• ADVANCES IN ATMOSPHERIC SCIENCES, 2017, 34(12): 1381-1394
    doi: 10.1007/s00376-017-6313-1
    Sensitivity of Potential Evapotranspiration Estimation to the Thornthwaite and Penman-Monteith Methods in the Study of Global Drylands
    Qing YANG1,, Zhuguo MA1,2, Ziyan ZHENG1, Yawen DUAN1,2


    Drylands are among those regions most sensitive to climate and environmental changes and human-induced perturbations. The most widely accepted definition of the term dryland is a ratio, called the Surface Wetness Index (SWI), of annual precipitation to potential evapotranspiration (PET) being below 0.65. PET is commonly estimated using the Thornthwaite (PET_Th) and Penman-Monteith equations (PET_PM). The present study compared spatiotemporal characteristics of global drylands based on the SWI with PET_Th and PET_PM. Results showed vast differences between PET_Th and PET_PM; however, the SWI derived from the two kinds of PET showed broadly similar characteristics in the interdecadal variability of global and continental drylands, except in North America, with high correlation coefficients ranging from 0.58 to 0.89. It was found that, during 1901-2014, global hyper-arid and semi-arid regions expanded, arid and dry sub-humid regions contracted, and drylands underwent interdecadal fluctuation. This was because precipitation variations made major contributions, whereas PET changes contributed to a much lesser degree. However, distinct differences in the interdecadal variability of semi-arid and dry sub-humid regions were found. This indicated that the influence of PET changes was comparable to that of precipitation variations in the global dry-wet transition zone. Additionally, the contribution of PET changes to the variations in global and continental drylands gradually enhanced with global warming, and the Thornthwaite method was found to be increasingly less applicable under climate change.

    Key words: potential evapotranspiration; global drylands; Thornthwaite; Penman-Monteith;
    摘要: 干旱区是对气候变化和人类活动响应最为敏感的地区之一. 通常将地表湿润指数(SWI, 年降水量与潜在蒸散发PET的比值)小于0.65的区域定义为干旱区. Thornthwaite方法和Penman–Monteith方法是当前估算PET的两种常用算法. 本文在年代际尺度上比较分析了基于这两种PET算法时全球干旱区面积的时空变化特征. 结果发现虽然两种方法估算的PET在时空特征上存在显著的差异, 但基于这两种PET得到的全球和各大陆(北美洲除外)的干旱区面积呈现出相似的年代际变化, 相关系数为0.58~0.89. 二者均显示出1901-2014年全球总干旱区面积呈现出明显的年代际振荡, 其中极端干旱区和半干旱区显著扩张, 干旱区和干湿过渡带显著缩小. 这是因为全球降水的年代际变化主导了全球干旱区面积的年代际变化, 而PET变化的贡献次之. 同时也发现, 在干湿过渡带上, PET与降水变化的贡献相当, 这使得两种算法得到的全球半干旱区和干湿过渡带面积的年代际变化存在明显的差异, 且这种现象在北美最为明显. 此外, 上世纪80年代以后, 两种算法均显示PET的年代际变化对全球干旱区面积年代际变化的贡献逐渐加大. 因此在当前和未来情景下, 在全球干旱区面积变化的研究中, 采用Penman–Monteith方法估算PET更为合理.
    关键词: 潜在蒸散发 ; 全球干旱区 ; Thornthwaite方法 ; Penman–Monteith方法

    1. Introduction

    Drought is the world's costliest natural disaster. It manifests over multiple temporal and spatial scales, and can have considerable influence on ecosystems, economies and society (Heim Jr, 2002). To monitor, detect and quantify drought, many drought indices have been developed (Heim Jr, 2002; Keyantash and Dracup, 2002; Mishra and Singh, 2010; Valipour, 2013). Precipitation is the most important factor regarding water availability in land hydrological systems, and thus various measures of precipitation over a given period of time are incorporated in meteorological drought definitions (Heim Jr, 2002). Additionally, it has been generally recognized that the capabilities of drought indices that consider potential evapotranspiration (PET) to depict land water conditions are better (Vicente-Serrano et al., 2012).

    PET represents the maximum amount of water capable of being lost through evaporation from the soil surface and via transpiration at the canopy level under a given set of atmospheric conditions, assuming complete vegetation cover of the ground and an adequate water supply (Food and Agriculture Organization of the United Nations, 2008). Compared with actual evapotranspiration, PET can be more easily estimated from meteorological data and provides a reasonable representation for surface evapotranspiration to some extent (Valipour et al., 2017); especially in humid areas, PET tends to equal to actual evapotranspiration (Gao et al., 2007). Currently, many methods are available for the calculation of PET (e.g. Thornthwaite, 1948; Shuttleworth and Wallace, 1985; Allen et al., 1994a, 1994b; Hargreaves and Allen, 2003; Tegos et al., 2015; McMahon et al., 2016; Valipour et al., 2017). For instance, (Thornthwaite, 1948) proposed a method to estimate PET (known as the Thornthwaite method) based only on daily averaged temperature and the maximum amount of sunshine duration, which is calculated based on latitude. The Penman-Monteith equation is a physically based approach that considers wind speed, humidity and solar and longwave radiation in addition to temperature (Allen et al., 1994a, 1994b). A two-source PET model (Yuan and Quiring, 2014), which is also known as the Shuttleworth-Wallace model (Shuttleworth and Wallace, 1985; Zhou et al., 2008), is considered an improvement over the Penman-Monteith equation because it addresses the radiation balance at the canopy level and the soil surface separately.

    The choice of proper methods for the calculation of PET has recently received considerable attention and has sparked notable controversy (e.g. Trenberth et al., 2014; Tegos et al., 2015; Rezaei et al., 2016; Zhang et al., 2016; Valipour et al., 2017; Feng et al., 2017). Global drought trends under climate change are still a matter of debate, caused by the differences between the Thornthwaite-based and Penman-Monteith-based PET (Sheffield et al., 2012; Dai, 2013; van der Schrier et al., 2013; Trenberth et al., 2014; Yuan and Quiring, 2014). The Palmer Drought Severity Index (PDSI; Palmer, 1965) is calculated using a complex water budget system based on precipitation, temperature and the soil characteristics of the site. It has been found to be not very sensitive to different methods for calculating PET in the formulation of the PDSI (Dai, 2011; van der Schrier et al., 2011; Yuan and Quiring, 2014). Consequently, (Dai, 2011) reported that when the PDSI is calculated using either the Thornthwaite or Penman-Monteith method for calculating PET, there are no significant differences in global drought patterns, and significant global drying trends can be found with both approaches. However, (Sheffield et al., 2012) suggested there has been little change in global drought over the past 60 years when using the Penman-Monteith-based PDSI, and that the global drying trend revealed by the Thornthwaite-based PDSI is overestimated.

    Drylands are considered to be areas where average rainfall is less than the potential moisture losses though evapotranspiration, and they are among those regions most sensitive to climate and environmental changes and human-induced perturbations (Reynolds et al., 2007; Huang Jr, 2016a). Understanding the response of drylands to climate change is essential for developing adaptation and mitigation strategies, and thus has become a subject of widespread concern (Hulme et al., 1992; Lioubimtseva and Henebry, 2009; Feng and Fu, 2013). It has been demonstrated that global drylands expanded remarkably during 1948 to 2005, especially in Africa and Eurasia (Ma and Fu, 2007). In China, the boundary between arid and semi-arid land has noticeably expanded eastwards and southwards in the past 100 years, and dryland expansion in northern China is evident because of decreasing precipitation, together with increasing evaporation (Ma and Fu, 2003, 2005, 2006; An et al., 2014; Li et al., 2015).

    Most climatological studies on dryland, as above (e.g. Sherwood and Fu, 2014), tend to be based on a common definition of the term "drylands". This definition, which is provided by the World Atlas of Desertification (UNEP, 1992), employs a ratio of annual precipitation to PET, called the Surface Wetness Index (SWI; Hulme et al., 1992; UNEP, 1992). Various methods for the calculation of PET have been used in the SWI; for instance, the Thornthwaite method (Ma and Fu, 2003, 2005, 2006, 2007) and Penman-Monteith method (Liu and Ma, 2007; Feng and Fu, 2013; Li et al., 2015; Huang Jr, 2016a). Of note is that, different from the PDSI, the SWI does not feature any parametrization, standardization or post-processing, and is therefore certainly affected by different estimates of PET. Consequently, notable differences in the spatiotemporal characteristics of global drylands, attributable to different estimates of PET, are expected. However, sensitivity of the SWI to different methods for the calculation of PET, in the study of the spatial distribution and temporal evolution of global drylands, has yet to be investigated. Therefore, the present study aimed to quantitatively identify the differences in the spatiotemporal variabilities of global drylands between the Thornthwaite and Penman-Monteith parameterizations for PET.

    The paper is organized as follows: Section 2 introduces the data and method. This is followed by a comparison of the PET values derived using the Thornthwaite and Penman-Monteith methods in section 3. Section 4 presents the spatiotemporal characteristics of global drylands defined by the SWI with the two estimates of PET. A discussion and conclusions are summarized in section 5.

    2. Data and methods
    2.1. Data

    Several datasets were used in this study: (1) Global land monthly precipitation, air temperature, cloud cover, vapor pressure, and PET, from 1901 to 2014, with a high resolution of 0.5°× 0.5°, were obtained from the CRU TS3.23 (Harris et al., 2014). The PET was calculated using the Penman-Monteith formula, as developed and recommended by the Food and Agricultural Organization (FAO) (Allen et al., 1994a, 1994b). Because of its high reliability, this PET dataset has been used for the calculation of SPEIbase v2.4 (Vicente-Serrano et al., 2010a, 2010b; Beguería et al., 2014). (2) The Global Land Cover Map (GlobCover) for 2009, representing 22 land cover classes, with a horizontal resolution of 300 m, was obtained from the European Space Agency (Bontemps et al., 2011).

    2.2. Estimation of PET

    2.2.1. Thornthwaite method

    (Thornthwaite, 1948) correlated monthly mean temperature with PET, as determined from the water balance, for valleys in the eastern USA, where there was a supply of surface water. (Willmott et al., 1985) modified Thornthwaite's original approach slightly by introducing parameterization for a limited range of average air temperature T (Units: °C): \begin{equation} {\rm PET}=\left\{ \begin{array}{l@{\quad}l} 0 & T<0\\ 16\left(\dfrac{10T}{I}\right)^\alpha & 0\leq T<26.5\\ -415.85+32.24T-0.43T^2 & T\geq 26.5 \end{array} \right. , \ \ (1)\end{equation}

    where I is the heat index and α is estimated using an I-related third-order polynomial: \begin{eqnarray} I&\!=\!&\sum_{i=1}^{12}\left(\dfrac{T}{5}\right)^{1.514}\quad T>0 ;\ \ (2)\\ \alpha&\!=\!&0.49239+1.792\times 10^{-2}I-7.71\times 10^{-5}I^2+6.75\times 10^{-7}I^3\;.\nonumber\\ \ \ (3) \end{eqnarray}

    To account for the variability of day h and month length θ, PET is adjusted to \begin{equation} {\rm PET}={\rm PET}\left(\dfrac{\theta}{30}\right)\left(\dfrac{h}{12}\right) . \end{equation} Descriptions of each component in the above formulas are provided in Table 1.

    2.2.2. Penman-Monteith method

    The Penman-Monteith equation is a physically based method that uses a "big leaf" assumption. It defines a reference PET based on a hypothetical land cover, which closely resembles a clipped grass surface with uniform height (0.12 m), fixed surface resistance (70 s m-1), and surface albedo (0.23) (Allen et al., 1994a, 1994b). In addition, water is abundantly available at the reference evapotranspiration rate. Here, the FAO Penman-Monteith equation is given as \begin{equation} {\rm PET}=\dfrac{0.408\Delta(R_{\rm n}-G)+\gamma\frac{900}{T+273.16}u_2(e_{\rm s}-e_{\rm a})}{\Delta+\gamma(1+0.34u_2)} . \ (5)\end{equation} Definitions of the various components used in this formula are provided in Table 1.

