Global trends and patterns of drought from space

Abstract

This paper analyzes changes in areas under droughts over the past three decades and alters our understanding of how amplitude and frequency of droughts differ in the Southern Hemisphere (SH) and Northern Hemisphere (NH). Unlike most previous global-scale studies that have been based on climate models, this study is based on satellite gauge-adjusted precipitation observations. Here, we show that droughts in terms of both amplitude and frequency are more variable over land in the SH than in the NH. The results reveal no significant trend in the areas under drought over land in the past three decades. However, after investigating land in the NH and the SH separately, the results exhibit a significant positive trend in the area under drought over land in the SH, while no significant trend is observed over land in the NH. We investigate the spatial patterns of the wetness and dryness over the past three decades, and we show that several regions, such as the southwestern United States, Texas, parts of the Amazon, the Horn of Africa, northern India, and parts of the Mediterranean region, exhibit a significant drying trend. The global trend maps indicate that central Africa, parts of southwest Asia (e.g., Thailand, Taiwan), Central America, northern Australia, and parts of eastern Europe show a wetting trend during the same time span. The results of this satellite-based study disagree with several model-based studies which indicate that droughts have been increasing over land. On the other hand, our findings concur with some of the observation-based studies.

Appendix

Appendix Estimating the Standardized Precipitation Index (SPI) involves describing frequency distribution of precipitation using a gamma probability density function:

$$ g(x)= \frac{1}{\beta^{\alpha}\Gamma(\alpha)}x^{\alpha-1}e^{\frac{-x}{\beta}} $$

(5)

where α and β are the shape and scale parameters, respectively. In Eq. 5, x denotes positive precipitation amounts and Γ(α) is the gamma function. The parameters α and β can be estimated using the maximum likelihood method as (Edwards 1997):

$$ \alpha=\frac{1}{4\left(ln(\overline{x})-\frac{\Sigma ln(x)}{n}\right)} \left(1+\sqrt{1+\frac{4\left(ln(\overline{x})-\frac{\Sigma ln(x)}{n}\right)}{3}}\right) $$

(6)

and

$$ \beta=\frac{\overline{x}}{\alpha} $$

(7)

where n is the number of observations. The estimated parameters will then be used to derive the cumulative probability of observed precipitation values for the given month and time scale (e.g., 6 months) over each pixel:

$$ G(x)= \frac{1}{\beta^{\alpha}\Gamma(\alpha)} \int_{0}^{x} x^{\alpha-1}e^{\frac{-x}{\beta}} dx $$

(8)

Assuming $t=\frac {x}{\beta }$, Eq. 8 reduces to the so-called incomplete cumulative gamma distribution function (Edwards 1997):

$$ G(x)= \frac{1}{\Gamma(\alpha)} \int_{0}^{x} t^{\alpha-1}e^{-t} dt $$

(9)

The above equation is not valid for x = 0 (zero precipitation values). To account for zeros, the complete cumulative probability distribution, H(x), can be written as:

$$ H(x)= q + (1-q)G(x) $$

(10)

where q and 1 − q denote the probabilities of zero and nonzero precipitations, respectively. The SPI is then derived by transforming the cumulative probability (Eq. 10) to the standard normal distribution with a mean of 0 and variance of 1 (McKee et al. 1993).