Xiangying Xu,∗,∗∗,∗∗∗,∗∗∗∗ Xinkai Zhu,∗,∗∗∗ Yonglong Zhang,∗∗∗∗ Chunyan Li,∗,∗∗∗ Jinfeng Ding,∗,∗∗∗ Junwu Zhu,∗∗∗∗ Bin Li,∗∗∗∗ and Wenshan Guo,∗,∗∗∗
[1] M. Zampieri, A. Ceglar, F. Dentener, and A. Toreti, Wheatyield loss attributable to heat waves, drought and water excessat the global, national and subnational scales, EnvironmentalResearch Letters, 12(6), 2017, 064008. [4],[22], [23], we calculated the dekad-scale SPI by the followingsteps:Firstly, the multi-decadal precipitations are accumu-lated and denoted by P sequences. Because the wholegrowing periods of winter wheat in Northern and SouthernJiangsu are 24 and 22 dekads, respectively, we selected sixdifferent dekad scales from 1 to 6 to investigate the shorttimescale SPI.Secondly, the parameters of P sequences under gammadistribution are estimated. L-moment of the P sequencesis used to obtain the parameters ing (x) =1βαΓ (α)xα−1e−x/β(1)where g(x) is the probability density function of gammadistribution, fitting to the frequency distribution of Psequence. α and β are the shape and scale parameters, andΓ(α) is the gamma function. The calculation of L-momentsand the parameters is performed with lmomco package ofR software.Once the parameters are determined, SPI values canbe computed under standard normal distribution whichis transformed from the gamma probability distributionfunction. The normalized index obtained temporal andspecial comparability.2.3 Calculations of SPEI with Two MethodsThe calculation of SPEI with dekad scales is similar to thatof SPI, except that the P sequences are replaced by climaticwater balance sequences, which are the differences betweenprecipitations and ET0. In addition to precipitations aswater input, ET0 is incorporated in SPEI to quantify thewater output. However, the calculation of ET0 is so com-plex that it involves numerous parameters. Two widelyused methods, Penman–Monteith method (PM) and Har-greaves method (HG), are applied in our study to obtainET0. The PM method is considered as a standardizedmethod for computing ET0 because of its high accuracy.The calculation is using [24], [25]:ETPM =0.408Δ (Rn − G) + γ 900T +273 U2 (es − ea)Δ + γ (1 + 0.34U2)(2)where ETP M denotes the ET0 calculated by PM method;Δ is the slope of the vapor pressure curve; Rn is the netradiation obtained by difference between net short waveradiation absorbed and net long wave radiation emitted. Gis the soil heat flux density, which is small and negligible.γ is the psychometric constant. T and U2 are the averagedaily temperature and the wind speed at 2 m above ground,respectively. es and ea are the saturated vapor pressureand actual vapor pressure.HG method is another widely used method that re-quires relatively fewer parameters than PM method [25],[26]. The HG equation isETHG = 0.0023Ra(Tmax − Tmin)0.5(Ta + 17.8) (3)where ETHG denotes the ET0 calculated by HG method.Tmax, Tmin, and Ta are the maximum, minimum, and mean480Table 1Key Growing Stages of Winter Wheat in Jiangsu Province. NIC is the North Irrigation Channel in JiangsuRegion Seedling (S1) Over-Wintering (S2) Reviving to Anthesis (S3) After Anthesis (S4)North of the NIC Oct. 11st ∼ Dec. 20th Dec. 21st ∼ Feb. 20th Feb. 21st ∼ Apr.30th May. 1st ∼ Jun. 10thSouth of the NIC Oct. 21st ∼ Dec. 31th Jan. 1st ∼ Feb. 10th Feb. 11th ∼ Apr. 20th Apr. 21st ∼ May. 30thFigure 1. Locations of the meteorological sites in Jiangsu province.air temperature of the day. Ra is the theoretical solarradiation, which is calculated usingRa = (24 × 60/π) × Gsc × dr × (ωs × sin(ϕ) × sin(δ)+ cos(ϕ) × cos(δ) × sin(ωs)) (4)where J is the Julian day. Gsc is the solar constant,Gsc = 0.082 (MJ/(m2· min)). dr is the average distancebetween the Sun and the Earth. ωs is the hourly angle ofSun rising. ϕ is the latitude, δ is the solar declination, andthey are both in radians [5].With the values of ET0 computed by two differentmethods, the differences between precipitation and ET0could be calculated to obtain the climatic water balancesequences, denoted by D. It is different from SPI that theD sequence is modelled using a three-parameter