    2.3. SWI

    The SWI, which is the ratio of the annual accumulated precipitation to PET, is also known as the Humidity Index (Hulme et al., 1992; UNEP, 1992) and the Aridity Index (Huang Jr, 2016a, 2016b): \begin{equation} {\rm SWI}=\dfrac{\sum_{i=1}^{12}P_i}{\sum_{i=1}^{12}{\rm PE}_i} , \ \ (6)\end{equation}

    Table 1. Parameters used in the Thornthwaite and Penman-Monteith methods.
    Thornthwaite Penman-Monteith
    T, 2-m average air temperature (°C); θ, the length of the month (days); Latitude, which is used for calculating the duration of daylight on the 15th day of the month; h (hour) T, 2-m average air temperature (°C); $R_n, crop surface net radiation (MJ m-2 d-1G, soil heat flux (MJ m-2 d-1);u2, 2-m wind speed (m s-1e s, saturation vapor pressure (kPa);e a, actual vapor pressure (kPa);∆, slope of the vapor pressure curve (kPa °C-1\(\par \), psychrometric constant (kPa °C$^{-1}$); 900, coefficient for the reference crop; 0.34, wind coefficient for the reference crop

    Table 1. Parameters used in the Thornthwaite and Penman-Monteith methods.

    Fig.1. Zonally averaged values of (left-hand axis) annual mean air temperature (units: °C), cloud cover (units: %) and vapor pressure deficit (× 5; units: hPa), and (right-hand axis) annual accumulated precipitation, PET_Th and PET_PM (units: mm), for the period 1951-2014.

    where Pi and PEi are the monthly precipitation and PET, respectively. Drylands are defined as regions where the SWI is below 0.65, including hyper-arid ( SWI<0.05), arid (0.05≤ SWI<0.20), semi-arid (\(0.20\leq\rm SWI<0.50\)) and dry sub-humid regions (\(0.50\leq\rm SWI<0.65\)).

    In this study, the PET estimated using the Thornthwaite and Penman-Monteith method is denoted as PET_Th and PET_PM, respectively. The SWI forced by the same precipitation amount but with the PET_Th or PET_PM is referred to as SWI_Th and SWI_PM, respectively.

    2.4. Method

    The Ensemble Empirical Mode Decomposition (EEMD) method (Huang and Wu, 2008; Wu and Huang, 2009) is a recently developed data-adaptive filter, which has been employed to decompose time series into various timescale components (Wu et al., 2011; Xia et al., 2013; Qian and Zhou, 2014). In this study, the EEMD method was used to decompose the annual time series of global drylands for the period 1901-2014 to obtain their multidecadal variability and nonlinear trends. The Student's t-test (Wilks, 2005) was used to calculate the significance of the difference between two time series.

    3. Comparison of PET values

    Figures 1a and b show distinct differences between the spatial distributions of PET_Th and PET_PM, with significant zonal characteristics (Fig. 1c). Compared with PET_PM, PET_Th was much lower in the subtropics, whereas it was much higher in the tropics and high northern latitudes.

    As shown in Fig. 2, PET_Th and air temperature had similar zonal distributions, i.e., a unimodal distribution with a peak at approximately 10°N. However, PET_PM showed a bimodal distribution, with two peaks in the subtropics and a low in the tropics. Abundant convective clouds and precipitation in the tropics reduce solar radiation and vapor pressure deficit, resulting in low values of PET, whereas the subtropics are associated with the opposite conditions. Consequently, PET values in the tropics should be much lower than in the subtropics. This indicates that PET_PM is more reasonable and reliable than PET_Th; the latter overestimates PET in the tropics but underestimates it in the subtropics, because of the exclusion of cloud cover and vapor pressure deficit in the Thornthwaite parameterization. This result is consistent with that of (van der Schrier et al., 2011), who investigated the dependence of the PDSI on the alternative Thornthwaite and Penman-Monteith methods for PET.

    Despite the large differences in the spatial distributions, the interannual variabilities of PET_Th and PET_PM were quite similar. As shown in Fig. 3a, significant positive correlations between PET_Th and PET_PM were found in most areas. For example, regions with correlation coefficients above 0.8 were located in North Africa, Southern Europe, Central Asia, and the Brazilian highlands. However, the long-term trends of PET_PM differed from those of PET_Th. Figure 3b shows regions with significant warming accounted for approximately 87% of the global land area, excluding Antarctica. Among these regions, approximately 87% of areas had significantly increasing PET_Th, while only around 54% of areas had significantly increasing PET_PM (Figs. 3c and d). This means that PET_Th increases with global warming, whereas the long-term trends of PET_PM are not determined by air temperature alone (Xu et al., 2006; Fu et al., 2009). Many studies have demonstrated a decrease in PET in many places throughout the world over the past 50 years (e.g., Roderick and Farquhar, 2002; Xu et al., 2006; Gao et al., 2006; Fu et al., 2009)——a trend that is associated with widespread decreases in solar radiation resulting from increasing cloud coverage and aerosol concentration (Roderick and Farquhar, 2002), wind speed (Gao et al., 2006), and vapor pressure deficit (Cong et al., 2009; Fu et al., 2009). Therefore, PET_PM shows a more reasonable long-term trend.

    Fig.2. Spatial distributions of average (1951-2014) annual accumulated PET (units: mm) using (a) Thornthwaite (PET_Th) and (b) Penman-Monteith (PET_PM) equations, and (c) their differences (PET_PM minus PET_Th). The shaded areas in (c) denote differences that are statistically significant at the 0.001 level.

    Fig.3. (a) Correlation between PET_Th and PET_PM for the period 1951-2014. Shaded areas denote correlation coefficients statistically significant at the 0.001 level. (b-d) Long-term tendencies from 1951 to 2014 for (b) annual mean air temperature [units: °C (10 yr)-1], (c) annual accumulated PET_Th and (d) PET_PM [units: mm (10 yr)-1]. Stippling indicates the trend is statistically significant at the 0.001 level.

    Table 2. Statistical values of annual accumulated PET_Th and PET_PM over northern South America, the USA, North Australia, and Central Asia. Difference means PET_PM minus PET_Th.
    1951-2014 mean (mm) 1901 (1951)-2014 linear trend [mm (10 yr)-1] 1901 (1951)-2014
    PET_Th PET_PM Difference PET_Th PET_PM correlation coefficient
    South America 1460.7 1243.6 -217.1* 4.7* (10.2*) -2.5* (-15.0*) 0.1 (0.1)
    USA 791.3 1290.0 498.7* 2.5* (4.9*) -1.0 (-3.0) 0.6* (0.5*)
    North Australia 1477.7 2316.0 838.3* 2.5* (6.3*) -6.5* (-6.9) 0.4* (0.4*)
    Central Asia 1055.0 1341.1 286.1* 2.5* (5.1*) -1.5* (-2.3) 0.5* (0.5*)

    *Indicates difference, linear trend or correlation coefficient is statistically significant at the 0.05 level.

    Table 2. Statistical values of annual accumulated PET_Th and PET_PM over northern South America, the USA, North Australia, and Central Asia. Difference means PET_PM minus PET_Th.

    To elaborate on the temporal variabilities of the two types of PET, the regional-averaged PET and associated statistical information for northern South America, the USA, North Australia, and Central Asia are shown in Fig. 4 and Table 2. Considerable differences between PET_Th and PET_PM were evident in these regions, with differences ranging from -217.1 (northern South America) to 838.3 mm (North Australia). The long-term trends of PET were opposing, i.e., there was a significant increasing trend in PET_Th but a significant decreasing trend in PET_PM for the periods 1901-2014 and 1951-2014. In addition, the interannual variations of PET_Th and PET_PM over northern South America were markedly different, with a correlation coefficient of only 0.1.

    Fig.4. Evolution of annual accumulated PET_Th and PET_PM (units: mm) from 1901 to 2014 over (a) northern South America (5°S-11°N, 60°-80°W), (b) USA (30°-45°N, 80°-120°W), (c) North Australia (23°-12°S, 120°-150°E) and (d) Central Asia (25°-38°N, 70°-80°E).

    4. Comparison of temporal and spatial characteristics of global drylands attributed to the two estimates of PET
    4.1. Variability in spatial distribution

    The spatial distributions of global drylands based on multi-year averages of SWI_ PM and SWI_Th are displayed in Fig. 5. Although the two patterns were broadly similar, the spatial extents and sizes for each arid region were obviously different. As shown in Fig. 6, drylands classified by SWI_PM and SWI_Th accounted for approximately 44.8% and 40.4%, respectively, of the global land area. Most drylands were distributed within the subtropics, where the underestimation of PET_Th resulted in larger SWI_Th and, consequently, fewer areas were classified as drylands. Between the classifications of SWI_Th and SWI_PM, differences in the areal percentages of drylands (4.4%) mainly derived from that in arid regions (4.1%). Although the areal percentages of semi-arid regions were approximately equal, their spatial extents were obviously different. It was apparent that high northern latitudes, where PET_Th was overestimated (Fig. 1c and Fig. 2), were classified as semi-arid and dry sub-humid regions by SWI_Th (Fig. 5a). This is not a reasonable result.

    Fig.5. Areal percentages of hyper-arid, arid, semi-arid, and dry sub-humid regions, using the 1951-2014 average SWI_Th and SWI_PM, respectively, over global and continental land areas. The blue number above each column indicates the areal percentage of drylands.

    Consistent with the above results, more areas were defined as drylands by SWI_PM than by SWI_Th in all continents, excluding Antarctica (Fig. 6). For instance, drylands percentage classified by SWI_PM (16.8%) was twice that by SWI_Th (8.4%) over Europe. The spatial extent of drylands classified by SWI_ PM and SWI_Th in Oceania was the largest among the continents, at approximately 86.1% and 77.7%, respectively. Half of Oceania (51.4%) was classified as arid regions by SWI_ PM, whereas only 18.2% of the continental area was classified as arid regions by SWI_Th, which yielded a relatively wetter result because of the underestimation of PET. In Africa, the severity of aridity was the greatest among the continents, although the spatial extent of drylands was only second largest. Most of the world's hyper-arid regions were found to be concentrated within Africa, with 23.1% and 20.0% of the continental area classified as hyper-arid regions by SWI_ PM and SWI_Th, respectively. In Asia, only 3.2% of the continental area was classified as hyper-arid regions by SWI_Th, which is an obvious underestimation, i.e., the Taklamakan Desert in northwestern China should be classified as hyper-arid regions rather than arid regions. In North America, the semi-arid area based on SWI_Th comprised the north of Alaska and northern Canada instead of most of the western United States. In South America, the distributions of drylands defined by SWI_PM and SWI_Th were similar; however, the sizes of each arid region based on SWI_Th were relatively smaller.

    Fig.6. Spatial distributions of global drylands using the 1951-2014 average: (a) SWI_Th; (b) SWI_PM.

    It is known that vegetation species respond not only to surface moisture conditions but also to effective cumulative temperature, soils, geomorphological and topographical features, and human activities. Therefore, surface vegetation types do not always match climatic zones exactly. As the main land cover type in hyper-arid and arid areas, the response of barren land to surface moisture deficit is much stronger and more durable with respect to other vegetation types. This is because of its short-term (months to years) resistance to change due to climatic variations and/or human activities. Generally, barren land tends to occur in drylands and drier regions have more barren land. As classified based on SWI_Th (Table 3), approximately 34.3%, 39.2%, 16.3% and 2.9% of global barren land was located in hyper-arid, arid, semi-arid and dry sub-humid regions, respectively. Of note is that the areal percentage of global barren land in arid regions (39.2%) was slightly larger than that in hyper-arid regions (34.3%), and more than half (62.4%) of areas were barren land in arid regions. For SWI_PM, global barren land was mainly concentrated in hyper-arid regions, with an areal percentage of 44.5%, and areal percentages of barren land declined sharply in regions with decreasing severity of aridity, ranging from 39.4% (arid regions) to 1.3% (dry sub-humid regions). Compared with SWI_Th-based classification, hyper-arid regions defined by SWI_PM had more barren land (95.4%), whereas arid regions had less barren land (46.5%). Thus, SWI_PM presents a more reasonable and reliable spatial distribution of global drylands with respect to SWI_Th.

