individuals, communities, and businesses prepare for and cope with drought impacts.

1.3. Purpose of the Document

This document aims to provide a comprehensive overview of drought and the key indicators and indices used to monitor and assess its characteristics. It can also be considered as a guide for understanding and interpreting common drought indices.

It will cover the different types of drought, explain the methodologies behind various indicators, discuss their strengths and limitations, and highlight their role in drought monitoring and impact assessment.

• Important point to keep in mind when deciding which indicators to use in a study, consider:
• The region you are focusing on: Some indicators are more relevant in certain climate zones or hydrological regimes.
• The type of drought you want to emphasize: Agricultural drought will benefit from soil moisture and vegetation indices, while hydrological drought will focus on streamflow and water storage.
• The availability of data: Some indicators require more complex or less readily available data.

2. Types of Drought

2.1. Meteorological Drought

Meteorological drought is primarily defined by a significant deviation from normal precipitation patterns over a specified period. This definition is region-specific, as normal precipitation varies greatly geographically.

Key characteristics include the duration of the dry period, the intensity of the precipitation deficit, and its timing relative to the annual precipitation cycle.

Indicators like the Standardized Precipitation Index (SPI) and Percentage of Normal Precipitation are commonly used to quantify meteorological drought.

2.2. Agricultural Drought

Agricultural drought occurs when there is insufficient soil moisture available to meet the water demands of crops during different growth stages, ultimately affecting yields.

It takes into account factors like precipitation deficits, evapotranspiration rates, soil water holding capacity, and the specific water requirements of different crops.

Agricultural drought can occur even if meteorological drought is not yet severe, especially if there are prolonged dry spells during critical crop growth periods.

Indicators such as soil moisture content, the Palmer Drought Severity Index (PDSI), and vegetation indices (like NDVI and VCI) are relevant for monitoring agricultural drought.

2.3. Hydrological Drought

Hydrological drought refers to deficiencies in surface and subsurface water resources. It typically lags behind meteorological and agricultural drought because it takes time for precipitation deficits to translate into reduced streamflow, lake and reservoir levels, and groundwater storage.

The severity and duration of hydrological drought depend on factors like precipitation amounts and timing, evapotranspiration, surface runoff, and subsurface geological conditions.

Impacts include reduced water availability for irrigation, hydropower generation, industrial and domestic use, and negative effects on aquatic ecosystems.

Indicators used to monitor hydrological drought include streamflow discharge, reservoir and lake levels, groundwater levels, and the Surface Water Supply Index (SWSI).

2.4. Socioeconomic Drought

Socioeconomic drought is the impact of meteorological, agricultural, or hydrological drought on human activities and the economy. It occurs when water shortages begin to affect the supply and demand of economic goods and services.

The impacts can be wide-ranging and include reduced agricultural production leading to food shortages and price increases, loss of income for farmers and related industries, increased energy costs (due to reduced hydropower), health problems, and social unrest.

Socioeconomic drought is often context-specific and depends on the vulnerability of the population and the water management infrastructure in place.

While not directly measured by a single index, socioeconomic drought is assessed by analyzing the economic and social consequences of the other types of drought.

3. Drought Indicators and Indices

3.1. Standardized Precipitation Index (SPI)

• Description: The Standardized Precipitation Index (SPI) is a widely used index to characterize meteorological drought on a range of timescales (e.g., 1, 3, 6, 12, 24, 48 months). It quantifies precipitation deficits (or surpluses) relative to the long-term average for a specific location and time period. These different durations reflect the impact of precipitation anomalies on different components of the hydrological system and various human activities.

• Calculation/Methodology (Simplified): The SPI is calculated by fitting a probability distribution (typically a Gamma distribution) to the long-term precipitation data for a given location and timescale. The cumulative probability is then transformed to a standard normal distribution, resulting in the SPI value. A negative SPI indicates drought, and the magnitude of the negative value reflects the severity.

SPI Value	Category	General Interpretation (Meteorological Drought)	General Relationship to Crop Hazards
≥ 2.00	Extremely Wet	Significantly above average precipitation for the specified duration.	Generally beneficial, but excessive wetness can also cause issues (e.g., waterlogging for some crops).
1.50 to 1.99	Very Wet	Well above average precipitation for the specified duration.	Generally favorable, but potential for waterlogging in susceptible crops/soils.
1.00 to 1.49	Moderately Wet	Above average precipitation for the specified duration.	Generally positive for crop growth.
-0.99 to 0.99	Near Normal	Precipitation close to the long-term average for the specified duration.	Generally adequate for most crops under normal conditions.
-1.00 to -1.49	Moderately Dry	Below average precipitation, indicating a moderate drought for the duration.	Potential for moisture stress, especially for water-sensitive crops or during critical growth stages. Yield reductions possible.
-1.50 to -1.99	Severely Dry	Significantly below average precipitation, indicating a severe drought.	Likely to cause significant moisture stress, impacting growth and potentially leading to substantial yield losses for many crops.
≤ -2.00	Extremely Dry	Exceptionally low precipitation, indicating an extreme drought.	High probability of severe crop failure or significant yield losses for most crops without irrigation.

• Temporal and Spatial Scale: SPI can be calculated for various time scales, allowing for the monitoring of short-term (e.g., agricultural drought) and long-term (e.g., hydrological drought) precipitation deficits. It is spatially flexible and can be calculated for individual stations, regions, or even globally.

  SPI Timescale (Months)	Phenomena Reflected	Applications
  1-3 (Short-Term)	Topsoil moisture, small streamflow, early vegetation stress, fire risk	Agricultural drought monitoring (early warning), short-term water resource management, fire risk assessment
  6-12 (Medium-Term)	Larger streamflow, smaller to medium reservoir levels, early groundwater recharge impacts, established agricultural drought	Agricultural drought assessment, water resource management (rivers, medium reservoirs), hydropower planning
  24-48+ (Long-Term)	Large reservoir and lake levels, major aquifer levels, ecological drought, socio-economic impacts	Long-term water resource planning, groundwater monitoring, ecological drought assessment, drought preparedness and mitigation

• Strengths:

  • Simple to calculate and interpret.
  • Can be used to analyze drought at multiple timescales, making it useful for different applications.
  • Allows for comparisons of drought severity across different regions and time periods.
  • Probabilistically based, providing a statistical measure of drought.

• Limitations:

  • Only considers precipitation and does not account for other factors like temperature, evapotranspiration, or soil moisture.
  • Requires a long period of historical precipitation data for reliable calculation.
  • The choice of the probability distribution can influence the results in some cases.

• Data Sources: Historical precipitation data from rain gauge stations or gridded precipitation datasets.

3.2. Palmer Drought Severity Index (PDSI)

• Description: The Palmer Drought Severity Index (PDSI) is a more complex index that attempts to measure the cumulative deficit in the water balance. It considers precipitation, temperature, and evapotranspiration, as well as factors like soil moisture, runoff, and recharge.
• Calculation/Methodology (Simplified): The PDSI uses a water balance equation to estimate the amount of moisture supply needed for normal conditions in a region. It then compares this with the actual moisture supply to determine the severity of drought or wet spells. The index values typically range from -4.0 (extreme drought) to +4.0 (extremely wet).

PDSI Value	Category	General Interpretation (Long-Term Moisture Conditions)	General Relationship to Crop Hazards
≥ +4.00	Extremely Wet	Prolonged period of exceptionally high moisture surplus. Soil moisture is excessive, and water resources are abundant.
+3.00 to +3.99	Very Wet	Extended period of significant moisture surplus. Soil moisture is well above average, and water resources are plentiful.
+2.00 to +2.99	Moderately Wet	Extended period of moderate moisture surplus. Soil moisture is above average, and water resources are generally good.
+1.00 to +1.99	Slightly Wet	Extended period with a small moisture surplus. Soil moisture is slightly above average.
+0.5 to +0.99	Incipient Wet Spell	Beginning of a period with slightly above normal moisture.
-0.49 to +0.49	Near Normal	Moisture conditions are close to the long-term average.
-0.50 to -0.99	Incipient Dry Spell	Beginning of a period with slightly below normal moisture.
-1.00 to -1.99	Mild Drought	Extended period of mild moisture deficit. Soil moisture is below average, and some water stress may begin to appear.
-2.00 to -2.99	Moderate Drought	Extended period of moderate moisture deficit. Soil moisture is significantly below average, and crop stress is likely. Water shortages may develop.
-3.00 to -3.99	Severe Drought	Extended period of substantial moisture deficit. Soil moisture is very low, and significant crop damage and water shortages are expected.
≤ -4.00	Extreme Drought	Prolonged period of exceptionally severe moisture deficit. Soil moisture is critically low, widespread crop failure and severe water shortages are highly probable.