log-logisticdistribution, whose probability density function f(x) isf (x) =βαx − yαβ−11 +x − yαβ −2(5)where α, β, and γ are the scale, shape, and location param-eters. Similar to the procedures used in computing SPI,the parameters of log-logistic distribution are estimatedby L-moment, and then the SPEI values are computedas the standardized values of the probability distributionfunction.2.4 Yield Data De-trendingWith the improvement of varieties and cultivation tech-niques, the yield per unit area of winter wheat increasedyear by year in the research area. Therefore, in orderto analyse the relationships between wheat yields and thewater conditions, it is necessary to de-trend the yields.Among several de-trend methods available, the first-orderdifference method is simple and objective and is able to re-move the increasing characteristics of yield series and makeit a stationary sequence [3], [27]. With the de-trendedwheat yields, the correlation analysis and regression anal-ysis between yields and SPI or SPEI values are carried outto investigate the relationship.48140005000600070002009 2010 2011 2012 2013 2014YearOriginalwheatyield(kg/ha)-600-30003006002010 2011 2012 2013 2014YearDe-trendedwheatyield(kg/ha)Site12345678910111213141516171819202122232425Figure 2. The de-trended wheat yields of 25 sites.2009 2010 2011 2012 2013 2014yearTotalprecipitiations0100200300400500600Northern JiangsuSouthern Jiangsua2009 2010 2011 2012 2013 2014yearTotalprecipitiations050100150200250300S1S2S3S4S1S2S3S4Northern Jiangsu2009 2010 2011 2012 2013 2014yearTotalprecipitiations050100150200250300S1S2S3S4Southern JiangsuFigure 3. Site-averaged total precipitations of Northern and Southern Jiangsu during the whole growing stages (a) and fourkey growth stages of winter wheat in Jiangsu.3. Results3.1 De-trended Wheat YieldsThe de-trended wheat yields of 25 sites between 2010 and2014 are shown in Fig. 2. Although the year span of originalyield sequences is too small to show obvious upward trends,the first-order difference of yields weakens the effects oftechnology and reflects much more influences of randomfactors including water conditions. The de-trended yieldsfor all sites range from −600 to 600 kg/ha, exhibitingrandom fluctuations.3.2 Moisture Conditions of the Wheat-GrowingStagesThe site-averaged total precipitations of Northern andSouthern Jiangsu during the whole growing stages andfour key growth stages of the winter wheat are displayedin Fig. 3. It shows that the precipitations of the wholegrowing stages are higher in the southern sites than in thenorthern sites within all 6 years. In 2011, both regions hada low rainfall. Comparing four key growing stages, rainfallin S4 of the north and in S3 of the south is more prominentthan other periods during these years.482-2-10122008 2009 2010 2011 2012 2013 2014Northern Jiangsu SPI-1-2-10122008 2009 2010 2011 2012 2013 2014Southern Jiangsu SPI-1-2-10122008 2009 2010 2011 2012 2013 2014Northern Jiangsu SPEIHG-1-2-10122008 2009 2010 2011 2012 2013 2014Southern Jiangsu SPEIHG-1-2-10122008 2009 2010 2011 2012 2013 2014Northern Jiangsu SPEIPM-1-2-10122008 2009 2010 2011 2012 2013 2014Southern Jiangsu SPEIPM-1Figure 4. SPI and SPEI of 1-dekad scale in Northern and Southern Jiangsu.The site-averaged SPI and SPEI of 1-dekad scale arecalculated and shown in Fig. 4. It is obvious that the SPI-1has more negative values than SPEIHG-1 and SPEIP M -1 both in the north and in the south. When there isa lack of precipitation, SPI will be calculated negative,and if the value is less than −0.5, drought is indicated.However, when considering the evapotranspiration, thelow precipitation and low evapotranspiration may lead toan opposite wet condition in SPEI. Therefore, in severalcases, such as in 2011, the values of SPI-1 and SPEI-1 areopposite in positive and negative symbols.3.3 Correlations between Wheat Yields and SPI orSPEISix different dekad-scale SPI sequences have been calcu-lated. To analyse the relationships between the SPI andthe wheat yields, the first-order differences of SPI valuesshould be obtained. Then the Spearman correlation