    Table 3. Areal percentages of global barren land (P1) located in hyper-arid, arid, semi-arid, and dry sub-humid regions, and areal percentages of barren land (P2) over each arid region using 1951-2014 averages of SWI_Th and SWI_PM*.
    Hyper-arid Arid Semi-arid Dry sub-humid
    SWI_Th P1 34.3 39.2 16.3 2.9
    P2 93.5 62.4 12.0 3.6
    SWI_PM P1 44.5 39.4 9.2 1.3
    P2 95.4 46.5 8.1 2.3

    *P1i=ai/(∑i=15ai)× 100%; P2i=ai/bi× 100%, where ai is the area of barren land in each climate zone, i=1,…,5 indicates hyper-arid, arid, semi-arid, dry sub-humid and humid regions, respectively, and then i=15ai represents the total area of global barren land; bi is the area of each climate zone.

    Table 3. Areal percentages of global barren land (P1) located in hyper-arid, arid, semi-arid, and dry sub-humid regions, and areal percentages of barren land (P2) over each arid region using 1951-2014 averages of SWI_Th and SWI_PM*.

    Fig.7. Areal percentages (units: %) of global (a) hyper-arid, (b) arid, (c) semi-arid, (d) dry sub-humid regions, and (e) drylands during 1901-2014, defined by SWI_Th and SWI_PM, together with SWI_Th and SWI_PM with precipitation only (no PET changes, denoted by "p only") or PET only (no precipitation changes, denoted by "pet only").

    4.2. Variability in temporal evolution

    Differences in the interdecadal variabilities of global drylands classified by SWI_Th and SWI_PM were compared on global and continental scales, after variations shorter than 20 years were removed using the EEMD method. Additionally, to quantitatively assess the contributions of precipitation and PET variations to dryland changes, dryland evolutions caused by precipitation or PET changes only are discussed separately.

    4.2.1. Global mean

    Figure 7a shows the interdecadal variabilities of areal percentages of global hyper-arid regions. Although there are differences among the curves, a sharp upward trend is evident during 1901-2014. Hyper-arid region evolutions caused by precipitation changes only presented similar interdecadal characteristics to those caused by both precipitation and PET changes, while those caused by PET_Th-only and PET_PM-only changes both showed a sustained upward trend since 1901, especially after the 1980s, in response to global warming. From the mid-1980s, the areal percentage of hyper-arid regions defined by SWI_Th exhibited a distinct interdecadal fluctuation without a long-term trend, whereas that defined by SWI_Th with precipitation changes only showed a significant downward trend. For the areal percentage of hyper-arid regions defined by SWI_PM, there was an obvious upward trend since the mid-1980s, whereas interdecadal fluctuation was apparent in that defined by SWI_PM with precipitation changes only. These findings indicate a global expansion of hyper-arid regions over the past 100 years, and the trend is insensitive to the two estimates for PET. Also of note is that the result of SWI_Th showed a greater (twice as large) upward trend [0.085% (10 yr-1)] than that of SWI_PM [0.040% (10 yr-1)]. Therefore, the global expansion of hyper-arid regions can be attributed to both increasing PET and decreasing precipitation, with the latter's contribution being approximately 70.9% and 61.6% in SWI_Th and SWI_PM, respectively.

    The areal percentages of global arid regions (Fig. 7b) defined by SWI_Th and SWI_PM had similar variations, with a high correlation coefficient of 0.91 (Table 4). They both showed a significant downward trend during 1901-2014, at -0.104% (10 yr)-1 and -0.102% (10 yr)-1 respectively, and a shift from a positive to negative anomaly in the 1960s, as did those defined by precipitation changes only. However, arid region evolutions caused by PET_Th-only and PET_PM-only changes both showed a rising trend, and the upward trend of the former was statistically significant. This suggested that the areal percentages of global arid regions declined significantly during 1901-2014, because of the increases in precipitation, without obvious differences between the two estimates for PET. With respect to increasing PET, increasing precipitation plays a dominant role, which offsets the drying effect of increasing PET and eventually results in the contraction of arid regions. However, the expansion of arid regions was visible since the late 1970s because of both decreasing precipitation and increasing PET.

    As shown in Fig. 7c, consistent with SWI_Th and SWI_PM, the SWI with PET_Th-only and PET_PM-only changes showed that a significant rising trend existed in the areal percentages of global semi-arid regions during 1901-2014, with an accelerated upward trend since the 1960s (Huang et al., 2016b). However, a weak declining trend was found in semi-arid region evolutions caused by precipitation changes only. This finding indicates that the dominant contributor to the expansion of global semi-arid regions is increasing PET, especially since the 1960s.

    Table 4. Correlation coefficients (R) between interdecadal variations of each arid region defined by SWI_PM and SWI_PM over global and continental areas.
    Dry sub-
    R Hyper-arid Arid Semi-arid humid Dryland
    Global 0.82* 0.91* 0.67* 0.03 0.66*
    Asia 0.92* 0.92* 0.73* 0.20 0.78*
    Africa 0.87* 0.81* 0.49* 0.27* 0.89*
    Europe - - 0.74* 0.14 0.84*
    North America 0.96* 0.78* -0.11 0.12 0.58*
    Oceania 0.84* 0.80* 0.68* 0.83* 0.80*
    South America 0.39* 0.82* 0.77* 0.59* 0.80*

    *Indicates correlation coefficient is statistically significant at the 0.01 level.

    Table 4. Correlation coefficients (R) between interdecadal variations of each arid region defined by SWI_PM and SWI_PM over global and continental areas.

    Areal percentages of global dry sub-humid regions (Fig. 7d) defined by SWI_Th and SWI_Th with precipitation changes only both presented a shift from a positive to negative anomaly in the early 1940s and a significant declining trend during 1901-2014. Also, the tendency for dry sub-humid region evolutions caused by precipitation changes only, i.e., -0.090% (10 yr)-1, was approximately twice that caused by both precipitation and PET_Th changes [-0.045% (10 yr)-1]. For the areal percentages of dry sub-humid regions defined by SWI_PM, obvious interdecadal fluctuation and an insignificant downward trend existed, whereas significant rising and declining trends were found in dry sub-humid region evolutions caused by PET_PM-only and precipitation-only changes, at 0.057% (10 yr)-1 and -0.043% (10 yr)-1, respectively. Notably, dry sub-humid region evolutions associated with SWI_PM differed considerably from those associated with SWI_Th, with a correlation coefficient of only 0.03 (Table 4); although, they both showed a contraction of global dry sub-humid regions that could be attributed to increases in precipitation. The contribution of increasing precipitation was approximately twice that of increasing PET in the evolution of dry sub-humid regions defined by SWI_Th, whereas the contributions of increasing precipitation and increasing PET approximately offset each other in that defined by SWI_PM.

    Figure 7e shows the interdecadal variabilities of global drylands were broadly analogous to those of global semi-arid regions (Fig. 7c), which accounted for approximately 40.2% and 37.0% of global drylands defined by SWI_Th and SWI_PM, respectively. Distinct interdecadal fluctuations were presented clearly in dryland evolutions based on both SWI_Th and SWI_PM during 1901-2014. The evolutions of drylands caused by PET_Th-only and PET_PM-only changes both showed a significant rising trend, whereas a significant declining trend was exhibited in that caused by precipitation changes only, with a shift from a positive to negative anomaly during the 1940s. These results indicate the wetting effect of increasing precipitation approximately offsets the drying effect of increasing PET, resulting in no obvious long-term trend in global drylands defined by SWI_Th and a weak declining trend in that defined by SWI_PM.

    Fig.8. Areal percentages (units: %) of drylands over (a) Asia, (b) Africa, (c) Europe, (d) South America, (e) Oceania, and (f) North America during 1901-2014, defined by SWI_Th and SWI_PM, together with SWI_Th and SWI_PM with precipitation only (no PET changes, denoted by "p only") or PET only (no precipitation changes, denoted by "pet only").

    Generally, the interdecadal variabilities of global drylands, including each arid region, were broadly similar between the classification of SWI_Th and SWI_PM, with high correlation coefficients ranging from 0.66 to 0.91; although, several differences existed in dry sub-humid regions, with a correlation coefficient of only 0.03. They both showed expansion of global hyper-arid and semi-arid regions, contraction of arid and dry sub-humid regions, and interdecadal fluctuation of drylands, during 1901-2014. This is because precipitation changes make a major contribution in the interdecadal variabilities of global drylands, whereas PET changes contribute to a much lesser degree except in semi-arid regions. However, the contribution of PET changes has evidently increased since the 1980s, in response to global warming.

    4.2.2. Continental mean

    Figure 8a shows distinct interdecadal fluctuations in areal percentages of drylands over Asia defined by SWI_Th and SWI_PM during 1901-2014. A shift from a positive to negative anomaly occurred during the early 1940s, followed by a transition from a negative to positive anomaly during the late 1960s and early 1970s, and a reversal to a negative anomaly during the late 2000s. A significant upward trend was found in dryland evolutions caused by PET_Th-only and PET_PM-only changes, whereas that caused by precipitation-only changes presented a significant declining trend, and the tendency in the areal percentage of drylands defined by SWI_Th with precipitation-only changes was approximately twice that defined by SWI_PM with precipitation-only changes. After the 1980s, an accelerated upward trend in dryland evolutions caused by PET_Th-only and PET_PM-only changes was evident, as were enhanced differences between the evolutions of drylands defined by SWI_Th and SWI_Th with precipitation-only changes, as well as SWI_PM and SWI_PM with precipitation-only changes. This means that the influence of PET changes on drylands over Asia has intensified since the 1980s.

    Unlike in Asia, an obvious upward trend was evident in the areal percentages of drylands over Africa, especially since the late 1950s, with a shift from a negative to positive anomaly during the late 1970s and early 1980s, albeit with some differences among the curves apparent (Fig. 8b). These trends could be attributed to sustained decreasing precipitation since the late 1950s and increasing PET since the 1970s. The contributions of PET changes accounted for approximately 60.4% in the evolutions of drylands defined by SWI_Th, and approximately 51.1% in those defined by SWI_PM. It has also been noted that a declining trend existed in dryland changes during the early 1990s because of substantially increased precipitation across the Sahel and southern Africa (Maidment et al., 2015).

    Among the continents, Europe had the smallest areal percentage of drylands, containing no hyper-arid or arid regions (Fig. 6). Both SWI_Th and SWI_PM showed obvious interdecadal fluctuations in the evolutions of drylands over Europe during 1901-2014 (Fig. 8c). Two transitions from a negative to positive anomaly occurred during the early 1920s and the mid-2000s, respectively, and a shift from a positive to negative anomaly appeared during the mid-1950s. In contrast to the sustained upward trend in dryland changes caused by PET_Th-only changes, that induced by PET_PM-only changes showed similar interdecadal fluctuations to the evolutions of drylands defined by SWI_PM and SWI_PM with precipitation-only changes. Since the early 2000s, a sharply rising trend was evident among all curves, which could be attributed to decreasing precipitation plus increasing PET.

    As shown in Fig. 8d, interdecadal variabilities of drylands over South America were analogous to those over Europe in terms of cycle and transitions. It was noted that a significant upward trend was apparent in dryland evolutions caused by PET_Th-only changes, whereas that caused by PET_PM-only changes presented a significant downward trend. This was because PET_Th and PET_PM had opposite long-term trends over South America, i.e., a significant upward and downward trend, respectively (Table 2). The wetting effect of increasing precipitation was partly offset and, consequently, there was no distinct long-term trend in the evolutions of drylands defined by SWI_Th; whereas, the wetting effect of increasing precipitation was enhanced and significant contraction of drylands was associated with SWI_PM-based classification.