• Temporal and Spatial Scale: PDSI is typically calculated on a monthly basis and is suitable for assessing long-term drought conditions. It is often used at regional or larger scales.

  PDSI Characteristic	Phenomena Reflected	Key Applications
  Timescale Relevance	Primarily reflects long-term drought conditions (months to years) due to its cumulative nature. Responds slower to short-term changes.	Assessing prolonged drought impacts on agriculture and water resources. Historical drought analysis.
  Phenomena Reflected	Cumulative moisture deficit or surplus, considering precipitation, temperature, and soil moisture. Good for broad-scale, long-term conditions.	Identifying long-lasting drought events and their severity. Comparing drought severity across different regions.
  Key Applications	Historical drought analysis, broad-scale drought monitoring, assessing long-term agricultural and hydrological impacts.	Policy decisions related to long-term drought management and water allocation.

• Strengths:

  • Considers both precipitation and temperature, providing a more comprehensive assessment of drought.
  • Attempts to account for soil moisture conditions.
  • Has been widely used for decades, providing a long historical record.

• Limitations:

  • Can be slow to respond to rapidly changing conditions due to its cumulative nature.
  • The underlying model relies on several assumptions and empirical relationships that may not be universally applicable.
  • Can be influenced by the accuracy of temperature and evapotranspiration estimates.

• Data Sources: Monthly precipitation and temperature data, as well as estimates of potential evapotranspiration and soil water holding capacity.

3.3. Vegetation Condition Index (VCI)

• Description: The Vegetation Condition Index (VCI) uses satellite-derived Normalized Difference Vegetation Index (NDVI) data to assess the health and vigor of vegetation relative to its historical range. It expresses the current NDVI as a percentage of the historical maximum-minimum range for a given location and time of year.
• Calculation/Methodology (Simplified): VCI = (NDVI_current - NDVI_min) / (NDVI_max - NDVI_min) * 100. Where NDVI_current is the NDVI for the current period, and NDVI_min and NDVI_max are the minimum and maximum NDVI values observed in the historical record for the same period.
• Temporal and Spatial Scale: VCI can be calculated at various temporal resolutions (e.g., weekly, bi-weekly, monthly) and spatial resolutions depending on the satellite data used. It is particularly useful for monitoring agricultural drought and vegetation stress.

VCI Characteristic	Phenomena Reflected	Key Applications
Timescale Relevance	Typically used for short-to-medium term impacts on vegetation health (weeks to months), aligning with vegetation growth cycles.	Monitoring real-time vegetation stress due to drought. Early warning of agricultural drought impacts.
Phenomena Reflected	Vegetation health and vigor relative to its historical range, indicating moisture stress affecting plant growth.	Assessing the spatial extent and severity of vegetation drought stress. Identifying areas with potential crop yield reductions.
Key Applications	Agricultural drought monitoring, vegetation stress assessment, early warning of famine or food insecurity, land degradation monitoring.	Guiding targeted interventions for agricultural support and disaster relief.

• Strengths:
  • Provides a direct measure of vegetation health and response to moisture stress.
  • Utilizes readily available satellite data, allowing for broad spatial coverage.
  • Can provide early indications of agricultural drought impacts.
• Limitations:
  • Can be influenced by factors other than drought, such as pests, diseases, and land management practices.
  • May not be suitable for areas with sparse or non-uniform vegetation.
  • The accuracy depends on the quality and resolution of the satellite data.
• Data Sources: Satellite imagery providing NDVI data (e.g., MODIS, AVHRR).

3.4. Standardized Precipitation-Evapotranspiration Index (SPEI)

• Description: The Standardized Precipitation-Evapotranspiration Index (SPEI) is an extension of the SPI that considers the impact of temperature on drought. It quantifies the deficit or surplus of water supply (precipitation) relative to atmospheric water demand (potential evapotranspiration - PET) over a specific period.
• Calculation/Methodology (Simplified):
  1. Calculate the difference between monthly precipitation and potential evapotranspiration (PET). Various methods can be used to estimate PET (e.g., Thornthwaite, Hargreaves).
  2. Aggregate these monthly differences over different timescales (similar to SPI: 1, 3, 6, 12, etc. months).
  3. Fit a probability distribution (often a Log-logistic distribution) to the aggregated water balance data.
  4. Transform the cumulative probability to a standard normal distribution, resulting in the SPEI value. Negative SPEI values indicate drought, with the magnitude reflecting severity.
• Temporal and Spatial Scale: SPEI can be calculated for various time scales, making it suitable for monitoring different types of drought. It is spatially flexible and can be applied at local, regional, and global levels.

SPEI Timescale (Months)	Phenomena Reflected	Applications
1-3 (Short-Term)	Short-term climatic water balance impacting topsoil moisture under evaporative demand, stress on rain-fed agriculture considering temperature, fire risk influenced by dryness and heat.	Agricultural drought monitoring (early warning considering temperature impacts), short-term water resource management under evaporative stress, fire risk assessment.
6-12 (Medium-Term)	Medium-term climatic water balance affecting streamflow in larger rivers under thermal influences, reservoir levels considering evaporation, evolving agricultural drought under changing water demand.	Agricultural drought assessment considering temperature, water resource management for rivers and medium reservoirs accounting for evaporation, hydropower planning under climate influences.
24-48+ (Long-Term)	Long-term climatic water balance impacting large reservoir and lake levels with significant evaporation effects, major aquifer recharge under changing climate, prolonged ecological and socio-economic impacts influenced by both precipitation and temperature.	Long-term water resource planning under climate change, groundwater monitoring considering long-term water balance, assessment of ecological drought under thermal stress, drought preparedness and mitigation in a warming climate.

• Strengths:
  • Incorporates the effect of temperature and potential evapotranspiration, making it more sensitive to the impacts of climate change on drought.
  • Allows for the assessment of drought severity in terms of water balance rather than just precipitation deficits.
  • Can be used across different timescales, similar to SPI.
  • Provides a standardized measure for comparing drought conditions across different climates.
• Limitations:
  • The accuracy depends on the method used to estimate potential evapotranspiration, and different methods can yield varying results.
  • Requires both precipitation and temperature data.
  • Interpretation can be slightly more complex than SPI due to the inclusion of PET.
• Data Sources: Monthly precipitation and temperature data.

3.5. Rainfall Anomaly Index (RAI)

• Description: The Rainfall Anomaly Index (RAI) is another index used to quantify meteorological drought. It measures the deviation of precipitation from the long-term mean, taking into account whether the anomaly is positive (wet) or negative (dry). The calculation differs slightly for positive and negative anomalies to account for the skewed nature of rainfall data.
• Calculation/Methodology (Simplified):
  1. Calculate the long-term mean precipitation for a specific period (e.g., monthly, seasonal) and location.
  2. Calculate the mean of the positive deviations from the long-term mean and the mean of the negative deviations from the long-term mean.
  3. For a given period's precipitation ($P_i$):
     • If $P_i \ge \bar{P}$ (long-term mean): $$RAI = +3 \times \frac{P_i - \bar{P}}{\overline{P}{H10} - \bar{P}}$$ where $\overline{P}{H10}$ is the mean of the 10 highest precipitation values in the historical record for that period.
     • If $P_i < \bar{P}$: $$RAI = -3 \times \frac{P_i - \bar{P}}{\bar{P} - \overline{P}{L10}}$$ where $\overline{P}{L10}$ is the mean of the 10 lowest precipitation values in the historical record for that period.
• Temporal and Spatial Scale: RAI can be calculated for various time scales (monthly, seasonal, annual) and is applicable at different spatial scales depending on the availability of precipitation data.