coef-ficients between de-trended wheat yields and SPI are com-puted and shown in Fig. 5. The northern and southernstations are calculated separately because of the differentlengths of wheat growth periods. In Northern Jiangsu,the negative correlation coefficients of 3-dekad scale SPI inthe first dekad of January (Jan-1) are the most remark-able (−0.77), while the positive correlation coefficients of3-dekad scale SPI in the third dekads of October are thehighest (0.68). In southern Jiangsu, the maximum is 0.24and the minimum is −0.35, which appeared in March andNovember, respectively.Similarly, SPEI values using HG method are computedwith six different scales. The correlation coefficients areshown in Fig. 6. In the north, the highest (0.73) and thelowest (−0.68) correlation coefficients appear in the lastdekad of October, the second dekad of November, and thefirst dekad of February. In the south, the maximum valueis 0.29 in October and the minimum value is −0.37 in thesecond dekad of November.In parallel with HG method, SPEI values are computedwith PM method. The results of correlation analysisare shown in Fig. 7, where the maximum and minimumcoefficients are 0.76 and −0.73 for the north in Octoberand January, as well as 0.27 and −0.39 for the south inOctober and November, respectively.The correlation analysis suggests that correlations ofwheat yields and SPI or SPEI in the northern sites aremore significant than that in the southern sites. The rela-tionships show consistent periodic changes during wheat-growing stages, especially in the north, where there are twodry (red) periods when wheat is at the seedling and the re-viving to anthesis stages, and two wet (blue) periods whenthe stages are about over-wintering and after anthesis.In terms of the coefficients at the significant level(P ≤ 0.05), the SPI, SPEIHG, and SPEIPM are accor-dant with each other on the positive or negative relationswith wheat yields, except that in the second dekad ofMarch of the southern sites, 1-dekad scale of SPI sequenceis positively correlated to yields significantly (r = 0.24,P = 0.03), but the SPEIHG sequence is negatively cor-related (r = −0.22, P = 0.05), and the SPEIPM se-quence is not significantly correlated (r = 0.07, P = 0.51).However, the other timescales of all three indices at thisdekad show remarkable negative correlation with wheatyields.4830.48 0.37 0.06 -0.05 0.62 0.48 -0.7 -0.46 0.45 -0.18 -0.44 -0.41 0.67 -0.14 0.39 0.17 0.67 0.09 0.44 0.28 -0.54 -0.2 -0.49 0.460.17 0.45 0.21 0.14 0.45 0.55 -0.24 -0.74 -0.22 0.2 -0.3 -0.38 0.27 0.44 0.22 0.01 0.57 0.66 0.46 0.46 -0.34 -0.45 -0.31 -0.180.15 0.68 0.23 0.23 0.28 0.46 0.04 -0.23 -0.77 -0.13 -0.2 -0.36 0.05 0.05 0.47 -0.17 0.49 0.51 0.54 0.46 0.07 -0.21 -0.5 -0.070.17 0.44 0.2 0.22 0.32 0.35 0.1 0 -0.2 -0.75 -0.23 -0.34 0.06 -0.27 0.12 0.42 0.47 0.51 0.48 0.5 0.14 -0.02 -0.4 -0.33-0.53 0.36 0.3 0.19 0.33 0.37 0.14 0.05 0.07 -0.18 -0.72 -0.4 0.11 -0.27 -0.24 0.1 0.6 0.48 0.47 0.49 0.31 0.06 -0.32 -0.27-0.36 -0.47 0.27 0.32 0.33 0.37 0.2 0.11 0.12 0.07 -0.23 -0.7 0.08 -0.26 -0.25 -0.12 0.53 0.61 0.42 0.47 0.36 0.48 -0.3 -0.231-dekad2-dekads3-dekads4-dekads5-dekads6-dekadsOct-2Oct-3Nor-1Nov-2Nov-3Dec-1Dec-2Dec-3Jan-1Jan-2Jan-3Feb-1Feb-2Feb-3Mar-1Mar-2Mar-3Apr-1Apr-2Apr-3May-1May-2May-3Jun-1-1.0-0.50.00.51.0Correlation0.23 -0.28 -0.31 0.02 -0.22 -0.18 0.1 -0.13 0.14 -0.06 -0.28 -0.07 -0.08 -0.25 0.24 -0.12 -0.22 -0.2 0.08 -0.16 0.02 00.23 -0.06 -0.33 -0.23 -0.15 -0.28 -0.13 -0.09 0.02 -0.07 -0.22 -0.27 -0.1 -0.26 -0.28 -0.21 -0.24 -0.26 -0.16 -0.2 -0.01 0.040.22 -0.05 -0.19 -0.27 -0.24 -0.17 -0.17 -0.11 0.09 -0.12 -0.19 -0.22 -0.24 -0.22 -0.3 -0.27 -0.24 -0.24 -0.22 -0.18 -0.02 -0.020.12 -0.16 -0.19 -0.16 -0.27 -0.25 -0.15 -0.19 -0.09 -0.03 -0.19 -0.19 -0.24 -0.29 -0.24 -0.29 -0.26 -0.25 -0.22 -0.2 -0.08 -0.040.12 -0.14 -0.35 -0.16 -0.17 -0.32 -0.18 -0.15 -0.13 -0.09 -0.15 -0.17 -0.24 -0.31 -0.3 -0.23 -0.28 -0.27 -0.23 -0.2 -0.13 -0.030.05 -0.07 -0.28 -0.31 -0.16 -0.2 -0.26 -0.21 -0.09 -0.11 -0.21 -0.18 -0.23 -0.31 -0.3 -0.26 -0.24 -0.26 -0.27 -0.23 -0.17 -0.091-dekad2-dekads3-dekads4-dekads5-dekads6-dekadsOct-3Nor-1Nov-2Nov-3Dec-1Dec-2Dec-3Jan-1Jan-2Jan-3Feb-1Feb-2Feb-3Mar-1Mar-2Mar-3Apr-1Apr-2Apr-3May-1May-2May-3-1.0-0.50.00.51.0CorrelationFigure 5. The Spearman correlation coefficients between wheat yields and SPI. The upper part of the figure exhibits thecorrelation coefficients in the north over 24 dekads of wheat growth periods (In x axis, 1, 2, 3 represent the first, second, andthird dekad of the month, respectively.) for six scales of SPI (In y axis, 1, 2, 3, 4, 5, 6 represent the six dekad scales). Thelower part of the figure exhibits the correlations in southern sites over 22 dekads of wheat growth periods (x axis) for sixscales of SPI (y axis).0.52 0.73 -0.14 0.24 0.52 0.49 -0.55 -0.23 0.14 -0.59 -0.66 -0.6 0.46 -0.01 0.21 0.08 0.62 0.64 0.18 -0.23 -0.32 -0.12 -0.32 0.260.45 0.68 0.22 -0.01 0.46 0.53 -0.1 -0.55 -0.22 -0.27 -0.62 -0.68 -0.2 0.2 0.03 -0.01 0.53 0.68 0.26 0.02 -0.25 -0.35 -0.23 -0.340.37 0.62 0.28 0.28 0.3 0.47 0.2 -0.15 -0.51 -0.3 -0.41 -0.67 -0.4 -0.21 0.23 -0.01 0.52 0.55 0.43 0.17 -0.17 -0.33 -0.34 -0.20.34 0.56 0.31 0.38 0.48 0.39 0.21 0.1 -0.07 -0.54 -0.31 -0.61 -0.45 -0.32 -0.17 0.22 0.48 0.57 0.39 0.27 0.14 -0.33 -0.34 -0.34-0.63 0.53 0.51 0.38 0.55 0.51 0.11 0.13 0.1 -0.14 -0.52 -0.46 -0.39 -0.41 -0.35 -0.04 0.46 0.51 0.4 0.29 0.21 -0.2 -0.32 -0.33-0.5 -0.55 0.48 0.73 0.59 0.56 0.17 0.07 0.13 0.06 -0.3 -0.55 -0.36 -0.4 -0.44 -0.35 0.4 0.51 0.34 0.33 0.21 0.18 -0.31 -0.321-dekad2-dekads3-dekads4-dekads5-dekads6-dekadsOct-2Oct-3Nor-1Nov-2Nov-3Dec-1Dec-2Dec-3Jan-1Jan-2Jan-3Feb-1Feb-2Feb-3Mar-1Mar-2Mar-3Apr-1Apr-2Apr-3May-1May-2May-3Jun-1-1.0-0.50.00.51.0Correlation0.29 -0.24 -0.29 -0.09 -0.14 -0.26 -0.07 -0.15 0.15 -0.13 -0.29 -0.19 -0.11 -0.25 -0.22 -0.18 -0.2 -0.31 -0.18 -0.18 0.03 -0.170.28 0.05 -0.37 -0.26 -0.11 -0.26 -0.18 -0.09 -0.04 -0.09 -0.24 -0.31 -0.16 -0.29 -0.28 -0.21 -0.19 -0.3 -0.26 -0.19 -0.12 -0.060.19 0.1 -0.21 -0.28 -0.25 -0.19 -0.17 -0.21 -0.02 -0.1 -0.2 -0.26 -0.29 -0.28 -0.31 -0.28 -0.19 -0.29 -0.29 -0.26 -0.17 -0.130.09 -0.02 -0.13 -0.17 -0.28 -0.28 -0.14 -0.2 -0.18 -0.08 -0.2 -0.23 -0.28 -0.32 -0.3 -0.27 -0.25 -0.29 -0.32 -0.28 -0.25 -0.130.07 -0.03 -0.26 -0.12 -0.18 -0.29 -0.23 -0.16 -0.14 -0.16 -0.14 -0.24 -0.25 -0.32 -0.33 -0.29 -0.26 -0.3 -0.29 -0.31 -0.28 -0.170 -0.04 -0.22 -0.28 -0.13 -0.23 -0.26 -0.25 -0.12 -0.12 -0.19 -0.2 -0.26 -0.3 -0.32 -0.3 -0.28 -0.31 -0.29 -0.3 -0.25 -0.21-dekad2-dekads3-dekads4-dekads5-dekads6-dekadsOct-3Nor-1Nov-2Nov-3Dec-1Dec-2Dec-3Jan-1Jan-2Jan-3Feb-1Feb-2Feb-3Mar-1Mar-2Mar-3Apr-1Apr-2Apr-3May-1May-2May-3-1.0-0.50.00.51.0CorrelationFigure 6. The Spearman correlation coefficients between wheat yields and SPEIHG.4840.64 0.69 -0.22 0 0.54 0.53 -0.72 -0.5 0.21 -0.62 -0.63 -0.35 0.65 -0.17 0.41 0 0.65 0.49 0.41 0.18 -0.36 -0.05 -0.38 0.380.57 0.73 0.09 -0.16 0.47 0.51 -0.19 -0.72 -0.46 -0.18 -0.62 -0.48 0.26 0.32 0.11 0.04 0.51 0.64 0.41 0.37 -0.08 -0.27 -0.19 -0.240.21 0.76 0.16 0.12 0.17 0.52 0.14 -0.24 -0.72 -0.5 -0.59 -0.54 -0.06 0.07 0.35 -0.05 0.53 0.57 0.47 0.36 0.11 -0.17 -0.37 -0.10.21 0.5 0.21 0.19 0.31 0.38 0.15 0.03 -0.25 -0.73 -0.5 -0.52 -0.07 -0.26 0.12 0.4 0.48 0.56 0.45 0.46 0.22 0 -0.33 -0.28-0.61 0.44 0.51 0.22 0.37 0.45 0.01 0 0.04 -0.31 -0.7 -0.56 -0.06 -0.28 -0.22 0.13 0.57 0.5 0.42 0.46 0.26 0.11 -0.28 -0.26-0.45 -0.57 0.43 0.5 0.43 0.46 0.11 -0.01 0.02 0.04 -0.39 -0.69 -0.14 -0.26 -0.24 -0.14 0.5 0.59 0.38 0.45 0.31 0.4 -0.26 -0.241-dekad2-dekads3-dekads4-dekads5-dekads6-dekadsOct-2Oct-3Nor-1Nov-2Nov-3Dec-1Dec-2Dec-3Jan-1Jan-2Jan-3Feb-1Feb-2Feb-3Mar-1Mar-2Mar-3Apr-1Apr-2Apr-3May-1May-2May-3Jun-1-1.0-0.50.00.51.0Correlation0.27 -0.31 -0.3 0.04 -0.15 -0.2 0.11 -0.16 0.15 -0.1 -0.3 -0.08 -0.09 -0.28 0.07 -0.19 -0.22 -0.22 -0.11 -0.19 0.05 -0.120.27 -0.07 -0.39 -0.25 -0.07 -0.27 -0.11 -0.02 -0.02 -0.09 -0.24 -0.28 -0.1 -0.27 -0.27 -0.21 -0.24 -0.27 -0.2 -0.2 -0.1 0.010.2 -0.02 -0.24 -0.28 -0.22 -0.17 -0.17 -0.15 0.05 -0.13 -0.23 -0.24 -0.23 -0.22 -0.29 -0.26 -0.22 -0.27 -0.22 -0.22 -0.1 -0.070.07 -0.14 -0.23 -0.16 -0.28 -0.27 -0.15 -0.18 -0.12 -0.04 -0.22 -0.24 -0.24 -0.29 -0.24 -0.27 -0.26 -0.25 -0.25 -0.22 -0.12 -0.050.06 -0.14 -0.35 -0.16 -0.19 -0.3 -0.18 -0.15 -0.14 -0.16 -0.18 -0.23 -0.24 -0.31 -0.29 -0.24 -0.26 -0.26 -0.23 -0.23 -0.18 -0.08-0.04 -0.09 -0.28 -0.32 -0.16 -0.21 -0.24 -0.19 -0.1 -0.13 -0.24 -0.17 -0.24 -0.3 -0.31 -0.26 -0.25 -0.26 -0.27 -0.24 -0.21 -0.091-dekad2-dekads3-dekads4-dekads5-dekads6-dekadsOct-3Nor-1Nov-2Nov-3Dec-1Dec-2Dec-3Jan-1Jan-2Jan-3Feb-1Feb-2Feb-3Mar-1Mar-2Mar-3Apr-1Apr-2Apr-3May-1May-2May-3-1.0-0.50.00.51.0CorrelationFigure 7. The Spearman correlation coefficients between wheat yields and SPEIP M .3.4 Regression of De-trended Wheat Yields withSPI and SPEITwo sequences of SPI, SPEIHG, and SPEIPM with thehighest positive or lowest negative correlations to wheatyields are selected to build the regression formulas inNorthern and Southern Jiangsu. The relations of the indexvalues and de-trended wheat yields are shown in Fig. 8.In each formula displayed, dependent variable y representsthe de-trended wheat yields and independent variables x1and x2 represent the moisture conditions with the greatestpositive or negative impact on wheat yields. The R2ofregression formulas indicates that wheat yields can be wellexplained by the indices in northern sites (R2between 0.53and 0.66). However, in the southern sites, the performancesof all indices are poor (R2between 0.07 and 0.09). Inaddition, the results of SPI, SPEIPM, and SPEIHG are veryclose to each other.4. ConclusionAccording to the high correlations and goodness of fitsobtained in the northern sites, we can conclude that allthree indices with dekad scales in particular growth stagesare able to effectively reflect the water conditions that in-fluence wheat yield fluctuations in the study period. Onthe other hand, it is less effective in the southern sitesto use these short-term indices to evaluate wheat yields.The reason may lie in the different climatic conditions ofthe two regions. In Northern Jiangsu, lower precipitationslead to more sensitive yield responses to short-term watersupply, but in Southern Jiangsu, abundant water resourcesmake it insensitive for wheat yields to short-term moisturevariations. The negative correlations between wheat yieldsand indices in most dekads of the southern sites are in linewith several previous studies [3], [17] reflecting the suffi-cient water supply and un-negligible risk of waterloggingfor wheat production in this area. Furthermore, the mostrelevant growth stages are different in this study from thosewith a long research periods [3], whose conclusion is thatthe late growth stages of winter wheat are most sensitiveperiods of moisture for wheat yields. In this study, therelated periods are mainly in the vegetative growth stagesbecause the time span of this research is different from theprevious study, and it reflects the climatic features of therecent six years.Comparing the maximum and minimum correlationcoefficients and the R2of regression formulas in the northand south, the performance of SPEIPM is close to thatof SPI, though SPI does not take evapotranspiration intoaccount. This may be due to the temperature duringwheat growth stages, which results in a small amountof evapotranspiration and thus has little effects on waterbalance. Moreover, the calculation of ET0 cannot be soaccurate as to avoid errors, thereby affecting the accuracyof SPEIPM. Similarly, using a simplified ET0 calculationmethod, SPEIHG may have some deviations.Among the six timescales, performances of indices withshort scales such as 1–3 dekads are not inferior to those oflong-scale indices, in addition, 10 of the 12 selected inputindices in the regression formulas belong to 1–3-dekadscales. Although longer timescales have cumulative effects,485-1 0 1 2-400-2000200400600800SPI valueDe-trendedwheatyield(kg/ha)spi_Oct(3)_3: x1spi_Jan(1)_3: x2y=62.20+223.78x1-113.65x2R2=0.66Northern Jiangsu-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0-5000500SPI valueDe-trendedwheatyield(kg/ha)spi_Mar(2)_1: x1spi_Nov(2)_5: x2y=74.16+20.19x1-68.38x2R2=0.07Southern Jiangsu-2.0 -1.5 -1.0 -0.5 0.0 0.5-400-2000200400600800SPEIHG valueDe-trendedwheatyield(kg/ha)spei_Oct(3)_1: x1spei_Feb(1)_2: x2y=85.68+220.06x1-293.48x2R2=0.53Northern Jiangsu-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-5000500SPEIHG valueDe-trendedwheatyield(kg/ha)spei_Oct(3)_1: x1spei_Nov(2)_2: x2y=58.63+37.22x1-82.42x2R2=0.09-1.0 -0.5 0.0 0.5-400-2000200400600800SPEIPM valueDe-trendedwheatyield(kg/ha)spei_Oct(3)_3: x1spei_Jan(2)_4: x2y=101.76+349.46x1-283.59x2R2=0.63Northern Jiangsu-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-5000500SPEIPM valueDe-trendedwheatyield(kg/ha)spei_Oct(3)_1: x1spei_Nov(2)_2: x2y=69.70+57.97x1-51.38x2R2=0.09Southern JiangsuFigure 8. The relations of index values and de-trended wheat yields. The dependent variable y in regression formulasrepresents the de-trended wheat yields and the independent variables x1 and x2 are index values with the highest positiveor lowest negative correlations to wheat yields. Each index is denoted by the name, dekad, and timescale, for example,spi Oct(3) 3 means the index of spi in the third dekad of October with a 3-dekad scale.486the coefficients of long-scale indices are not better than thatof the short ones in most cases of the study, indicating thatsmoothing effects of long scales may weaken the sensitivityof indices in moisture assessment. Therefore short-scaleindices may be more sensitive to reflect the water conditionsfor wheat production, especially in Northern Jiangsu, andthey can be used as an alternative method to evaluate thewheat yields in this area. Our next work is to add othertechnologies such as remote sensing in accurate wheat yieldevaluations [28].References[1] M. Zampieri, A. Ceglar, F. Dentener, and A. Toreti, Wheatyield loss attributable to heat waves, drought and water excessat the global, national and subnational scales, EnvironmentalResearch Letters, 12(6), 2017, 064008.[2] S.Wang, X. Mo, S. Hu, S. Liu, and Z. Liu, Assessment ofdroughts and wheat yield loss on the north China plain with anaggregate drought index (ADI) approach, Ecological Indicators,87, 2018,107–116.[3] X. Xu, P. Gao, X. Zhu, W. Guo, and C. Li, Estimating theresponses of winter wheat yields to moisture variations in thepast 35 years in Jiangsu Province of China, PLoS One, 13(1),2018, e0191217.[4] T.B. McKee, N.J. Doesken, and J. Kleist, The relationship ofdrought frequency and duration to time scales, Proc. EighthConference on Applied Climatology, Anaheim, California, 1993,179–184.[5] S.M. Vicente-Serrano, S. Beguer´ıa, and J.I. L´opez-Moreno, Amultiscalar drought index sensitive to global warming: Thestandardized precipitation evapotranspiration index, Journalof Climate, 23(7), 2010, 1696–1718. [6] R.A. Seiler, M. Hayes, and L. Bressan, Using the standardizedprecipitation index for flood risk monitoring, InternationalJournal of Climatology, 22(11), 2002, 1365–1376. [7] K. Yildirak, and A.S. Selcuk-Kestel, Adjusting SPI for cropspecific agricultural drought, Environmental and EcologicalStatistics, 22(4), 2015, 681–691. [8] M. Yu, Q. Li., M.J. Hayes, M.D. Svoboda, and R.R. Heim,Are droughts becoming more frequent or severe in China basedon SPEI: 1951–2010? International Journal of Climatology,34(3), 2014, 545–558. [9] S.M. Vicente-Serrano, S. Beguer´ıa, J. Lorenzo-Lacruz, J.J.Camarero, J.I. L´opez-Moreno, C. Azorin-Molina, J. Revuelto,E. Mor´an-Tejeda, and A. Sanchez-Lorenzo, Performance ofdrought indices for ecological, agricultural, and hydrologicalapplications, Earth Interactions, 16(10), 2012, 1–27. [10] E. Lu, Determining the start, duration, and strength of floodand drought with daily precipitation: rationale, GeophysicalResearch Letters, 36(12), 2009, L12707. [11] V. Potopov´a, P. ˇSt`ıp´anek, M. Moˇznı, L. T¨urkott, and J.Soukup, Performance of the standardised precipitation evap-otranspiration index at various lags for agricultural droughtrisk assessment in the Czech Republic, Agricultural and ForestMeteorology, 202, 2015, 26–38. [12] V. Potopov´a, C. Boroneant, B. Boincean, and J. Souokup,Impact of agricultural drought on main crop yieldsin theRepublic of Moldova, International Journal of Climatology,36(4), 2016, 2063–2082. [13] B. Ming, Y.Q. Guo, H.B. Tao, G.Z. Liu, S.K. Li, and