    For the evolutions of drylands over Oceania (Fig. 8e), consistent interdecadal fluctuations with a downward trend were shown in SWI_Th, SWI_PM and those with precipitation-only changes. However, areal percentages of drylands defined by SWI_Th and SWI_Th with precipitation-only changes had a larger amplitude, and their fluctuations were out of phase with those defined by SWI_PM and SWI_PM with precipitation-only changes since the mid-1990s. Consistent with South America, opposing long-term trends of the two estimates for PET were also found. This finding indicates that precipitation changes dominate the interdecadal variabilities of drylands and the contribution of PET changes is relatively less.

    In contrast to the other continents, there were distinct differences between the evolutions of drylands defined by SWI_Th and SWI_PM over North America; although, a declining trend was shown in both (Fig. 8f). In the classification of SWI_PM, obvious interdecadal fluctuations were found, with two transitions from a negative to positive anomaly, and from a positive to negative anomaly, during the late 1910s and the mid-1950s, respectively. However, areal percentages of drylands defined by SWI_Th showed relatively higher frequency variations and an opposing long-term trend since the mid-1960s. This was because high northern latitudes over North America were classified as humid regions by SWI_PM, but as semi-arid and dry sub-humid regions by SWI_Th (Fig. 5a). Consequently, the areal percentages of semi-arid (dry sub-humid) regions defined by SWI_Th and SWI_PM showed distinct differences during 1901-2014, with a correlation coefficient of only -0.11 (0.12) (Table 4). Also of note was that the interdecadal variations in drylands caused by PET_PM-only changes were comparable with those defined by SWI_PM and SWI_PM with precipitation-only changes, in terms of amplitude and long-term trends, and this was also true in the classification of the three kinds of SWI_Th. This means that the contributions of precipitation and PET changes are approximately equal and offset each other over North America.

    Besides North America, the interdecadal variations of drylands defined by SWI_PM and SWI_PM were analogous and reasonably comparable among the continents, with high correlation coefficients ranging from 0.58 to 0.89 (Table 4). This was because precipitation changes made a major contribution to the interdecadal variabilities of drylands over each continent. Also of note was that the spatial extent of the climatic dry-wet transition zone was very sensitive to PET values, and thus differences attributable to the two estimates for PET tended to manifest there.

    5. Discussion and conclusions

    PET represents the maximum amount of water capable of being lost from the land surface, and is a critical component of the land water cycle and an important input to the SWI in defining global drylands. The Thornthwaite method is a popular way to estimate PET because of the simplicity of the computations required and the minimal demand regarding meteorological variables. The Penman-Monteith method is considered more realistic physically, but it requires some additional meteorological variables. Various estimates of PET in the SWI will certainly induce different classifications of global drylands. Therefore, the present study assessed the sensitivity of the SWI to the two estimates for PET, in the study of the spatial distributions and temporal evolutions of global drylands, especially on interdecadal timescales, for the purpose of providing background and information helpful in selecting an appropriate PET parameterization in the analysis of global drylands.

    Considerable differences were found between the two kinds of PET. In terms of spatial extent, the differences exhibited distinct zonal characteristics. With respect to PET_PM, PET_Th was significantly lower in the subtropics, whereas it was significantly higher in the tropics and high northern latitudes. This is because the Thornthwaite-based PET cannot capture the influence of solar radiation, vapor pressure deficit, and wind speed. Because most drylands are distributed within the subtropics, the underestimation of PET by the Thornthwaite method in this region results in fewer areas being classified as drylands on global and continental scales. The classifications given by SWI_PM and SWI_Th showed drylands as covering approximately 44.8% and 40.4% of the global land area, respectively. In terms of long-term trends, PET_Th exhibited a direct response to the effects of global warming, and showed a significant rising trend over most global land areas. In contrast, regions with increasing PET_PM and global warming both only accounted for approximately 47% of theglobal land area, excluding Antarctica. Compared with SWI_Th, SWI_PM presented a more reasonable and reliable spatial distribution of global drylands, which could be confirmed by the global distribution of barren land.

    Besides North America, broadly similar results, with high correlation coefficients ranging from 0.58 to 0.89, were presented in the interdecadal variabilities of global drylands defined by SWI_PM and SWI_Th. Global expansion of hyper-arid and semi-arid regions, contraction of arid and dry sub-humid regions, and interdecadal fluctuation of drylands, were evident during 1901-2014, and these trends were not very sensitive to differences between the two estimates for PET. This is because precipitation changes make a major contribution in the interdecadal variabilities of drylands, whereas PET changes contribute to a lesser degree. For North America, the spatial extent of drylands defined by SWI_Th was obviously different from that defined by SWI_PM. The north of Alaska and northern Canada, instead of most of the western United States, were classified as semi-arid and dry sub-humid regions by SWI_Th. Consequently, SWI_Th failed to provide a reasonable result for the interdecadal variations in drylands over North America. Additionally, it should be noted that the influences of PET changes on the interdecadal variabilities of semi-arid and dry sub-humid regions were comparable to those of precipitation changes, and thus estimates of PET based on the different methods could yield diverse results.

    It has been noted that the influences of PET changes on the interdecadal variabilities of global drylands have gradually enhanced with global warming. The response of drylands to PET variations in the future could be significantly different from that over the past 100 years. Compared with the Thornthwaite method, the Penman-Monteith method is recommended in the analysis of global drylands in the future, especially in the climatic dry-wet transition zone. Additionally, the applicability of some minimalistic PET models, such as a simplified equation developed by (Hargreaves and Allen, 2003), which can provide very similar estimates to the Penman-Monteith method, in the analysis of global drylands, has yet to be further investigated but should be addressed in future work.

    Acknowledgements. This study was jointly sponsored by the National K&D Program of China (Grant No. 2016YFA0600404), the China Special Fund for Meteorological Research in the Public Interest (Grant No. GYHY201106028 and GYHY201506001-1), the National Natural Science Foundation of China (Grant No.41530532), and the Jiangsu Collaborative Innovation Center for Climate Change.