RAI Characteristic	Phenomena Reflected	Key Applications
Timescale Relevance	Calculated for various timescales (monthly, seasonal, annual), focusing purely on precipitation deviations.	Simple meteorological drought monitoring, particularly in regions where precipitation data is the primary available variable.
Phenomena Reflected	Departure of precipitation from the long-term mean, with separate calculations for positive and negative anomalies.	Identifying and classifying the severity of wet and dry periods based solely on rainfall.
Key Applications	Basic meteorological drought assessment, historical rainfall variability studies.	Providing a straightforward measure of precipitation deficits for non-complex analyses.

• Strengths:
  • Relatively simple to calculate.
  • Considers the magnitude of both wet and dry anomalies in a way that acknowledges the typical distribution of rainfall.
  • Can be useful in regions where the statistical assumptions of SPI might not be fully met.
• Limitations:
  • The use of the 10 highest and lowest values can make it sensitive to extreme events in the historical record.
  • Does not take into account evapotranspiration or other water balance components.
  • The scaling factor of 3 is somewhat arbitrary.
• Data Sources: Historical precipitation data.

3.6. Percentage of Normal Precipitation (PNP)

• Description: Percentage of Normal Precipitation (PNP) is a straightforward indicator that expresses the current precipitation for a specific period as a percentage of the long-term average (normal) precipitation for the same period.
• Calculation/Methodology (Simplified): $$PNP = \frac{\text{Current Period Precipitation}}{\text{Long-Term Average Precipitation}} \times 100$$
• Temporal and Spatial Scale: PNP can be calculated for any time scale (e.g., monthly, seasonal, annual) and at any location where precipitation data is available.

PNP Characteristic	Phenomena Reflected	Key Applications
Timescale Relevance	Can be calculated for any timescale, providing a simple snapshot of precipitation relative to the average.	Quick and easy communication of precipitation status to a general audience.
Phenomena Reflected	Current precipitation as a percentage of the long-term average precipitation for the same period.	Identifying areas with precipitation deficits or surpluses relative to their normal amounts.
Key Applications	Initial drought screening, public awareness campaigns, simple climate summaries.	Providing a basic understanding of how current precipitation compares to the norm.

• Strengths:
  • Very simple to calculate and easy to understand.
  • Provides a quick and intuitive measure of precipitation deficit or surplus.
  • Requires only precipitation data.
• Limitations:
  • Does not account for the variability of precipitation or the statistical significance of the departure from normal. A 70% of normal precipitation might be a severe drought in a dry region but less so in a wet region.
  • Does not consider the timing or intensity of rainfall events.
  • Ignores other important factors like temperature, evapotranspiration, and soil moisture.
  • Can be less meaningful for short time scales or in regions with highly variable precipitation.
• Data Sources: Current and historical precipitation data.

3.7. Soil Moisture Content

• Description: Soil Moisture Content refers to the amount of water present in a given volume or mass of soil. It is a direct measure of the water available in the root zone and is a key factor in agricultural drought. It can be expressed in various units, such as volumetric water content (volume of water per unit volume of soil) or gravimetric water content (mass of water per unit mass of dry soil).
• Calculation/Methodology (Simplified):
  • Direct Measurement: Typically involves collecting soil samples, weighing them, drying them in an oven, and re-weighing them. The difference in weight represents the water content. Various in-situ sensors (e.g., time domain reflectometry - TDR, capacitance sensors) can also provide continuous measurements.
  • Modeling: Land surface models use meteorological inputs (precipitation, temperature, radiation, etc.) and soil properties to simulate soil moisture at different depths.
• Temporal and Spatial Scale: Soil moisture can be measured or modeled at various temporal resolutions (e.g., hourly, daily, weekly) and spatial scales (from point measurements to regional or global grids).
• Strengths:
  • Provides a direct indication of the water available to plants.
  • Highly relevant for assessing agricultural drought.
  • In-situ measurements offer high accuracy at specific locations.
  • Models can provide spatially continuous estimates.
• Limitations:
  • Direct measurements are labor-intensive and provide only point information.
  • The spatial variability of soil moisture can be high, making it challenging to extrapolate point measurements.
  • Model accuracy depends on the quality of input data and the complexity of the model.
  • Interpretation can be influenced by soil type and depth.
• Data Sources: In-situ soil moisture sensors, soil surveys, land surface models (e.g., GLDAS, SMAP, Sentinel satellite data with soil moisture algorithms).

3.8. Soil Moisture Anomaly (SMA)

• Description: Soil Moisture Anomaly (SMA) quantifies the difference between the current soil moisture conditions and the long-term average (climatology) for the same period of the year. It helps to identify areas where soil moisture is significantly above or below normal.
• Calculation/Methodology (Simplified):
  1. Calculate the long-term average soil moisture for each time step (e.g., daily, weekly) based on historical data (either from measurements or models).
  2. Subtract the long-term average soil moisture from the current soil moisture value for the corresponding time step.
  3. The anomaly can be expressed in absolute terms (e.g., mm of water) or standardized by dividing by the standard deviation of the historical soil moisture data, similar to the SPI.
• Temporal and Spatial Scale: SMA can be calculated at the same temporal and spatial scales as the underlying soil moisture data (measurements or models).
• Strengths:
  • Provides a context for the current soil moisture conditions relative to what is typical for the time of year.
  • Useful for identifying regions experiencing unusually dry or wet soil conditions.
  • Standardized SMA allows for comparisons across different regions and soil types.
• Limitations:
  • The accuracy depends on the quality and length of the historical soil moisture data.
  • Interpretation can still be influenced by soil type and the specific water holding characteristics of the soil.
  • May not directly reflect the impact on plants without considering plant-available water.
• Data Sources: Historical and current soil moisture data from in-situ sensors or models (e.g., those used for Soil Moisture Content).

3.9. Percent of Plant Available Water (PAW)

• Description: Percent of Plant Available Water (PAW) estimates the fraction of water in the soil that plants can readily access. It considers the soil's field capacity (the upper limit of water that soil can hold against gravity) and wilting point (the soil moisture level at which plants can no longer extract water).
• Calculation/Methodology (Simplified):
  1. Determine the field capacity (FC) and wilting point (WP) for the specific soil type and depth. These values are often obtained from soil surveys or laboratory analyses.
  2. Measure or model the current soil moisture content (SMC).
  3. Calculate the Plant Available Water (PAW) as: $$PAW = SMC - WP$$
  4. Calculate the Percent of Plant Available Water (%PAW) as: $$%PAW = \frac{SMC - WP}{FC - WP} \times 100$$
• Temporal and Spatial Scale: %PAW can be determined at the same temporal and spatial scales as the soil moisture content data, provided that information on FC and WP is available for the corresponding locations and depths.
• Strengths:
  • Directly relates soil moisture to plant water availability, making it highly relevant for agricultural drought assessment.
  • Accounts for the soil's physical properties that influence water retention and release.
  • Provides a more ecologically relevant measure of drought stress for vegetation.
• Limitations:
  • Requires knowledge of soil-specific parameters (FC and WP), which may not be readily available for all locations or depths.
  • The actual water availability to plants can also be influenced by root depth and plant physiology.
  • The accuracy depends on the accuracy of the soil moisture data and the FC/WP values.
• Data Sources: In-situ soil moisture sensors, soil surveys (for FC and WP), land surface models that simulate soil moisture and sometimes provide related information.