P. Wang,SPEIPM-based research on drought impact on maize yield innorth China plain, Journal of Integrative Agriculture, 14(4),2015, 660–669. [14] S. Beguer´ıa, S.M. Vicente-Serrano, F. Reig, and B. Latorre,Standardized precipitation evapotranspiration index (SPEI)revisited: Parameter fitting, evapotranspiration models, tools,datasets and drought monitoring, International Journal ofClimatology, 34(10), 2014, 3001–3023. [15] G. Zhao, Study on chinese wheat planting regionalization (I),Journal of Triticeae Crops, 30(5), 2010, 886–895. [17] reflecting the suffi-cient water supply and un-negligible risk of waterloggingfor wheat production in this area. Furthermore, the mostrelevant growth stages are different in this study from thosewith a long research periods [3], whose conclusion is thatthe late growth stages of winter wheat are most sensitiveperiods of moisture for wheat yields. In this study, therelated periods are mainly in the vegetative growth stagesbecause the time span of this research is different from theprevious study, and it reflects the climatic features of therecent six years.Comparing the maximum and minimum correlationcoefficients and the R2of regression formulas in the northand south, the performance of SPEIPM is close to thatof SPI, though SPI does not take evapotranspiration intoaccount. This may be due to the temperature duringwheat growth stages, which results in a small amountof evapotranspiration and thus has little effects on waterbalance. Moreover, the calculation of ET0 cannot be soaccurate as to avoid errors, thereby affecting the accuracyof SPEIPM. Similarly, using a simplified ET0 calculationmethod, SPEIHG may have some deviations.Among the six timescales, performances of indices withshort scales such as 1–3 dekads are not inferior to those oflong-scale indices, in addition, 10 of the 12 selected inputindices in the regression formulas belong to 1–3-dekadscales. Although longer timescales have cumulative effects,485-1 0 1 2-400-2000200400600800SPI valueDe-trendedwheatyield(kg/ha)spi_Oct(3)_3: x1spi_Jan(1)_3: x2y=62.20+223.78x1-113.65x2R2=0.66Northern Jiangsu-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0-5000500SPI valueDe-trendedwheatyield(kg/ha)spi_Mar(2)_1: x1spi_Nov(2)_5: x2y=74.16+20.19x1-68.38x2R2=0.07Southern Jiangsu-2.0 -1.5 -1.0 -0.5 0.0 0.5-400-2000200400600800SPEIHG valueDe-trendedwheatyield(kg/ha)spei_Oct(3)_1: x1spei_Feb(1)_2: x2y=85.68+220.06x1-293.48x2R2=0.53Northern Jiangsu-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-5000500SPEIHG valueDe-trendedwheatyield(kg/ha)spei_Oct(3)_1: x1spei_Nov(2)_2: x2y=58.63+37.22x1-82.42x2R2=0.09-1.0 -0.5 0.0 0.5-400-2000200400600800SPEIPM valueDe-trendedwheatyield(kg/ha)spei_Oct(3)_3: x1spei_Jan(2)_4: x2y=101.76+349.46x1-283.59x2R2=0.63Northern Jiangsu-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-5000500SPEIPM valueDe-trendedwheatyield(kg/ha)spei_Oct(3)_1: x1spei_Nov(2)_2: x2y=69.70+57.97x1-51.38x2R2=0.09Southern JiangsuFigure 8. The relations of index values and de-trended wheat yields. The dependent variable y in regression formulasrepresents the de-trended wheat yields and the independent variables x1 and x2 are index values with the highest positiveor lowest negative correlations to wheat yields. Each index is denoted by the name, dekad, and timescale, for example,spi Oct(3) 3 means the index of spi in the third dekad of October with a 3-dekad scale.486the coefficients of long-scale indices are not better than thatof the short ones in most cases of the study, indicating thatsmoothing effects of long scales may weaken the sensitivityof indices in moisture assessment. Therefore short-scaleindices may be more sensitive to reflect the water conditionsfor wheat production, especially in Northern Jiangsu, andthey can be used as an alternative method to evaluate thewheat yields in this area. Our next work is to add othertechnologies such as remote sensing in accurate wheat yieldevaluations [28].References[1] M. Zampieri, A. Ceglar, F. Dentener, and A. Toreti, Wheatyield loss attributable to heat waves, drought and water excessat the global, national and subnational scales, EnvironmentalResearch Letters, 12(6), 2017, 064008.