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    In this study, the water balance methodology introduced by Thornthwaite and Mather (1955) is modified to estimate monthly actual evapotranspiration for 686 stations over China during 1960-2002. The modification is done by replacing the Thornthwaite potential evapotranspiration estimation with the Penman-Monteith method. Temporal trend and spatial distribution of the estimated annual actual evapotranspiration during the past 43 years are analyzed. The results show that (1) the actual evapotranspiration had a decreasing trend in most areas east of 100℃E, and there was an increasing trend in the west and the north parts of northeast China; (2) the spatial distribution of the trend for the actual evapotranspiration is similar to that of the potential evapotranspiration in south China, while the trends are opposite in north China; (3) for most parts of China, the change in precipitation played a key role for the change of estimated actual evapotranspiration, while in southeast China, the change of potential evapotranspiration appeared to be the major factor; and (4) in general, the hydrological cycle was intensified in western China, whereas it was weakened from the Yellow River basin northward.
    DOI:10.1029/2006JD008010      URL     [Cited within:]
    [15] Hargreaves G. H., R. G. Allen, 2003: History and Evaluation of Hargreaves Evapotranspiration Equation.Journal of Irrigation and Drainage Engineering,129,53-63,doi: 10.1061/(ASCE)0733-9437(2003)129:1(53).
    DOI:10.1061/(ASCE)0733-9437(2003)129:1(53)      URL     [Cited within:1]
    [16] Harris I., P. D. Jones, T. J. Osborn, and D. H. Lister, 2014: Updated high-resolution grids of monthly climatic observations-the CRU TS3.10 Dataset.International Journal of Climatology,34,623-642,doi: 10.1002/joc.3711.
    This paper describes the construction of an updated gridded climate dataset (referred to as CRU TS3.10) from monthly observations at meteorological stations across the world's land areas. Station anomalies (from 1961 to 1990 means) were interpolated into 0.5℃ latitude/longitude grid cells covering the global land surface (excluding Antarctica), and combined with an existing climatology to obtain absolute monthly values. The dataset includes six mostly independent climate variables (mean temperature, diurnal temperature range, precipitation, wet-day frequency, vapour pressure and cloud cover). Maximum and minimum temperatures have been arithmetically derived from these. Secondary variables (frost day frequency and potential evapotranspiration) have been estimated from the six primary variables using well-known formulae. Time series for hemispheric averages and 20 large sub-continental scale regions were calculated (for mean, maximum and minimum temperature and precipitation totals) and compared to a number of similar gridded products. The new dataset compares very favourably, with the major deviations mostly in regions and/or time periods with sparser observational data. CRU TS3.10 includes diagnostics associated with each interpolated value that indicates the number of stations used in the interpolation, allowing determination of the reliability of values in an objective way. This gridded product will be publicly available, including the input station series (http://www.cru.uea.ac.uk/ and http://badc.nerc.ac.uk/data/cru/). 2013 Royal Meteorological Society
    DOI:10.1002/joc.3711      URL     [Cited within:]
    [17] Heim R. R., Jr., 2002: A review of twentieth-century drought indices used in the United States.Bull. Amer. Meteor. Soc.,83,1149-1165,doi: 10.1175/1520-0477(2002)083<1149: AROTDI>2.3.CO;2.
    The monitoring and analysis of drought have long suffered from the lack of an adequate definition of the phenomenon. As a result, drought indices have slowly evolved during the last two centuries from simplistic approaches based on some measure of rainfall deficiency, to more complex problem-specific models. Indices developed in the late nineteenth and early twentieth century included such measures as percent of normal precipitation over some interval, consecutive days with rain below a given threshold, formulae involving a combination of temperature and precipitation, and models factoring in precipitation deficits over consecutive days. The incorporation of evapotranspiration as a measure of water demand by Thornthwaite led to the landmark development in 1965 by Palmer of a water budget-based drought index that is still widely used. Drought indices developed since the 1960s include the Surface Water Supply Index, which supplements the Palmer Index by integrating snowpack, reservoir storage, streamflow, and precipitation at high elevations; the Keetch-Byram Drought Index, which is used by fire control managers; the Standardized Precipitation Index; and the Vegetation Condition Index, which utilizes global satellite observations of vegetation condition. These models continue to evolve as new data sources become available. The twentieth century concluded with the development of the Drought Monitor tool, which incorporates Palmer's index and several other (post Palmer) indices to provide a universal assessment of drought conditions across the entire United States. By putting the development of these drought indices into a historical perspective, this paper provides a better understanding of the complex Palmer Index and of the nature of measuring drought in general.
    DOI:10.1175/1520-0477(2002)0832.3.CO;2      URL     [Cited within:3]
    [18] Huang J. P., H. P. Yu, X. D. Guan, G. Y. Wang, and R. X. Guo, 2016a: Accelerated dryland expansion under climate change.Nat. Clim. Change,6,166-171,doi: 10.1038/nclimate2837.
    Drylands are home to more than 38% of the total global population and are one of the most sensitive areas to climate change and human activities(1,2). Projecting the areal change in drylands is essential for taking early action to prevent the aggravation of global desertification(3,4). However, dryland expansion has been underestimated in the Fifth Coupled Model Intercomparison Project (CMIP5) simulations(5) considering the past 58 years (1948-2005). Here, using historical data to bias-correct CMIP5 projections, we show an increase in dryland expansion rate resulting in the drylands covering half of the global land surface by the end of this century. Dryland area, projected under representative concentration pathways (RCPs) RCP8.5 and RCP4.5, will increase by 23% and 11%, respectively, relative to 1961-1990 baseline, equalling 56% and 50%, respectively, of total land surface. Such an expansion of drylands would lead to reduced carbon sequestration and enhanced regional warming(6,7), resulting in warming trends over the present drylands that are double those over humid regions. The increasing aridity, enhanced warming and rapidly growing human population will exacerbate the risk of land degradation and desertification in the near future in the drylands of developing countries, where 78% of dryland expansion and 50% of the population growth will occur under RCP8.5.
    DOI:10.1038/nclimate2837      URL     [Cited within:3]
    [19] Huang J. P., M. X. Ji, Y. K. Xie, S. S. Wang, Y. L. He, and J. J. Ran, 2016b: Global semi-arid climate change over last 60 years.Climate Dyn.,46,1131-1150,doi: 10.1007/s00382-015-2636-8.
    This study analyzes areal changes and regional climate variations in global semi-arid regions over 61 years (1948-2008) and investigates the dynamics of global semi-arid climate change. The results reveal that the largest expansion of drylands has occurred in semi-arid regions since the early 1960s. This expansion of semi-arid regions accounts for more than half of the total dryland expansion. The area of semi-arid regions in the most recent 15 years studied (1990-2004) is 7 % larger than that during the first 15 years (1948-1962) of the study period; this expansion totaled 0.4 10and 1.2 10kmwithin the American continents and in the Eastern Hemisphere, respectively. Although semi-arid expansion occurred in both regions, the shifting patterns of the expansion are different. Across the American continents, the newly formed semi-arid regions developed from arid regions, in which the climate became wetter. Conversely, in the continental Eastern Hemisphere, semi-arid regions replaced sub-humid/humid regions, in which the climate became drier. The climate change in drying semi-arid regions over East Asia is primarily dominated by a weakened East Asian summer monsoon, while the wetting of semi-arid regions over North America is primarily controlled by enhanced westerlies.
    DOI:10.1007/s00382-015-2636-8      URL     [Cited within:1]
    [20] Huang N. E., Z. H. Wu, 2008: A review on Hilbert-Huang transform: Method and its applications to geophysical studies. Rev. Geophys., 46,RG2006, doi: 10.1029/2007 RG000228.
    [1] Data analysis has been one of the core activities in scientific research, but limited by the availability of analysis methods in the past, data analysis was often relegated to data processing. To accommodate the variety of data generated by nonlinear and nonstationary processes in nature, the analysis method would have to be adaptive. Hilbert-Huang transform, consisting of empirical mode decomposition and Hilbert spectral analysis, is a newly developed adaptive data analysis method, which has been used extensively in geophysical research. In this review, we will briefly introduce the method, list some recent developments, demonstrate the usefulness of the method, summarize some applications in various geophysical research areas, and finally, discuss the outstanding open problems. We hope this review will serve as an introduction of the method for those new to the concepts, as well as a summary of the present frontiers of its applications for experienced research scientists.
    DOI:10.1029/2007RG000228      URL     [Cited within:1]
    [21] Hulme M., R. Marsh, and P. D. Jones, 1992: Global changes in a humidity index between 1931-60 and 1961-90.Climate Research,2,1-22,doi: 10.3354/cr002001.
    The desertification assessment presented at the 1977 UN Conference on Desertification used the ratio of annual precipitation to potential evapotranspiration (P/PE) as a simple and appropriate index of humidity to define the drylands of the world. Using global data sets of temperature and precipitation an annual humidity index (HI) was calculated on a 5℃ resolution for two independent 30 yr periods, 1931-60 and 1961-90. PE was calculated from surface air temperature using the Thornthwaite method, adjusted using selected regional data sets of Penman PE estimates for Europe and Sudan. An assessment was made of the sensitivity of dryland boundaries in Africa to recent climatic change. Between 1931-60 and 1961-90, 7.3% of the continent has shifted into a drier moisture zone and only 1.7% into a wetter zone. The net areas of hyper-arid and arid lands in Africa have increased from 1931-60 to 1961-90 by 50 and 3 million hectares respectively.
    DOI:10.3354/cr002001      URL     [Cited within:3]
    [22] Keyantash J., J. A. Dracup, 2002: The quantification of drought: An evaluation of drought indices.Bull. Amer. Meteor. Soc.,83,1167-1180,doi: 10.1175/1520-0477(2002)083 <1191:TQODAE>2.3.CO;2.
    Indices for objectively quantifying the severity of meteorological, agricultural, and hydrological forms of drought are discussed. Indices for each drought form are judged according to six weighted evaluation criteria: robustness, tractability, transparency, sophistication, extendability, and dimensionality. The indices considered most promising for succinctly summarizing drought severity are computed for two climate divisions in Oregon for 24 water years, 1976-99. The assessment determined that the most valuable indices for characterizing meteorological, hydrological, and agricultural droughts are rainfall deciles, total water deficit, and computed soil moisture, respectively.
    DOI:10.1175/1520-0477(2002)0832.3.CO;2      URL     [Cited within:1]
    [23] Li Y., J. P. Huang, M. X. Ji, and J. J. Ran, 2015: Dryland expansion in northern China from 1948 to 2008.Adv. Atmos. Sci.,32,870-876,doi: 10.1007/s00376-014-4106-3.
    This study examines the expansion of drylands and regional climate change in northern China by analyzing the variations in aridity index(AI), surface air temperature(SAT), precipitation and potential evapotranspiration(PET) from 1948 to 2008.It is found that the drylands of northern China have expanded remarkably in the last 61 years. The area of drylands of the last 15 years(1994–2008) is 0.65 × 106km2(12%) larger than that in the period 1948–62. The boundary of drylands has extended eastward over Northeast China by about 2° of longitude and by about 1° of latitude to the south along the middleto-lower reaches of the Yellow River. A zonal band of expansion of semi-arid regions has occurred, stretching from western Heilongjiang Province to southern Gansu Province, while shifts to the east of semi-arid regions in dry subhumid regions have also occurred. Results show that the aridity trend of drylands in northern China is highly correlated with the long-term trend of precipitation and PET, and the expansion of semi-arid regions plays a dominant role in the areal extent of drylands, which is nearly 10 times larger than that in arid and subhumid regions.
    DOI:10.1007/s00376-014-4106-3      URL     [Cited within:2]
    [24] Lioubimtseva E., G. M. Henebry, 2009: Climate and environmental change in arid Central Asia: Impacts,vulnerability, and adaptations. Journal of Arid Environments , 73, 963-977, doi:10.1016/j.jaridenv.2009.04.022.
    Vulnerability to climate change and other hazards constitutes a critical set of interactions between society and environment. As transitional economies emerging from the collapse of the Soviet Union, the republics of Central Asia are particularly vulnerable due to (1) physical geography (which dominated by temperate deserts and semi-deserts), (2) relative underdevelopment resulting from an economic focus on monoculture agricultural exports before 1991, and (3) traumatic social, economic, institutional upheavals following independence. Aridity is expected to increase across the entire Central Asian region, but especially in the western parts of Turkmenistan, Uzbekistan, and Kazakhstan. Temperature increases are projected to be particularly high in summer and fall, accompanied by decreases in precipitation. We examine the concepts of vulnerability, adaptation, and mitigation in the context of climate change in Central Asia. We explore three major aspects of human vulnerability攆ood security, water stress, and human health攁nd propose a set of indicators suitable for their assessment. Non-climatic stresses are likely to increase regional vulnerability to climate change and reduce adaptive capacity due to resource deployment to competing needs.
    DOI:10.1016/j.jaridenv.2009.04.022      URL     [Cited within:1]
    [25] Liu B., Z. G. Ma, 2007: Area change of dry and wet regions in China in the past 45 years.Arid Land Geography,30,7-15,doi: 10.3321/j.issn:1000-6060.2007.01.002. (in Chinese with English abstract)