3.10. Streamflow Index

• Description: Streamflow Index refers to various indices that characterize drought based on the flow of rivers and streams. These indices typically compare current streamflow to historical streamflow data for the same time period. Different variations exist, such as the Standardized Streamflow Index (SSI).
• Calculation/Methodology (Simplified for SSI):
  1. Obtain long-term historical streamflow data for a specific river or gauging station.
  2. Fit a probability distribution (often a Gamma or Log-normal distribution) to the streamflow data for a specific time period (e.g., monthly).
  3. Transform the cumulative probability to a standard normal distribution, resulting in the SSI value. Similar to SPI, negative SSI values indicate hydrological drought, with the magnitude reflecting severity. Other simpler streamflow indices might just use percentiles or deviations from the mean.
• Temporal and Spatial Scale: Streamflow indices can be calculated for various time scales (e.g., monthly, seasonal, annual) and are specific to the river or stream being monitored at a particular gauging station. Regional indices can be created by aggregating data from multiple stations.
• Strengths:
  • Directly reflects the availability of surface water resources.
  • Integrates the effects of precipitation, evapotranspiration, and storage in the watershed.
  • Crucial for managing water supplies for irrigation, municipal use, and hydropower.
  • SSI provides a standardized measure for comparison across different rivers and time periods.
• Limitations:
  • Requires long-term historical streamflow data.
  • Can be influenced by upstream water management practices (e.g., dam releases, diversions).
  • May not fully represent groundwater contributions to streamflow, especially in the short term.
  • The choice of probability distribution for SSI can affect results.
• Data Sources: Streamflow data from hydrologic gauging stations operated by government agencies (e.g., USGS, local water authorities).

3.11. Reservoir and Lake Levels

• Description: Monitoring the water levels (or storage volumes) of reservoirs and lakes is a direct way to assess hydrological drought, particularly concerning water availability for human uses and ecosystem health. Declining levels indicate water shortages.
• Calculation/Methodology (Simplified): Typically involves regular measurements of water surface elevation using gauging stations installed at reservoirs and lakes. These levels are often converted to storage volumes using known bathymetry (depth contours). Drought conditions are assessed by comparing current levels/volumes to historical averages, operational thresholds, or minimum pool levels.
• Temporal and Spatial Scale: Reservoir and lake levels are monitored at various time intervals (e.g., daily, weekly, monthly) and are specific to each individual water body.
• Strengths:
  • Directly indicates the amount of stored surface water available.
  • Crucial for managing water supply, irrigation releases, hydropower generation, and recreational activities.
  • Easy to understand and communicate to the public.
  • Historical data on reservoir and lake levels are often readily available.
• Limitations:
  • Levels are heavily influenced by management decisions (e.g., releases, diversions) and may not solely reflect natural drought conditions.
  • The relationship between precipitation deficits and reservoir/lake level declines can be complex and time-lagged.
  • Does not provide information on streamflow or groundwater conditions.
• Data Sources: Water level and storage data from agencies that manage reservoirs and lakes (e.g., dam operators, water management districts).

3.12. Groundwater Levels

• Description: Groundwater levels, measured in wells, provide an indication of the amount of water stored beneath the Earth's surface. Declining groundwater levels during a prolonged dry period signify hydrological drought and can lead to water shortages for wells and springs, as well as impact baseflow to rivers.
• Calculation/Methodology (Simplified): Water levels in wells are measured periodically using various techniques (e.g., electric tapes, pressure transducers). Drought conditions are assessed by comparing current water levels to historical averages, long-term trends, or established thresholds for concern. Indices like the Standardized Groundwater Index (SGI) can also be calculated, similar to SPI and SSI.
• Temporal and Spatial Scale: Groundwater levels are monitored at individual wells, with monitoring frequency varying (e.g., monthly, quarterly, annually). Regional assessments require data from a network of wells. The response of groundwater levels to drought can be slow and varies depending on aquifer characteristics.
• Strengths:
  • Represents a significant long-term water resource.
  • Provides insights into the sustainability of water supplies.
  • Can indicate the potential for future streamflow reductions (baseflow).
  • SGI provides a standardized measure for assessing groundwater drought.
• Limitations:
  • Groundwater levels respond slowly to precipitation changes, so declines may lag behind meteorological drought.
  • Influenced by pumping rates and other human activities.
  • Data availability can be limited in some areas.
  • Interpretation requires understanding of local hydrogeology and aquifer properties.
• Data Sources: Groundwater level data from monitoring well networks operated by government agencies (e.g., USGS, state geological surveys, water resource agencies).

3.13. Surface Water Supply Index (SWSI)

• Description: The Surface Water Supply Index (SWSI) is a composite index specifically designed for snowmelt-dominated regions. It integrates several hydrological variables, including snowpack, streamflow, and reservoir storage, to provide a comprehensive assessment of surface water availability.
• Calculation/Methodology (Simplified): SWSI typically combines standardized values of:
  1. Snow water equivalent (SWE) in mountain snowpack.
  2. Streamflow forecasts for the spring and summer runoff period.
  3. Current reservoir storage. The specific formula and weighting of these components can vary depending on the region and the relative importance of each water source. The index is often normalized to a scale where negative values indicate water supply deficits (drought) and positive values indicate surpluses.
• Temporal and Spatial Scale: SWSI is typically calculated and updated seasonally (e.g., monthly during the snowmelt season) and is relevant for specific river basins or regions where snowmelt is a major contributor to surface water supply.
• Strengths:
  • Accounts for the unique hydrological characteristics of snowmelt-driven systems.
  • Integrates key components of the surface water supply.
  • Provides a more holistic assessment of water availability in these regions compared to individual indicators.
  • Useful for forecasting water supply and managing water resources in snow-dependent areas.
• Limitations:
  • Only applicable to regions with significant seasonal snowpack.
  • The specific formula and weighting need to be carefully calibrated for each region.
  • Relies on accurate snowpack measurements, streamflow forecasts, and reservoir storage data.
• Data Sources: Snowpack data (e.g., from snow surveys or remote sensing), streamflow forecasts from hydrological models, and reservoir storage data from water management agencies.

3.14. Enhanced Vegetation Index (EVI)

• Description: The Enhanced Vegetation Index (EVI) is another satellite-derived index that quantifies vegetation greenness. It is designed to optimize the vegetation signal by reducing atmospheric influences (like aerosol scattering) and minimizing soil background effects, making it potentially more sensitive to vegetation changes than NDVI in some cases, especially in high biomass areas.
• Calculation/Methodology (Simplified): EVI uses the red, near-infrared (NIR), and blue bands of satellite imagery. The formula typically involves coefficients to correct for atmospheric and soil effects: $$EVI = G \times \frac{NIR - Red}{NIR + C_1 \times Red - C_2 \times Blue + L}$$ where:
  • $G$ is a gain factor (e.g., 2.5).
  • $C_1$ and $C_2$ are coefficients for atmospheric resistance (e.g., 6 and 7.5, respectively).
  • $L$ is a canopy background adjustment factor (e.g., 1).
• Temporal and Spatial Scale: Similar to NDVI, EVI can be calculated at various temporal resolutions (e.g., daily, weekly, monthly) and spatial resolutions depending on the satellite data used (e.g., MODIS, VIIRS).
• Strengths:
  • Reduced sensitivity to atmospheric effects and soil background noise compared to NDVI.
  • Improved sensitivity in high biomass regions where NDVI can saturate.
  • Can provide a better indication of vegetation health and vigor under certain conditions.
• Limitations:
  • The formula is more complex than NDVI.
  • Interpretation still requires understanding of vegetation phenology and other influencing factors.
  • Sensitivity might be reduced in very sparse vegetation areas.
• Data Sources: Satellite imagery with red, near-infrared (NIR), and blue spectral bands (e.g., MODIS, VIIRS, Landsat).

3.15. Land Surface Temperature (LST)

• Description: Land Surface Temperature (LST) is the radiative skin temperature of the Earth's surface, as measured by thermal infrared sensors on satellites. During drought, reduced soil moisture and vegetation stress can lead to increased LST. Anomalously high LST can therefore be an indicator of drought conditions.
• Calculation/Methodology (Simplified): LST is derived from the thermal infrared radiance measured by satellite sensors. The process involves atmospheric correction and often requires knowledge of surface emissivity (how efficiently the surface radiates energy), which can be estimated based on vegetation indices or other land cover information.
• Temporal and Spatial Scale: LST is available at various temporal resolutions (e.g., daily, 8-day, monthly) and spatial resolutions depending on the thermal sensors used (e.g., MODIS, Landsat thermal bands).
• Strengths:
  • Provides information on the surface energy balance, which is directly linked to moisture availability and evapotranspiration.
  • High LST can indicate water stress in vegetation and dry soil conditions.
  • Can be used to monitor the spatial extent and intensity of thermal anomalies associated with drought.
• Limitations:
  • LST is influenced by various factors other than drought, such as solar radiation, air temperature, and land cover type.
  • Interpretation as a drought indicator often requires analyzing LST anomalies relative to the long-term average or in conjunction with vegetation indices.
  • Accuracy depends on atmospheric correction and emissivity estimates.
• Data Sources: Thermal infrared satellite imagery (e.g., MODIS, VIIRS, Landsat thermal bands).

3.16. Normalized Difference Water Index (NDWI)

• Description: The Normalized Difference Water Index (NDWI) is a satellite-derived index used to monitor changes in the water content of vegetation and soil. Different versions of NDWI exist, but they typically use combinations of near-infrared (NIR) and short-wave infrared (SWIR) or green spectral bands. SWIR is particularly sensitive to liquid water in vegetation canopies and soil.
• Calculation/Methodology (Simplified - one common formulation using NIR and SWIR): $$NDWI = \frac{NIR - SWIR}{NIR + SWIR}$$ Another formulation uses Green and NIR bands, often more related to open water bodies. The specific bands used depend on the satellite sensor and the intended application (vegetation water content vs. open water).
• Temporal and Spatial Scale: NDWI can be calculated at various temporal and spatial resolutions depending on the availability of suitable satellite imagery (e.g., MODIS, Landsat).
• Strengths:
  • Sensitive to the water content of vegetation and soil.
  • Can provide information on vegetation water stress associated with drought.
  • SWIR-based NDWI can penetrate the atmosphere better than visible bands in some cases.
• Limitations:
  • Can be influenced by vegetation density and structure.
  • The relationship between NDWI and actual water content can be complex and may require calibration.
  • Sensitivity to soil background can still be an issue, especially in sparse vegetation areas.
• Data Sources: Satellite imagery with near-infrared (NIR) and short-wave infrared (SWIR) bands (e.g., MODIS, Landsat).

3.17. Evapotranspiration (ET) and Evaporative Stress Index (ESI)

• Description:
  • Evapotranspiration (ET): Represents the total water lost from the land surface to the atmosphere through evaporation from soil and water bodies and transpiration from plants. Reduced ET can be an indicator of water scarcity during drought.
  • Evaporative Stress Index (ESI): Specifically aims to capture anomalies in the ratio of actual to potential evapotranspiration (ET/PET). A low ESI indicates that actual ET is much lower than potential ET, suggesting water stress and drought conditions where the atmospheric demand for water is not being met by the surface supply.
• Calculation/Methodology (Simplified):
  • ET: Satellite-based ET is typically estimated using energy balance models that incorporate remotely sensed data (e.g., land surface temperature, vegetation indices, radiation) and meteorological data.
  • ESI: ESI is often derived from remotely sensed land surface temperature (LST). Anomalously high LST relative to vegetation greenness (e.g., as indicated by VCI) suggests high evaporative stress and low actual ET compared to PET. Various algorithms exist to calculate ESI.
• Temporal and Spatial Scale: ET and ESI are typically available at various temporal resolutions (e.g., daily, weekly, monthly) and spatial resolutions depending on the satellite data and models used.
• Strengths:
  • ET provides a direct measure of water fluxes from the surface.
  • ESI specifically highlights conditions where there is a mismatch between atmospheric water demand and surface water supply, which is a key aspect of drought.
  • Remote sensing allows for spatially continuous monitoring of ET and ESI.
• Limitations:
  • Accuracy of ET estimates depends on the complexity and parameterization of the models used.
  • ESI derived from LST can be influenced by factors other than water stress.
  • Interpretation may require understanding of vegetation types and phenology.
• Data Sources: Satellite imagery (e.g., MODIS, Landsat for LST and vegetation indices), meteorological reanalysis data, and land surface models that produce ET estimates.

3.18. Vegetation Health Index (VHI)

• Description: The Vegetation Health Index (VHI) is a composite index that combines information on vegetation greenness (typically from VCI) and thermal stress (typically derived from Land Surface Temperature or a related Temperature Condition Index - TCI). It aims to provide a more comprehensive assessment of vegetation health and drought impacts by considering both water availability and thermal conditions.
• Calculation/Methodology (Simplified): VHI is often calculated as a weighted average of the Vegetation Condition Index (VCI) and the Temperature Condition Index (TCI): $$VHI = \alpha \times VCI + (1 - \alpha) \times TCI$$ where $\alpha$ is a weighting factor (often 0.5). TCI is typically derived by normalizing the Land Surface Temperature (LST) relative to its historical range, similar to how VCI is derived from NDVI.
• Temporal and Spatial Scale: VHI has the same temporal and spatial resolution as the VCI and LST data used in its calculation.
• Strengths:
  • Integrates the effects of both moisture stress (from VCI) and thermal stress (from TCI) on vegetation health.
  • Can provide a more robust indicator of agricultural drought and vegetation condition than using VCI or LST alone.
  • Useful for monitoring the combined impacts of water scarcity and heat stress on vegetation.
• Limitations:
  • The choice of the weighting factor ($\alpha$) can influence the results and may need to be adjusted based on the region and vegetation type.
  • The accuracy depends on the quality of the underlying NDVI and LST data and the derivation of VCI and TCI.
  • Interpretation still requires consideration of vegetation phenology and other factors affecting plant health.
• Data Sources: Satellite imagery providing NDVI and Land Surface Temperature (LST) data (e.g., AVHRR, MODIS).

3.19. U.S. Drought Monitor (USDM)

• Description: The U.S. Drought Monitor (USDM) is a weekly map showing the location and intensity of drought across the United States. It is produced through a synthesis of multiple indices, climate observations, and reports from experts at the national, regional, and state levels. The USDM categorizes drought intensity into five levels: Abnormally Dry (D0), Moderate Drought (D1), Severe Drought (D2), Extreme Drought (D3), and Exceptional Drought (D4).
• Calculation/Methodology (Simplified): The USDM is not based on a single mathematical formula but rather on a "convergence of evidence" approach. It integrates various meteorological, hydrological, and agricultural drought indicators, including:
  • Meteorological: SPI, SPEI, Palmer indices (PDSI, Palmer Hydrological Drought Index - PHDI, Palmer Moisture Anomaly Index - Z-index), precipitation percentiles.
  • Hydrological: Streamflow, reservoir levels, groundwater levels, snow water equivalent.
  • Agricultural: Soil moisture, satellite-based vegetation health indices (NDVI, VCI), crop condition reports. Experts from various agencies and regions review these data, along with local impacts and conditions, to draw the weekly drought boundaries and assign intensity categories based on a set of descriptive criteria for each level.
• Temporal and Spatial Scale: The USDM is produced weekly and covers the entire United States, including Puerto Rico and other U.S. territories. The spatial resolution is at the county level, with finer-scale variations within counties based on the underlying data and expert input.
• Strengths:
  • Provides a comprehensive and integrated assessment of drought conditions by considering multiple lines of evidence.
  • Incorporates expert knowledge and local impacts, making it highly relevant for decision-making.
  • Widely recognized and used for drought monitoring, impact assessment, and triggering drought-related actions.
  • Available weekly, providing timely information on evolving drought conditions.
• Limitations:
  • Subjectivity can be introduced through the expert interpretation process.
  • The relative weight given to different indicators can vary depending on the region and the experts involved.
  • The spatial resolution is limited to counties, which may mask finer-scale drought variations.
  • Primarily focused on the United States.
• Data Sources: A wide range of federal, state, and local data sources, including NOAA (precipitation, temperature, streamflow, reservoirs), USDA (soil moisture, crop conditions), USGS (groundwater, streamflow), NASA (satellite data), and expert reports.