    The following experiment is based on the precipitation,air temperature,wind,maximum temperature, minimum temperature,and relative humidity data during 1960-2004 of 533 stations in China.According to the wet/dry classification function and the precipitation index,the climatic regions in China are delineated into three types:the arid region,the semi-arid region and the humid region,and furthermore,the area of each region is cal- culated by the histogram individually.The results reveal that no matter with what kind of precipitation index and wet/dry classification function as the reference standard,the total arid area,namely the sum of the arid area and the semi-arid area,shows the expanding trends in China in the past 45 years,and the case is more obvious in the latest 10 years.During the course of analysis,we find the scope of semi-arid area changed most markedly,and it is the sensitive region of arid/wet change.But the following results of two indexes also have differences:the precipita- tion index shows the decreasing trend in the arid and the humid region,and the increasing trend in the semi-arid region,respectively;the wet/dry classification function shows the increasing trend in the arid region,and the de- creasing trend in the semi-arid and the humid region.Through quantitative analysis,we find the area of arid region evaluated by wet/dry classification function is 15% larger than the result of the precipitation index,and the area of semi-arid and humid regions is individually 9% and 6% smaller than the result of precipitation index.Finally,we draw the conclusion that what regions could be evaluated only through the precipitation index and what regions must be analyzed by the wet/dry classification function to judge the status of arid/wet.
    DOI:10.1002/jrs.1570      URL     [Cited within:1]
    [26] Ma Z. G., C. B. Fu, 2003: Interannual characteristics of the surface hydrological variables over the arid and semi-arid areas of northern China.Global and Planetary Change,37,189-200,doi: 10.1016/S0921-8181(02)00203-5.
    The characteristics of the surface humid index (SHI) were analyzed based on 160 station data in China from 1951 to 1998. The surface humid index is defined as SHI=( P)/( P e), where P e is potential evaporation suggested by Thornthwaite's method. The difference between the evolutionary features of the SHI in typical arid regions of north China (Huabei and the northwest) was compared. The results show that the SHI is decreasing (drying trend) in the Huabei region of north China but is increasing in some areas of northwest China (wetting trend). Under regional warming, the drought in the center of north China mainly resulted from the decrease in precipitation and is partly due to the increase in evaporation. A dry period of about 40 years was revealed from the historical data over the area. Increasing evaporation caused by increasing temperature probably intensified the drought in that area, but is not the main reason for the drought. It is the less precipitation that mainly results in the present drought in north China. In addition, the SHI variations in different seasons were also analyzed; the result indicates the notable difference of SHI variation between seasons. Finally, the geographical distribution of annual SHI variation over China was given.
    DOI:10.1016/S0921-8181(02)00203-5      URL     [Cited within:2]
    [27] Ma Z. G., C. B. Fu, 2005: Decadal variations of arid and semi-arid boundary in China.Chinese Journal of Geophysics,48,519-525,doi: 10.3321/j.issn:0001-5733.2005.03.008. (in Chinese with English abstract)
    Decadal variations of arid and semi-arid boundary in China during last 100 years have been analyzed by using Thornthwaite's method. The results indicate that, during the last 50 years, there is a distinguished periodic variation of arid and semi-arid boundary in their locations in the middle part of northeast China and northern part of central northern China, and an obvious trend moving to east. In south part of Shannxi province and central northern China, the boundaries of arid and semi-arid areas have been moving to the south, and there is also a periodic variation in the locations, the boundary of semi-arid area reaches the largest extent to the south. During the last 100 years, there is a trend of the boundaries moving to the south or east, and in the south part of northern China and the central part of northeast China, the extent and intensity of arid and semi-arid area was the largest and severest in the 1920s. The location variation of arid and semi-arid boundaries is closely related to regional warming and precipitation reduction.
    DOI:10.1002/cjg2.690      URL     [Cited within:]
    [28] Ma Z. G., C. B. Fu, 2006: Some evidence of drying trend over northern China from 1951 to 2004.Chinese Science Bulletin,51,2913-2925,doi: 10.1007/s11434-006-2159-0.
    The surface wetness index, Palmer drought sererity index and the retrieval of soil moisture over China were calculated using monthly precipitation and monthly mean surface air temperature. Based on the contrast analysis of the variation of the above three indices and precipitation, the dry/wet spatio-temporal pattern of northern China in the last 54 years was revealed, and the evidence of drying trend over northern China was analyzed, especially. The results show the following four facts: (1) The drying trend is the main characteristic of the eastern part of Northwest China and the central part of North China since the 1980s and it was enhanced in the last 15 years mainly due to the precipitation decrease and the temperature increase; (2) During the last 54 years, there was only one dry/wet shift at the interdecadal scale occurring in the eastern part of Northwest China and the central part of North China in the late 1970s, which was related to 1977/1978 global abrupt change, whereas there were three shifts in Northeast China, one was in the mid 1990s and the other two were in 1965 and 1983, respectively; (3) Unlike the variation trend of other subregions of northern China, the western part of Northwest China is currently located in a relatively wetting period, which is weak-ened due to the temperature increase; (4) The extreme drought frequency is obviously increasing in the eastern part of Northwest China, the central part of North China and Northeast China since the 1980s, which is closely related to the precipitation decrease and temperature increase in these subregions.
    DOI:10.1007/s11434-006-2159-0      URL     [Cited within:]
    [29] Ma Z. G., C. B. Fu, 2007: Global aridification in the second half of the 20th century and its relationship to large-scale climate background.Science in China Series D: Earth Sciences,50,776-788,doi: 10.1007/s11430-007-0036-6.
    The variation in surface wetness index (SWI), which was derived from global gridded monthly precipi- tation and monthly mean surface air temperature datasets of Climatic Research Unit (CRU), from 1951― 2002 over global land was analyzed in this paper. The characteristics of the SWI variation in glob
    DOI:10.1007/s11430-007-0036-6      URL     [Cited within:1]
    [30] Maidment R. I., R. P. Allan, and E. Black, 2015: Recent observed and simulated changes in precipitation over Africa.Geophys. Res. Lett.,42,8155-8164,doi: 10.1002/2015gl065765.
    Abstract Multiple observational data sets and atmosphere-only simulations from the Coupled Model Intercomparison Project Phase 5 are analyzed to characterize recent rainfall variability and trends over Africa focusing on 1983–2010. Data sets exhibiting spurious variability, linked in part to a reduction in rain gauge density, were identified. The remaining observations display coherent increases in annual Sahel rainfall (29 to 4365mm65yr611 per decade), decreases in March–May East African rainfall (6114 to 616565mm65yr611 per decade), and increases in annual Southern Africa rainfall (32 to 4165mm65yr611 per decade). However, Central Africa annual rainfall trends vary in sign (6110 to +3965mm65yr611 per decade). For Southern Africa, observed and sea surface temperature (SST)-forced model simulated rainfall variability are significantly correlated ( r ~0.5) and linked to SST patterns associated with recent strengthening of the Pacific Walker circulation.
    DOI:10.1002/2015GL065765      URL     [Cited within:1]
    [31] McMahon T. A., B. L. Finlayson, and M. C. Peel, 2016: Historical developments of models for estimating evaporation using standard meteorological data.Wiley Interdisciplinary Reviews: Water,3,788-818,doi: 10.1002/wat2.1172.
    Abstract Evaporation plays a key role in the hydrology of a catchment. World-wide actual terrestrial evaporation is approximately two third of terrestrial precipitation. Evaporation is the focus of this study in which we describe the historical developments of models for estimating evaporation from standard meteorological data. Although Aristotle and Descartes made early contributions to understanding evaporation, Perrault is credited with having made the first experimental measurement of evaporation in about 1674 though in fact what he measured was sublimation by recording the loss of weight of a block of ice through time. In 1686, Halley carried out the first direct measurement of the evaporation of liquid water. Following a detailed set of experiments, Dalton in 1802 published an essay describing the relationship between evaporation, vapor pressure deficit, and wind speed which is the forerunner of the mass-transfer equation to estimate open-water evaporation. In 1921, Cummings proposed an approximate energy balance equation which in 1948 Penman combined with a mass-transfer equation based on Dalton's work to develop the Penman equation. A key input was the Bowen ratio published in 1926. Following Penman, the next major development was by Monteith in 1965. He modified Penman's equation for a single leaf to deal with a canopy which led to the Penman揗onteith model and is the basis of the FAO56 Reference Crop model. Priestley and Taylor introduced their model in 1972, which is based on the energy term in Penman's equation, and underpins other models. The application of the Complementary Relationship to estimating regional evaporation is credited separately to Brutsaert and Stricker and to Morton. Budyko offered two important contributions. First, he developed a potential evaporation equation in which the evaporating surface temperature was estimated by iteration, whereas Penman approximated a value from the Clausius揅lapeyron equation. Budyko's second contribution is a simple relationship to estimate runoff and, in turn, mean actual evaporation. For further resources related to this article, please visit the WIREs website.
    DOI:10.1002/wat2.1172      URL     [Cited within:1]
    [32] Mishra A. K., V. P. Singh, 2010: A review of drought concepts.Journal of Hydrology,391,202-216,doi: 10.1016/ j.jhydrol.2010.07.012.
    Owing to the rise in water demand and looming climate change, recent years have witnessed much focus on global drought scenarios. As a natural hazard, drought is best characterized by multiple climatological and hydrological parameters. An understanding of the relationships between these two sets of parameters is necessary to develop measures for mitigating the impacts of droughts. Beginning with a discussion of drought definitions, this paper attempts to provide a review of fundamental concepts of drought, classification of droughts, drought indices, historical droughts using paleoclimatic studies, and the relation between droughts and large scale climate indices. Conclusions are drawn where gaps exist and more research needs to be focussed.
    DOI:10.1016/j.jhydrol.2010.07.012      URL     [Cited within:1]
    [33] Palmer W. C., 1965: Meteorological drought. Research Paper No. 45. U.S. Weather Bureau, Washington, D.C.
    [Cited within:1]
    [34] Qian C., T. J. Zhou, 2014: Multidecadal variability of north China aridity and its relationship to PDO during 1900-2010.J. Climate,27,1210-1222,doi: 10.1175/JCLI-D-13-00235.1.
    North China has undergone a severe drying trend since the 1950s, but whether this trend is natural variability or anthropogenic change remains unknown due to the short data length. This study extends the analysis of dry–wet changes in north China to 1900–2010 on the basis of self-calibrated Palmer drought severity index (PDSI) data. The ensemble empirical mode decomposition method is used to detect multidecadal variability. A transition from significant wetting to significant drying is detected around 1959/60. Approximately 70% of the drying trend during 1960–90 originates from 50–70-yr multidecadal variability related to Pacific decadal oscillation (PDO) phase changes. The PDSI in north China is significantly negatively correlated with the PDO index, particularly at the 50–70-yr time scale, and is also stable during 1900–2010. Composite differences between two positive PDO phases (1922–45 and 1977–2002) and one negative PDO phase (1946–76) for summer exhibit an anomalous Pacific–Japan/East Asian–Pacific patternlike teleconnection, which may develop locally in response to the PDO-associated warm sea surface temperature anomalies in the tropical Indo-Pacific Ocean and meridionally extends from the tropical western Pacific to north China along the East Asian coast. North China is dominated by an anomalous high pressure system at mid–low levels and an anticyclone at 850 hPa, which are favorable for dry conditions. In addition, a weakened land–sea thermal contrast in East Asia from a negative to a positive PDO phase also plays a role in the dry conditions in north China by weakening the East Asian summer monsoon.
    DOI:10.1175/JCLI-D-13-00235.1      URL     [Cited within:1]
    [35] Rezaei M., M. Valipour, and M. Valipour, 2016: Modelling evapotranspiration to increase the accuracy of the estimations based on the climatic parameters.Water Conservation Science and Engineering,1,197-207,doi: 10.1007/s41101-016-0013-z.
    Abstract The potential evapotranspiration was estimated using different mass transfer-based models and was compared with the Food and Agriculture Organization Penman–Monteith model. The results showed that the Albrecht model estimates the potential evapotranspiration better than the other models in the most provinces of Iran (23 provinces). The best values of R2 were 0.9854 and 0.9826 for the Brockamp–Wenner and Albrecht models in Bushehr (BU) and Tehran provinces, respectively. Finally, a list of the best performance of each model has been presented. The best weather conditions (not only for Iran but also for all countries) to use mass transfer-based equations are 23.6–24.6 MJ m612 day611, 12–26 °C, 18–30 °C, 5–21 °C, and 2.50–3.25 m s611 (with the exception of Penman) for solar radiation, mean temperature, maximum temperature, minimum temperature, and wind speed, respectively. The results are also useful for selecting the best model when researchers must apply mass transfer (humidity)-based models on the basis of available data. In addition, the designed maps and categories are applicable for considering the role of climatic parameters in architectural evaluations over Iran.
    DOI:10.1007/s41101-016-0013-z      URL     [Cited within:1]
    [36] Reynolds, J. F., Coauthors, 2007: Global desertification: Building a science for dryland development.Science,316,847-851,doi: 10.1126/science.1131634.
    In this millennium, global drylands face a myriad of problems that present tough research, management, and policy challenges. Recent advances in dryland development, however, together with the integrative approaches of global change and sustainability science, suggest that concerns about land degradation, poverty, safeguarding biodiversity, and protecting the culture of 2.5 billion people can be confronted with renewed optimism. We review recent lessons about the functioning of dryland ecosystems and the livelihood systems of their human residents and introduce a new synthetic framework, the Drylands Development Paradigm (DDP). The DDP, supported by a growing and well-documented set of tools for policy and management action, helps navigate the inherent complexity of desertification and dryland development, identifying and synthesizing those factors important to research, management, and policy communities.
    DOI:10.1126/science.1131634      PMID:17495163      URL     [Cited within:]
    [37] Roderick, M. L. and G. D. Farquhar, 2002: The cause of decreased pan evaporation over the past 50 years. Science, 298, 1410- 1411.
    Abstract Changes in the global water cycle can cause major environmental and socioeconomic impacts. As the average global temperature increases, it is generally expected that the air will become drier and that evaporation from terrestrial water bodies will increase. Paradoxically, terrestrial observations over the past 50 years show the reverse. Here, we show that the decrease in evaporation is consistent with what one would expect from the observed large and widespread decreases in sunlight resulting from increasing cloud coverage and aerosol concentration.