3.20. Combined Drought Indicator (CDI)

• Description: A Combined Drought Indicator (CDI) is a general term for an index that integrates multiple drought-related variables or indicators across different domains (meteorological, agricultural, hydrological) to provide a more robust and holistic assessment of drought conditions and risks. The specific variables and methodologies used to create a CDI can vary significantly depending on the region, the intended application, and the data availability.
• Calculation/Methodology (Simplified - varies greatly): CDIs typically involve the following steps:
  1. Selection of Component Indicators: Identifying relevant indicators from different drought types (e.g., SPI for meteorological, soil moisture for agricultural, streamflow for hydrological).
  2. Standardization or Normalization: Transforming the component indicators to a common scale to allow for comparison and combination (e.g., using percentiles, z-scores, or other statistical methods).
  3. Weighting (Optional): Assigning weights to the component indicators based on their perceived importance or relevance for the specific region and application. Weights can be equal or based on statistical analysis or expert judgment.
  4. Aggregation: Combining the standardized (and potentially weighted) component indicators using mathematical formulas (e.g., averaging, weighted sum, or more complex multivariate techniques) to produce a single CDI value or category.
• Temporal and Spatial Scale: The temporal and spatial scale of a CDI depends on the scales of the input indicators used in its calculation. It can range from local to regional and can be updated at various time intervals (e.g., weekly, monthly).

CDI Characteristic	Phenomena Reflected	Key Applications
Timescale Relevance	Varies depending on the component indicators included, typically aiming for a multi-timescale perspective for a more robust assessment.	Region-specific drought monitoring and early warning systems, tailored to local conditions and vulnerabilities. Integrated assessment for specific sectors (e.g., agriculture, water supply).
Phenomena Reflected	Integrated measure of drought severity by combining standardized and potentially weighted information from meteorological, agricultural, and hydrological indicators. Aims for a holistic view of drought.	Providing a more reliable and context-specific assessment of drought conditions and risks. Enhancing the accuracy of drought monitoring and forecasts for targeted actions.
Key Applications	Regional drought management, triggering local drought response plans, sector-specific drought monitoring and decision support, research on integrated drought assessment methodologies.	Improving the effectiveness of drought management strategies by providing a more nuanced and locally relevant understanding of drought conditions. Supporting proactive drought risk management.

• Strengths:
  • Provides a more comprehensive assessment of drought by integrating information from multiple drought types.
  • Can potentially provide a more reliable indicator of drought onset, persistence, and severity compared to relying on a single indicator.
  • Can be tailored to the specific characteristics and data availability of a particular region.
  • Can be designed to better reflect the impacts of drought on specific sectors (e.g., agriculture, water resources).
• Limitations:
  • The development and interpretation of a CDI can be complex and require careful consideration of the selection, standardization, weighting, and aggregation methods.
  • The optimal combination of indicators and weights may vary across different regions and applications.
  • Data availability for all desired component indicators may be a limiting factor in some areas.
  • The "black box" nature of some CDIs can make it challenging to understand the contribution of individual components.
• Data Sources: Depends on the component indicators included in the CDI. Common sources include meteorological observations (precipitation, temperature), soil moisture data (in-situ or modeled), streamflow and reservoir data, and satellite-based vegetation indices.

4. Calculation Details of Drought Indices

This section provides more specific details on how the drought indices discussed earlier are calculated, the variables required, the general formulations, and relevant packages/functions available in R and Python.

4.1. Standardized Precipitation Index (SPI)

• How is it calculated? SPI calculation involves fitting a probability distribution (typically Gamma) to long-term precipitation data for a specific location and time scale (e.g., 1, 3, 6, 12 months). This fitted distribution is then transformed to a standard normal distribution (mean 0, standard deviation 1), and the SPI value is the z-score (number of standard deviations the observed precipitation deviates from the mean).
• What variables are needed? Long-term historical precipitation data (at least 30 years is recommended) for the desired location and at a consistent time step (e.g., monthly).
• Inputs: A time series of precipitation data.
• Formulation (Conceptual):
  1. Select a time scale ($k$).
  2. Aggregate precipitation over the chosen time scale for each period in the historical record.
  3. Fit a Gamma distribution to the aggregated precipitation data. The probability density function of the Gamma distribution is: $$f(x; \alpha, \beta) = \frac{1}{\Gamma(\alpha)\beta^\alpha} x^{\alpha-1} e^{-x/\beta} \quad \text{for } x > 0, \alpha > 0, \beta > 0$$ where $\alpha$ is the shape parameter and $\beta$ is the scale parameter, estimated from the data. $\Gamma(\alpha)$ is the Gamma function.
  4. Calculate the cumulative probability $H(x) = P(X \le x)$ from the fitted Gamma distribution. For periods with zero precipitation, a separate probability $q = P(X=0)$ is estimated.
  5. Transform the cumulative probability to a standard normal distribution (with mean zero and variance one). If $H(x) > 0.5$, the SPI is: $$SPI = z = \Phi^{-1}(H(x))$$ where $\Phi^{-1}$ is the inverse standard normal cumulative distribution function. A similar transformation is used if $H(x) \le 0.5$, adjusting for the probability of zero precipitation.
• R Packages/Functions:
  • SPEI package: spi() function. This is a dedicated package for drought indices and includes SPI calculation.
• Python Packages/Functions:
  • scipy.stats: While scipy.stats provides functions for fitting distributions (gamma.fit, gamma.cdf) and the inverse normal CDF (norm.ppf), you would need to implement the SPI calculation steps yourself.
  • climopy: This climate analysis library includes a function spi() in its drought module.
  • xclim: For climate data analysis, xclim has a standardized_precipitation_index function.
• Efficiency: The SPEI package in R and xclim in Python are generally efficient as they are designed for climate time series analysis and often optimized for speed. For Python, using vectorized operations with libraries like NumPy within climopy or xclim will be more efficient than manual looping with scipy.stats.

4.2. Palmer Drought Severity Index (PDSI)

• How is it calculated? PDSI is calculated based on a water balance equation that considers precipitation, evapotranspiration, soil moisture recharge, runoff, and soil moisture loss. It uses empirically derived coefficients that vary by location and attempts to quantify the cumulative moisture deficit or surplus.
• What variables are needed? Monthly precipitation and temperature data, as well as information on the soil's available water capacity.
• Inputs: Time series of monthly precipitation and temperature, and a value for the available water capacity of the soil.
• Formulation (Conceptual - highly simplified):
  1. Calculate potential evapotranspiration (PET) using a temperature-based method (e.g., Thornthwaite).
  2. Estimate potential runoff, potential recharge, and potential loss from the soil based on previous conditions and PET.
  3. Calculate the moisture anomaly for each month as the difference between the actual precipitation and the "required" precipitation for normal conditions (which depends on PET and the potential terms).
  4. Accumulate these moisture anomalies over time, weighted by empirically derived coefficients ($K_i$) that vary spatially and temporally. The PDSI value at time $t$ is a function of the PDSI at time $t-1$ and the current moisture anomaly.
• R Packages/Functions:
  • SPEI package: pdsi() function.
• Python Packages/Functions:
  • droughtindices: This package includes a pdsi() function.
• Efficiency: The SPEI package in R and droughtindices in Python provide relatively efficient implementations of the PDSI calculation.

4.3. Vegetation Condition Index (VCI)

• How is it calculated? VCI is calculated by normalizing the current Normalized Difference Vegetation Index (NDVI) value based on the historical range of NDVI for the same time of year and location. It expresses the current vegetation condition as a percentage of the historical extremes.
• What variables are needed? Time series of NDVI data (derived from satellite imagery) over a long period (to establish historical minimum and maximum values).
• Inputs: A time series of NDVI values for the area of interest.
• Formulation: $$VCI = \frac{NDVI_{current} - NDVI_{min}}{NDVI_{max} - NDVI_{min}} \times 100$$ where $NDVI_{current}$ is the NDVI value for the current period, and $NDVI_{min}$ and $NDVI_{max}$ are the minimum and maximum NDVI values observed in the historical record for the same period (e.g., same week or month of the year).
• R Packages/Functions:
  • While no dedicated VCI function might exist in standard drought packages, you can easily implement this using raster processing packages like raster or terra along with basic arithmetic.
• Python Packages/Functions:
  • rasterio or rioxarray for reading and processing raster (satellite) data. NumPy can then be used for the VCI calculation. Libraries like xarray can also be helpful for managing multi-dimensional raster data.
• Efficiency: Efficiency depends on the size of the raster datasets. Using vectorized operations in R (raster or terra) and Python (NumPy, rioxarray) is crucial for efficient processing of large satellite imagery.

4.4. Standardized Precipitation-Evapotranspiration Index (SPEI)

• How is it calculated? SPEI builds upon SPI by first calculating the monthly climatic water balance (precipitation minus potential evapotranspiration). This water balance series is then treated similarly to precipitation in the SPI calculation: fitting a probability distribution (typically Log-logistic), transforming it to a standard normal distribution.
• What variables are needed? Long-term historical monthly precipitation and temperature data (to estimate PET).
• Inputs: Time series of monthly precipitation and temperature.
• Formulation (Conceptual):
  1. Calculate monthly potential evapotranspiration (PET) using a suitable method (e.g., Thornthwaite, Hargreaves). The Hargreaves method requires temperature and extraterrestrial radiation.
  2. Calculate the monthly water balance $D_i = P_i - PET_i$.
  3. Aggregate the water balance over different time scales ($k$).
  4. Fit a Log-logistic probability distribution to the aggregated water balance series. The cumulative distribution function of the Log-logistic distribution is: $$F(x; \alpha, \beta) = \frac{1}{1 + (\frac{\alpha}{x})^\beta}$$ where $\alpha$ is a scale parameter and $\beta$ is a shape parameter, estimated from the data.
  5. Transform the cumulative probability to a standard normal distribution to obtain the SPEI value.
• R Packages/Functions:
  • SPEI package: spei() function.
• Python Packages/Functions:
  • SPEI package (a Python port of the R package).
  • xclim: Includes standardized_precipitation_evapotranspiration_index function.
• Efficiency: Similar to SPI, the SPEI package in both R and Python, and xclim in Python, are designed for efficiency in processing climate time series.

4.5. Rainfall Anomaly Index (RAI)

• How is it calculated? RAI measures the normalized departure of precipitation from the long-term mean, calculated separately for positive and negative anomalies using the means of the highest and lowest deciles.
• What variables are needed? Long-term historical precipitation data.
• Inputs: A time series of precipitation data.
• Formulation: (As provided in the previous detailed section for RAI).
• R Packages/Functions: No dedicated function readily available in standard drought packages, but it can be implemented using basic R functions.
• Python Packages/Functions: No dedicated function readily available in standard drought packages, but it can be implemented using NumPy.
• Efficiency: The calculation is straightforward and can be implemented efficiently using vectorized operations in both R and Python.

4.6. Percentage of Normal Precipitation (PNP)

• How is it calculated? PNP is a simple ratio of current period precipitation to the long-term average precipitation for the same period, multiplied by 100.
• What variables are needed? Current precipitation and long-term average precipitation.
• Inputs: Current precipitation value and the long-term average precipitation value for the corresponding time period.
• Formulation: $$PNP = \frac{\text{Current Precipitation}}{\text{Long-Term Average Precipitation}} \times 100$$
• R Packages/Functions: Can be easily calculated using basic R arithmetic.
• Python Packages/Functions: Can be easily calculated using basic Python arithmetic with libraries like NumPy if dealing with arrays of data.
• Efficiency: The calculation is very efficient.

4.7. Enhanced Vegetation Index (EVI)

• How is it calculated? EVI uses the red, NIR, and blue bands of satellite imagery with specific coefficients to improve vegetation signal and reduce atmospheric and soil effects.
• What variables are needed? Reflectance values from the red, near-infrared (NIR), and blue bands of satellite imagery.
• Inputs: Raster data containing reflectance values for the required bands.
• Formulation: (As provided in the previous detailed section for EVI).
• R Packages/Functions: raster, terra, rgdal for reading and manipulating raster data.
• Python Packages/Functions: rasterio, rioxarray for raster data handling, NumPy for the calculation.
• Efficiency: Efficient processing requires vectorized operations on raster arrays, which are well supported by the mentioned packages.

4.8. Land Surface Temperature (LST)

• How is it calculated? LST derivation involves converting thermal radiance measured by satellites to temperature, requiring atmospheric correction and emissivity estimation.
• What variables are needed? Thermal band radiance from satellite imagery, and potentially data for atmospheric correction and emissivity estimation (which can be derived from other bands or external datasets).
• Inputs: Raster data containing thermal band radiance.
• Formulation: The formulation is sensor-specific and involves radiative transfer equations and emissivity adjustments. It's often provided in the documentation for the satellite data.
• R Packages/Functions: raster, terra, ncdf4 (for NetCDF data) for reading satellite data. Specific LST algorithms might need to be implemented or are available in specialized remote sensing packages.
• Python Packages/Functions: rasterio, rioxarray, netCDF4 for data handling. Libraries like pyTSEB or eeepy (for Google Earth Engine) might offer LST processing capabilities or tools to access LST products.
• Efficiency: Depends on the complexity of the LST retrieval algorithm and the size of the data. Efficient processing involves optimized array operations.

4.9. Normalized Difference Water Index (NDWI)

• How is it calculated? NDWI uses the ratio of differences to sums of specific spectral bands (typically NIR and SWIR, or Green and NIR) to highlight water content.
• What variables are needed? Reflectance values from the required spectral bands (depending on the NDWI formulation).
• Inputs: Raster data containing reflectance values for the required bands.
• Formulation: (As provided in the previous detailed section for NDWI).
• R Packages/Functions: raster, terra.
• Python Packages/Functions: rasterio, rioxarray, NumPy.
• Efficiency: Efficient with vectorized raster operations.

4.10. Evapotranspiration (ET) and Evaporative Stress Index (ESI)

• How is it calculated? ET often involves complex energy balance models. ESI typically uses the anomaly of LST relative to vegetation conditions.
• What variables are needed? Depends on the ET model (can include radiation, temperature, humidity, wind speed, vegetation indices, LST). ESI often needs LST and a vegetation index like VCI or NDVI.
• Inputs: Various meteorological and remote sensing datasets.
• Formulation: ET formulations are model-dependent (e.g., Penman-Monteith). ESI formulations vary based on the specific algorithm used to relate LST and vegetation.
• R Packages/Functions: Packages like Evapotranspiration, SPEI (for PET calculation). Remote sensing packages for input data.
• Python Packages/Functions: Libraries like pyet, rioxarray, xarray. Google Earth Engine Python API (eeepy) provides access to ET products.
• Efficiency: Depends heavily on the complexity of the ET/ESI calculation and the size of the input data.

4.11. Vegetation Health Index (VHI)

• How is it calculated? VHI is a weighted combination of VCI and TCI (Temperature Condition Index, derived from LST).
• What variables are needed? NDVI (to calculate VCI) and Land Surface Temperature (LST) (to calculate TCI).
• Inputs: Raster data for NDVI and LST.
• Formulation: (As provided in the previous detailed section for VHI). TCI is often calculated similarly to VCI: $$TCI = \frac{LST_{max} - LST_{current}}{LST_{max} - LST_{min}} \times 100$$
• R Packages/Functions: raster, terra.
• Python Packages/Functions: rasterio, rioxarray, NumPy.
• Efficiency: Efficient with vectorized raster operations.

4.12. U.S. Drought Monitor (USDM)

• How is it calculated? Not a direct calculation but a synthesis of multiple indicators and expert input.
• What variables are needed? Numerous meteorological, hydrological, and agricultural variables (as listed in the previous detailed section).
• Inputs: Gridded and station-based data for various indicators, expert assessments.
• Formulation: No single formula. Relies on thresholds and expert judgment based on the convergence of evidence.
• R Packages/Functions: No direct package to replicate the USDM process. Packages for individual component indicators would be used.
• Python Packages/Functions: Similarly, no direct package. Libraries for individual component indicators would be used.
• Efficiency: Not applicable as it's a human-driven synthesis process.