    DOI:10.1126/science.1075390      PMID:12434057      URL     [Cited within:2]
    [38] Sheffield J., E. F. Wood, and M. L. Roderick, 2012: Little change in global drought over the past 60 years.Nature,491,435-438,doi: 10.1038/nature11575.
    Abstract Drought is expected to increase in frequency and severity in the future as a result of climate change, mainly as a consequence of decreases in regional precipitation but also because of increasing evaporation driven by global warming. Previous assessments of historic changes in drought over the late twentieth and early twenty-first centuries indicate that this may already be happening globally. In particular, calculations of the Palmer Drought Severity Index (PDSI) show a decrease in moisture globally since the 1970s with a commensurate increase in the area in drought that is attributed, in part, to global warming. The simplicity of the PDSI, which is calculated from a simple water-balance model forced by monthly precipitation and temperature data, makes it an attractive tool in large-scale drought assessments, but may give biased results in the context of climate change. Here we show that the previously reported increase in global drought is overestimated because the PDSI uses a simplified model of potential evaporation that responds only to changes in temperature and thus responds incorrectly to global warming in recent decades. More realistic calculations, based on the underlying physical principles that take into account changes in available energy, humidity and wind speed, suggest that there has been little change in drought over the past 60 years. The results have implications for how we interpret the impact of global warming on the hydrological cycle and its extremes, and may help to explain why palaeoclimate drought reconstructions based on tree-ring data diverge from the PDSI-based drought record in recent years.
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    [39] Sherwood S., Q. Fu, 2014: A drier future? Science,343, 737-739, doi: 10.1126/science.1247620.
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    [40] Shuttleworth W. J., J. S. Wallace, 1985: Evaporation from sparse crops-An energy combination theory.Quart. J. Roy. Meteor. Soc.,111,839-855,doi: 10.1002/qj.49711146910.
    Abstract A one-dimensional model is adopted to describe the energy partition of sparse crops. Theoretical development of this model yields a combination equation which describes evaporation in terms of controlling resistances associated with the plants, and with the soil or water in which they are growing. the equation provides a simple but physically plausible description of the transition between bare substrate and a closed canopy. Although the aerodynamic transfer resistances for incomplete canopies have, as yet, no experimental justification, typical values, appropriate to a specimen agricultural crop and soil, are shown to have limited sensitivity in the model. Processes which require further study if the equation is to be used to calculate evaporation throughout a crop season are also discussed.
    DOI:10.1002/qj.49711146910      URL     [Cited within:2]
    [41] Tegos A., N. Malamos, and D. Koutsoyiannis, 2015: A parsimonious regional parametric evapotranspiration model based on a simplification of the Penman-Monteith formula.J. Hydrol.,524,708-717,doi: 10.1016/j.jhydrol.2015.03.024.
    Evapotranspiration is a key hydrometeorological process and its estimation is important in many fields of hydrological and agricultural sciences. Simplified estimation proves very useful in absence of a complete data set. In this respect, a parametric model based on simplification of the Penman–Monteith formulation is presented. The basic idea of the parametric model is the replacement of some of the variables and constants that are used in the standard Penman–Monteith model by regionally varying parameters, which are estimated through calibration. The model is implemented in various climates on monthly time step (USA, Germany, Spain) and compared on the same basis with four radiation-based methods (Jensen–Haise, McGuiness and Bordne, Hargreaves and Oudin) and two temperature-based (Thornthwaite and Blaney–Criddle). The methodology yields very good results with high efficiency indexes, outperforming the other models. Finally, a spatial analysis including the correlation of parameters with latitude and elevation together with their regionalization through three common spatial interpolation techniques along with a recent approach (Bilinear Surface Smoothing), is performed. Also, the model is validated against Penman–Monteith estimates in eleven stations of the well-known CIMIS network. The total framework which includes the development, the implementation, the comparison and the mapping of parameters illustrates a new parsimonious and high efficiency methodology in the assessment of potential evapotranspiration field.
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    [42] Thornthwaite C. W., 1948: An approach toward a rational classification of climate.Geographical Review,38,55-94,doi: 10.2307/210739.
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    [43] Trenberth K. E., A. G. Dai, G. van der Schrier, P. D. Jones, J. Barichivich, K. R. Briffa, and J. Sheffield, 2014: Global warming and changes in drought.Nat. Clim. Change,4,17-22,doi: 10.1038/nclimate2067.
    Several recently published studies have produced apparently conflicting results of how drought is changing under climate change. The reason is thought to lie in the formulation of the Palmer Drought Severity Index (PDSI) and the data sets used to determine the evapotranspiration component. Here, we make an assessment of the issues with the PDSI in which several other sources of discrepancy emerge, not least how precipitation has changed and is analysed. As well as an improvement in the precipitation data available, accurate attribution of the causes of drought requires accounting for natural variability, especially El Ni o/Southern Oscillation effects, owing to the predilection for wetter land during La Ni a events. Increased heating from global warming may not cause droughts but it is expected that when droughts occur they are likely to set in quicker and be more intense.
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    [45] Valipour M., 2013: Use of surface water supply index to assessing of water resources management in Colorado and Oregon, US. Advances in Agriculture, Sciences and Engineering Research, 3, 631- 640.
    ABSTRACT Being aware of hydrological conditions in each region can help to thoughtful planning for reasonable allocation of water resources and agricultural water management. Surface water supply index (SWSI) is one of the most importance hydrologic parameters for study of drought and flood periods in basins. Author has used thirty years historical data from 1982 to 2011 for surviving of SWSI in two different climates includes 7 basins of Colorado (continental climate) and 14 basins of Oregon (mild climate) in United States. There was probability of being in 11 different hydrologic conditions from extremely wet to extreme drought, due to the variation of SWSI in each year.
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    [46] Valipour M., M. A. Gholami Sefidkouhi, and M. Raeini-Sarjaz, 2017: Selecting the best model to estimate potential evapotranspiration with respect to climate change and magnitudes of extreme events.Agricultural Water Management,180,50-60,doi: 10.1016/j.agwat.2016.08.025.
    There are a lot of investigations to select the best model to estimate potential evapotranspiration (ET o ) in a certain climate or region. In this paper, the types of climate include arid, semiarid, Mediterranean, and very humid. A spatial and temporal study of the ET o is the aim of this paper, according to the peak and low events (extreme events) and climate change alarms. For this purpose, 50 years (1961–2010) monthly meteorological data of 18 regions in Iran, with various climates, were collected. For estimating the ET o , 5 temperature61based, 5 radiation61based, and 5 mass transfer61based models, were selected with respect to better performance of them in different climates on the basis of past investigations. The results will especially be useful in the regions where the monthly (rather than daily) meteorological data are available. The results appear that the Blaney61Criddle (BC) (root mean square error (RMSE)02=021.3202mm02day 611 ) and Abtew (Ab) (RMSE02=020.8302mm02day 611 ) are the best models for estimating the ET o in the arid and semiarid regions, respectively. While, modified Hargreaves61Samani 2 (MHS2) represents the best performance in the Mediterranean and very humid regions (RMSE02=020.3002mm02day 611 & 0.6802mm02day 611 , respectively). In addition, radiation—and mass transfer61based models are proper tools to estimate the ET o in warm and cold seasons on the basis of improving values of evaluation indices in 40% and 70% of the study area, respectively. Increasing air temperature and decreasing minimum relative humidity for best performance of most models alarms a climate change in most regions of Iran. As a result, the radiation61based models were adapted with climate change better than the temperature61based and particularly mass transfer61based models. Finally, a step by step flowchart was presented for selecting the best model to estimate the ET o in each climate.
    DOI:10.1016/j.agwat.2016.08.025      URL     [Cited within:3]
    [47] van der Schrier, G., P. D. Jones, K. R. Briffa, 2011: The sensitivity of the PDSI to the Thornthwaite and Penman-Monteith parameterizations for potential evapotranspiration. J. Geophys. Res., 116,D03106, doi: 10.1029/2010JD015001.
    Potential evapotranspiration (PET) is one of the inputs to the Palmer Drought Severity Index (PDSI). A common approach to calculating PDSI is to use the Thornthwaite method for estimating PET because of its readily available input data: monthly mean temperatures. PET estimates based on Penman-type approaches are considered to be more physically realistic, but require more diverse input data. This study assesses the differences in global PDSI maps using the two estimates for PET. Annually accumulated PET estimates based on alternative Thornthwaite and Penman-Monteith, parameterizations have very different amplitudes. However, we show that PDSI values based on the two PET estimates are very similar, in terms of correlation, regional averages, trends, and in terms of identifying extremely dry or wet months. The reason for this insensitivity to the method of calculating PET relates to the calculations in the simple water balance model which is at the heart of the PDSI algorithm. It is shown that in many areas, actual evapotranspiration is limited by the availability of soil moisture and is at markedly lower levels compared to its potential value. In other areas, the water balance does change, but the quantity central to the calculation of the PDSI is, by construction, a reflection of the actual precipitation, which makes it largely insensitive to the use of the Thornthwaite PET rather than the Penman-Monteith PET. A secondary reason is that the impact of PET as input to a scaling parameter in the PDSI algorithm is very modest compared to the more dominant influence of the precipitation.
    DOI:10.1029/2010JD015001      URL     [Cited within:2]
    [48] van der Schrier, G., J. Barichivich, K. R. Briffa, P. D. Jones, 2013: A scPDSI-based global data set of dry and wet spells for 1901-2009.J. Geophys. Res.,118,4025-4048,doi: 10.1002/jgrd.50355.
    Global maps of monthly self-calibrating Palmer Drought Severity Index (scPDSI) have been calculated for the period 1901-2009 based on the CRU TS 3.10.01 data sets. This work addresses some concerns with regard to monitoring of global drought conditions using the traditional Palmer Drought Severity Index. First, the scPDSI has a similar range of variability in diverse climates making it a more suitable metric for comparing the relative availability of moisture in different regions. Second, the more physically based Penman-Monteith parameterization for potential evapotranspiration is used, calculated using the actual vegetation cover rather than a reference crop. Third, seasonal snowpack dynamics are considered in the water balance model. The leading mode of variability in the new data set represents a trend towards drying conditions in some parts of the globe between 1950 and 1985 but accounts for less than 9% of the total variability. Increasing temperature and potential evapotranspiration explain part of the drying trend. However, local trends in most of the drying regions are not significant. Previously published evidence of unusually strong or widespread drying is not supported by the evidence in this work. A fundamental aspect of the calculation of scPDSI is the selection of a calibration period. When this period does not include the most recent part of the record, trends towards more extreme conditions are amplified. It is shown that this is the principal reason for different published interpretations of the scale of recent global drying and not, as recently claimed, the use of simplified forcing data.
    DOI:10.1002/jgrd.50355      URL     [Cited within:1]
    [49] Vicente-Serrano S. M., S. Beguería, and J. I. López-Moreno, 2010a: A multiscalar drought index sensitive to global warming: The standardized precipitation evapotranspiration index.J. Climate,23,1696-1718,doi: 10.1175/2009JCLI2909.1.
    DOI:10.1175/2009JCLI2909.1      URL     [Cited within:]
    [50] Vicente-Serrano S. M., S. Beguerá, J. I. López-Moreno, M. Angulo, and A. El Kenawy, 2010b: A new global 0.5鎺� gridded dataset (1901-2006) of a multiscalar drought index: Comparison with current drought index datasets based on the palmer drought severity index. Journal of Hydrometeorology,11, 1033-1043, doi: 10.1175/2010JHM1224.1.
    ABSTRACT A monthly global dataset of a multiscalar drought index is presented and compared in terms of spatial and temporal variability with the existing continental and global drought datasets based on the Palmer drought severity index (PDSI). The presented dataset is based on the standardized precipitation evapotranspiration index (SPEI). The index was obtained using the Climatic Research Unit (CRU) TS3.0 dataset at a spatial resolution of 0.5 degrees. The advantages of the new dataset are that (i) it improves the spatial resolution of the unique global drought dataset at a global scale; (ii) it is spatially and temporally comparable to other datasets, given the probabilistic nature of the SPEI; and, in particular, (iii) it enables the identification of various drought types, given the multiscalar character of the SPEI. The dataset is freely available on the Web page of the Spanish National Research Council (CSIC) in three different formats [network Common Data Form (netCDF), binary raster, and plain text].
    DOI:10.1175/2010JHM1224.1      URL     [Cited within:]
    [51] Vicente-Serrano, S. M., Coauthors, 2012: Performance of drought indices for ecological, agricultural, and hydrological applications. Earth Interactions, 16,10, doi: 10.1175/ 2012EI000434.1.
    In this study, the authors provide a global assessment of the performance of different drought indices for monitoring drought impacts on several hydrological, agricultural, and ecological response variables. For this purpose, they compare the performance of several drought indices [the standardized precipitation index (SPI); four versions of the Palmer drought severity index (PDSI); and the standardized precipitation evapotranspiration index (SPEI)] to predict changes in streamflow, soil moisture, forest growth, and crop yield. The authors found a superior capability of the SPEI and the SPI drought indices, which are calculated on different time scales than the Palmer indices to capture the drought impacts on the aforementioned hydrological, agricultural, and ecological variables. They detected small differences in the comparative performance of the SPI and the SPEI indices, but the SPEI was the drought index that best captured the responses of the assessed variables to drought in summer, the season in which more drought-related impacts are recorded and in which drought monitoring is critical. Hence, the SPEI shows improved capability to identify drought impacts as compared with the SPI. In conclusion, it seems reasonable to recommend the use of the SPEI if the responses of the variables of interest to drought are not known a priori.
    DOI:10.1175/2012EI000434.1      URL     [Cited within:1]
    [52] Wilks D. S., 2005: Statistical Methods in the Atmospheric Sciences (International Geophysics). 2nd ed. Academic Press.
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    [53] Willmott C. J., C. M. Rowe, and Y. Mintz, 1985: Climatology of the terrestrial seasonal water cycle.J. Climatol.,5,589-606,doi: 10.1002/joc.3370050602.
    Calculations of the spatial and seasonal variations of the continental fields of snow-cover, soil moisture and evapotranspiration are presented and interpreted. The calculations were made with a water budget analysis that is based on observed average monthly precipitation and an estimate of potential evapotranspiration derived from observed average monthly surface temperature, using a modified version of the method of Thornthwaite. Monthly average water budget analyses were made for 13,332 stations over the globe and, then spatially interpolated to a regular grid at 1° by 1° latitude-longitude intervals. From the monthly fields on a 4° by 5° subset of the 1° by 1° grid, the annual mean and standard deviation as well as the first and second annual harmonics were extracted and are displayed on global maps. Of the three fields, soil moisture has the largest space-time variation; snow-cover the smallest variation; and evapotranspiration an intermediate level of variation.
    DOI:10.1002/joc.3370050602      URL     [Cited within:1]
    [54] Wu Z. H., N. E. Huang, 2009: Ensemble empirical mode decomposition: A noise-assisted data analysis method.Advances in Adaptive Data Analysis,1,1-41,doi: 10.1142/ S1793536909000047.
    A new Ensemble Empirical Mode Decomposition (EEMD) is presented. This new approach consists of sifting an ensemble of white noise-added signal (data) and treats the mean as the final true result. Finite, not infinitesimal, amplitude white noise is necessary to force the ensemble to exhaust all possible solutions in the sifting process, thus making the different scale signals to collate in the proper intrinsic mode functions (IMF) dictated by the dyadic filter banks. As EEMD is a timeu2013space analysis method, the added white noise is averaged out with sufficient number of trials; the only persistent part that survives the averaging process is the component of the signal (original data), which is then treated as the true and more physical meaningful answer. The effect of the added white noise is to provide a uniform reference frame in the timeu2013frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF. With this ensemble mean, one can separate scales naturall...
    DOI:10.1142/S1793536909000047      URL     [Cited within:1]
    [55] Wu Z. H., N. E. Huang, J. M. Wallace, B. V. Smoliak, and X. Y. Chen, 2011: On the time-varying trend in global-mean surface temperature.Climate Dyn.,37,759-773,doi: 10.1007/s00382-011-1128-8.
    The Earth has warmed at an unprecedented pace in the decades of the 1980s and 1990s (IPCC in Climate change 2007: the scientific basis, Cambridge University Press, Cambridge, 2007 ). In Wu et al. (Proc Natl Acad Sci USA 104:1488914894, 2007 ) we showed that the rapidity of the warming in the late twentieth century was a result of concurrence of a secular warming trend and the warming phase of a multidecadal (~65-year period) oscillatory variation and we estimated the contribution of the former to be about 0.08℃C per decade since ~1980. Here we demonstrate the robustness of those results and discuss their physical links, considering in particular the shape of the secular trend and the spatial patterns associated with the secular trend and the multidecadal variability. The shape of the secular trend and rather globally-uniform spatial pattern associated with it are both suggestive of a response to the buildup of well-mixed greenhouse gases. In contrast, the multidecadal variability tends to be concentrated over the extratropical Northern Hemisphere and particularly over the North Atlantic, suggestive of a possible link to low frequency variations in the strength of the thermohaline circulation. Depending upon the assumed importance of the contributions of ocean dynamics and the time-varying aerosol emissions to the observed trends in global-mean surface temperature, we estimate that up to one third of the late twentieth century warming could have been a consequence of natural variability.
    DOI:10.1007/s00382-011-1128-8      URL     [Cited within:1]
    [56] Xia J. J., Z. W. Yan, and P. L. Wu, 2013: Multidecadal variability in local growing season during 1901-2009.Climate Dyn.,41,295-305,doi: 10.1007/s00382-012-1438-5.
    Global warming exerts a lengthening effect on the growing season, with observational evidences emerging from different regions over the world. However, the difficulty for a global overview of this effect for the last century arises from limited availability of the long-term daily observations. In this study, we find a good linear relationship between the start (end) date of local growing season (LGS) and the monthly mean temperature in April (October) using the global gridded daily temperature dataset for 1960-1999. Using homogenized daily temperature records from nine stations where the time series go back to the beginning of the twentieth century, we find that the rate of change in the start (end) date of the LGS for per degree warming in April (October) mean temperature keeps nearly constant throughout the time. This enables us to study LGS changes during the last century using global gridded monthly mean temperature data. The results show that during the period 1901-2009, averaged over the observation areas, the LGS length has increased by a rate of 0.89 days decade, mainly due to an earlier start (芒藛0.58 days decade). This is smaller than those estimates for the late half of the twentieth century, because of multidecadal climate variability (MDV). A MDV component of the LGS index series is extracted by using Ensemble Empirical Mode Decomposition method. The MDV exhibits significant positive correlation with the Atlantic Multi-decadal Oscillation (AMO) over most of the Northern Hemisphere lands, but negative in parts of North America and Western Asia for start date of LGS. These are explained by analyzing differences in atmospheric circulation expressed by sea level pressure departures between the warm and cool phases of AMO. It is suggested that MDV in association with AMO accelerates the lengthening of LGS in Northern Hemisphere by 53 % for the period 1980-2009.
    DOI:10.1007/s00382-012-1438-5      URL     [Cited within:1]
    [57] Xu C.-Y., L. B. Gong, T. Jiang, D. L. Chen, and V. P. Singh, 2006: Analysis of spatial distribution and temporal trend of reference evapotranspiration and pan evaporation in Changjiang (Yangtze River) catchment.J. Hydrol.,327,81-93,doi: 10.1016/j.jhydrol.2005.11.029.
    In this study the Penman–Monteith reference evapotranspiration, pan evaporation measured by a 2002cm pan, and pan coefficient, i.e., the ratio of Penman–Monteith evapotranspiration to pan evaporation, at 150 meteorological stations during 1960–2000 in the Changjiang (Yangtze River) catchment in China are calculated, compared and regionally mapped. Their spatial distributions and temporal variations are examined and the causes for the variations are discussed. The spatial distributions of temporal trends in the reference evapotranspiration as well as in the meteorological variables that determine evapotranspiration are analyzed. The contributions of various meteorological variables to the temporal trend detected in the reference evapotranspiration and pan evaporation are then determined. The results show that: (1) the spatial distributions of reference evapotranspiration and pan evaporation are roughly similar. Spatial correlation coefficients between the reference evapotranspiration and the pan evaporation are high for both the seasonal and annual values. The temporal correlation between the two estimates is higher in the lower (humid) region than in the upper (semi-arid) region. The spatial distribution pattern of the pan coefficient is significantly influenced by wind speed and relative humidity in the region. Higher values of the pan coefficient were found in the central area of the catchment with a relatively high humidity (as compared with the upper area) and a very low wind speed (as compared with other areas); (2) for the whole catchment, there is a significant decreasing trend in both the reference evapotranspiration and the pan evaporation, which is mainly caused by a significant decrease in the net total radiation and to a lesser extent by a significant decrease in the wind speed over the catchment. No temporal trend is detected for the pan coefficient; (3) sensitivity analysis shows that the reference evapotranspiration is most sensitive to the net total radiation, followed by relative humidity, air temperature and wind speed.
    DOI:10.1016/j.jhydrol.2005.11.029      URL     [Cited within:2]
    [58] Yuan S. S., S. M. Quiring, 2014: Drought in the U.S.great plains (1980-2012): A sensitivity study using different methods for estimating potential evapotranspiration in the Palmer Drought Severity Index. J. Geophys. Res.,119,10 996-11 010,doi: 10.1002/2014JD021970.
    Abstract The Palmer Drought Severity Index (PDSI) has been widely used to evaluate drought conditions since it was developed in 1965. In the original formulation of the PDSI, potential evapotranspiration (PET) was estimated using the Thornthwaite equation. This study evaluates how using more physically based approaches for estimating PET influences the depiction of drought conditions over the U.S. Great Plains from 1980 to 2012. Both the Penman-Monteith equation and the two-source PET model are compared to the original Thornthwaite-based PDSI. The differences in PET between the three methods are much larger than the resulting differences in the PDSI. Results show that the original PDSI has a stronger drying trend than versions of PDSI that use more physically based methods of estimating PET. Spatially, all three versions of the PDSI show similar distributions of drying and wetting trends; however, there are significant regional variations that appear to be associated with land cover. PDSI and observed soil moisture in the top 1塵 are moderately correlated (correlation coefficient is ~0.5) over the U.S. Great Plains, except in Texas (correlation coefficient is ~0.3). Although all three approaches result in a similar area-averaged PDSI for the U.S. Great Plains, there are large differences in the area affected by drought, especially during extreme drought events.
    DOI:10.1002/2014JD021970      URL     [Cited within:3]
    [59] Zhang J., F. B. Sun, J. J. Xu, Y. N. Chen, Y.-F. Sang, and C. M. Liu, 2016: Dependence of trends in and sensitivity of drought over China (1961-2013) on potential evaporation model.Geophys. Res. Lett.,43,206-213,doi: 10.1002/2015GL067473.
    The Palmer Drought Severity Index (PDSI) can lead to controversial results in assessing droughtsresponding to global warming. Here we assess recent changes in the droughts over China (19612013) usingthe PDSI with two different estimates, i.e., the Thornthwaite (PDSI_th) and Penman-Monteith (PDSI_pm)approaches. We found that droughts have become more severe in the PDSI_th but slightly lessened inthe PDSI_pm estimate. To quantify and interpret the different responses in the PDSI_th and PDSI_pm, wedesigned numerical experiments and found that drying trend of the PDSI_th responding to the warmingalone is 3.4 times higher than that of the PDSI_pm, and the latter was further compensated by decreases inwind speed and solar radiation causing the slightly wetting in the PDSI_pm. Interestingly, we found thatinterbasin difference in the PDSI_th and PDSI_pm responses to the warming alone tends to be larger inwarmer basins, exponentially depending on mean temperature.
    DOI:10.1002/2015GL067473      URL     [Cited within:1]
    [60] Zhou M. C., H. Ishidaira, and K. Takeuchi, 2008: Comparative study of potential evapotranspiration and interception evaporation by land cover over Mekong basin.Hydrological Processes,22,1290-1309,doi: 10.1002/hyp.6939.
    Potential evapotranspiration is a key input to hydrological models. Its estimation has often been via the Penman-Monteith (P-M) equation, most recently in the form of an estimate of reference evapotranspiration (RET) as recommended by FAO-56. In this article, the Shuttleworth-Wallace (S-W) model is implemented to estimate the potential evapotranspiration from soil moisture (PET) and the potential evaporation from interception (PET0) directly in a form that recognizes vegetation diversity and temporal development without reference to experimental measurements and without calibration. The threshold values of vegetation parameters are drawn from the literature based on the International Geosphere-Biosphere Programme (IGBP) land cover classification. The spatial and temporal variation of the leaf area index (LAI) of vegetation is derived from the composite National Oceanic and Atmospheric Administration - Advanced Very High Resolution Radiometer (NOAA-AVHRR) normalized difference vegetation index (NDVI) using a method based on the SiB2 model, and the Climate Research Unit (CRU) database is used to provide the required meteorological data. All these data inputs are publicly and globally available. Consequently, the implementation of the S-W model developed in this study is applicable at the global scale, an essential requirement if it is to be applied in data-poor or ungauged large basins. A comparison is made between the FAO-56 method and the S-W model when applied to the Mekong River basin for the period 1981-2000. The resulting estimates of RET and PET and their association with vegetation types and LAI are examined over the whole basin both annual and monthly and at five specific points. The effect of NDVI on the PET estimate is further evaluated by replacing the monthly NDVI product with the 10-day product. Multiple regression relationships between monthly PET, RET, LAI, and climatic variables are explored for categories of vegetation types. The estimated RET is a good climatic index that adequately reflects the temporal change and spatial distribution of climate over the basin, but the PET estimated using the S-W model not only reflects the change in climate but also the vegetation distribution and the development of vegetation in response to climate. Although good statistical relationships can be established between PET, RET, and/or climatic variables, applying these relationships will likely result in large errors because of the strong non-linearity and scatter between the PET and the LAI of the vegetation. It is concluded that use of the implementation of the S-W model described in this study results in a physically sound estimate of PET, which accounts for changing land surface conditions. Copyright 2008 John Wiley & Sons, Ltd.
    DOI:10.1002/hyp.6939      URL     [Cited within:1]
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    Key words
    potential evapotranspiration
    global drylands

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