4.13. Combined Drought Indicator (CDI)

• How is it calculated? Varies greatly depending on the specific CDI. Involves selecting, standardizing, weighting, and aggregating multiple indicators.
• What variables are needed? Depends on the chosen component indicators.
• Inputs: Data for the chosen component indicators.
• Formulation: Highly variable, ranging from simple averages to complex weighted sums or multivariate methods.
• R Packages/Functions: Depends on the component indicators. Packages for time series analysis (zoo, xts), spatial analysis (raster, sf), and statistical methods would be used.
• Python Packages/Functions: Depends on the component indicators. Libraries like NumPy, Pandas, SciPy, xarray, rioxarray would be common.
• Efficiency: Depends on the complexity of the CDI and the size of the input datasets. Efficient implementations would leverage vectorized operations.

5. Drought Monitoring and Assessment

5.1. Early Warning Systems

Drought indicators play a critical role in early warning systems by providing timely information on the onset, severity, and spatial extent of drought.

Monitoring trends in meteorological indicators like SPI can signal the beginning of a precipitation deficit. Agricultural indicators like VCI can provide early warnings of vegetation stress.

Integrated monitoring of multiple indicators across different timescales can improve the accuracy and reliability of drought forecasts.

Early warning systems often involve disseminating drought information to stakeholders, including farmers, water managers, and policymakers, to facilitate proactive responses.

5.2. Drought Severity Classification

Drought indicators are often used to classify drought severity into different categories (e.g., D0 - Abnormally Dry, D1 - Moderate Drought, D2 - Severe Drought, D3 - Extreme Drought, D4 - Exceptional Drought, as used by the U.S. Drought Monitor).

These classifications are based on predefined thresholds of indicator values and help to communicate the intensity and potential impacts of drought.

Different indicators may have their own specific thresholds for defining drought severity. For example, SPI values of -1.0 to -1.5 often indicate moderate drought, while values below -2.0 indicate extreme drought.

Consistent and standardized classification systems are essential for effective drought management and communication.

5.3. Spatial Analysis and Mapping

Geographic Information Systems (GIS) and remote sensing technologies are crucial for visualizing and analyzing the spatial patterns of drought using indicator data.

Drought maps, generated from spatially interpolated indicator values, provide a clear picture of the geographical distribution and severity of drought.

This spatial information is vital for targeted interventions and resource allocation to the most affected areas.

Time series of drought maps can also be used to track the evolution and progression of drought over time.

5.4. Integration of Multiple Indicators

A comprehensive assessment of drought often requires considering multiple indicators across different drought types and timescales.

Relying on a single indicator can be misleading, as different indicators capture different aspects of the drought phenomenon.

A 'convergence of evidence' approach, where multiple indicators point towards similar drought conditions, provides a more robust and reliable assessment.

For example, severe agricultural drought is more likely when meteorological indicators show prolonged precipitation deficits, soil moisture levels are low, and vegetation indices indicate significant stress.

6. Impacts of Drought

6.1. Agriculture

• Reduced crop yields and quality due to insufficient water availability.
• Livestock losses due to lack of pasture and water.
• Increased risk of plant diseases and pest infestations.
• Economic losses for farmers and the agricultural sector.
• Food price increases and potential food insecurity.

6.2. Water Resources

• Reduced streamflow and river levels, impacting water supply for various uses.
• Lowering of lake and reservoir levels, affecting storage capacity and water availability.
• Depletion of groundwater resources, potentially leading to long-term water scarcity.
• Increased competition for limited water resources among different sectors.
• Deterioration of water quality due to reduced dilution of pollutants.

6.3. Ecosystems

• Vegetation stress and mortality, leading to changes in plant communities.
• Habitat loss and reduced water availability for wildlife.
• Increased risk of wildfires due to dry vegetation.
• Impacts on aquatic ecosystems due to low flows and reduced water quality.
• Increased susceptibility of ecosystems to invasive species.

6.4. Socioeconomic

• Economic losses in agriculture, tourism, energy production (hydropower), and other water-dependent sectors.
• Increased unemployment and reduced income in affected communities.
• Health problems related to water scarcity and poor water quality.
• Social unrest and conflicts over water resources.
• Displacement of populations due to severe water shortages or agricultural failures.
• Increased energy consumption and costs for pumping water from deeper wells.

7. Conclusion

Drought is a complex and multifaceted phenomenon with significant environmental, economic, and social consequences.

The use of various drought indicators and indices is crucial for effectively monitoring, assessing, and managing drought risks.

Understanding the strengths and limitations of different indicators is essential for their appropriate application.

An integrated approach that considers multiple indicators and incorporates spatial analysis is vital for a comprehensive understanding of drought conditions.

Continuous monitoring and the development of robust early warning systems are essential for building resilience to future drought events.

8. References (Optional)

o Svoboda, M., & Fuchs, B. A. (2016). Handbook of Drought Indicators and Indices. Integrated Drought Management Programme (IDMP), Integrated Drought Management Tools and Guidelines Series 2. World Meteorological Organization (WMO) and Global Water Partnership (GWP).
o Wilhite, D. A. (2000). Drought: A Global Assessment (Vol. 1). Routledge. o Heim Jr., R. R. (2002). A review of twentieth-century drought indices used in the United States. Bulletin of the American Meteorological Society, 83(8), 1149-1165.

o McKee, T. B., Doesken, N. J., & Kleist, J. (1993). The relationship of drought frequency and duration to time scales. In Eighth Conference on Applied Climatology (pp. 179-184). American Meteorological Society.
o Lloyd-Hughes, B., & Saunders, M. A. (2002). A drought climatology for Europe. International Journal of Climatology, 22(11), 1571-1592.

o Palmer, W. C. (1965). Meteorological drought. US Department of Commerce, Weather Bureau. o Alley, W. M. (1984). The Palmer drought severity index: Limitations and assumptions. Journal of Climate and Applied Meteorology, 23(7), 1100-1109.

o Kogan, F. N. (1990). Remote sensing of drought with AVHRR. In Seventh Conference on Applied Climatology (pp. 175-178). American Meteorological Society. o Kogan, F. N. (1995). Application of vegetation index and brightness temperature for drought detection. Advances in Space Research, 15(11), 91-100. o Vicente-Serrano, S. M., Beguería, S., & López-Moreno, J. I. (2010). A multiscalar drought index sensitive to global warming: The Standardized Precipitation Evapotranspiration Index. Journal of Climate, 23(7), 1696-1718.

o Van Rooy, M. P. (1965). A rainfall anomaly index independent of time and space. Notos, 14, 43-48.

o Huete, A., Didan, K., Miura, T., Rodriguez, E. P., Gao, X., & Ferreira, L. G. (2002). Overview of the radiometric and biophysical performance of the MODIS vegetation indices. Remote Sensing of Environment, 83(1-2), 195-213. o Gao, B. C. (1996). NDWI—A normalized difference water index for remote sensing of vegetation liquid water from space. Remote Sensing of Environment, 58(3), 257-266.

o Anderson, M. C., Norman, J. M., Kustas, W. P., Houborg, R., Starks, P. J., & Agnellus, C. (2013). Mapping daily evapotranspiration at field to continental scales using geostationary and polar orbiting satellite imagery. Hydrology and Earth System Sciences, 17(6), 2451-2469. o Anderson, M. C., Hain, C. R., Karnieli, A., Goetz, S. J.,лое, B. F., Kustas, W. P., ... & White, W. A. (2011). Evaluation of drought indices based on thermal remote sensing and мультисенсорные data. Remote Sensing of Environment, 115(10), 2655-2669.

o Kogan, F. N. (1995). Application of AVHRR in large-area drought monitoring. Remote Sensing of Environment, 51(1), 103-115.

o Svoboda, M., LeComte, D., Hayes, M., Gleason, K., Heim, R., предательство, T., ... & Rippey, B. (2002). The drought monitor. Bulletin of the American Meteorological Society, 83(8), 1181-1190.