[2] S.Wang, X. Mo, S. Hu, S. Liu, and Z. Liu, Assessment ofdroughts and wheat yield loss on the north China plain with anaggregate drought index (ADI) approach, Ecological Indicators,87, 2018,107–116.[3] X. Xu, P. Gao, X. Zhu, W. Guo, and C. Li, Estimating theresponses of winter wheat yields to moisture variations in thepast 35 years in Jiangsu Province of China, PLoS One, 13(1),2018, e0191217.[4] T.B. McKee, N.J. Doesken, and J. Kleist, The relationship ofdrought frequency and duration to time scales, Proc. EighthConference on Applied Climatology, Anaheim, California, 1993,179–184.[5] S.M. Vicente-Serrano, S. Beguer´ıa, and J.I. L´opez-Moreno, Amultiscalar drought index sensitive to global warming: Thestandardized precipitation evapotranspiration index, Journalof Climate, 23(7), 2010, 1696–1718.[6] R.A. Seiler, M. Hayes, and L. Bressan, Using the standardizedprecipitation index for flood risk monitoring, InternationalJournal of Climatology, 22(11), 2002, 1365–1376.[7] K. Yildirak, and A.S. Selcuk-Kestel, Adjusting SPI for cropspecific agricultural drought, Environmental and EcologicalStatistics, 22(4), 2015, 681–691.[8] M. Yu, Q. Li., M.J. Hayes, M.D. Svoboda, and R.R. Heim,Are droughts becoming more frequent or severe in China basedon SPEI: 1951–2010? International Journal of Climatology,34(3), 2014, 545–558.[9] S.M. Vicente-Serrano, S. Beguer´ıa, J. Lorenzo-Lacruz, J.J.Camarero, J.I. L´opez-Moreno, C. Azorin-Molina, J. Revuelto,E. Mor´an-Tejeda, and A. Sanchez-Lorenzo, Performance ofdrought indices for ecological, agricultural, and hydrologicalapplications, Earth Interactions, 16(10), 2012, 1–27.[10] E. Lu, Determining the start, duration, and strength of floodand drought with daily precipitation: rationale, GeophysicalResearch Letters, 36(12), 2009, L12707.[11] V. Potopov´a, P. ˇSt`ıp´anek, M. Moˇznı, L. T¨urkott, and J.Soukup, Performance of the standardised precipitation evap-otranspiration index at various lags for agricultural droughtrisk assessment in the Czech Republic, Agricultural and ForestMeteorology, 202, 2015, 26–38.[12] V. Potopov´a, C. Boroneant, B. Boincean, and J. Souokup,Impact of agricultural drought on main crop yieldsin theRepublic of Moldova, International Journal of Climatology,36(4), 2016, 2063–2082.[13] B. Ming, Y.Q. Guo, H.B. Tao, G.Z. Liu, S.K. Li, and P. Wang,SPEIPM-based research on drought impact on maize yield innorth China plain, Journal of Integrative Agriculture, 14(4),2015, 660–669.[14] S. Beguer´ıa, S.M. Vicente-Serrano, F. Reig, and B. Latorre,Standardized precipitation evapotranspiration index (SPEI)revisited: Parameter fitting, evapotranspiration models, tools,datasets and drought monitoring, International Journal ofClimatology, 34(10), 2014, 3001–3023.[15] G. Zhao, Study on chinese wheat planting regionalization (I),Journal of Triticeae Crops, 30(5), 2010, 886–895.[16] X. Wang, X. Li, G. Fischer, L. Sun, M. Tan, L. Xin, andZ. Liang, Impact of the changing area sown to winter wheaton crop water footprint in the North China Plain, EcologicalIndicators, 57, 2015, 100–109.[17] J. Ding, S. Su, Y. Zhang, C. Li, and W. Guo, Seedling growthand recovery in response to waterlogging of wheat cultivarsgrown in the Yangtze River Basin of China from three differentdecades, Journal of Agricultural Science, 9(4), 2017, 128. [18] X.Y. Meng, W. Hao, S.Y. Cai, X.S. Zhang, and Y. Shang,The China meteorological assimilation driving datasets for theSWAT model (CMADS) application in China: A case studyin Heihe River Basin, Preprints, 2016, 2016120091. [19] X. Meng, W. Hao, X. Lei, S. Cai, H. Wu, X. Ji, and J. Wang,Hydrological modeling in the Manas River Basin using soil andwater assessment tool driven by CMADS, Tehnicki vjesnik -Technical Gazette, 24(2), 2017, 525–534. [20] X. Meng, C. Shi, S. Liu, H. Wang, X. Lei, Z. Liu, X.N. Ji,S. Cai, and Q. Zhao, CMADS datasets and its application inwatershed hydrological simulation: a case study of the HeiheRiver Basin, Pearl River, 37(7), 2016, 1–19. [22], [23], we calculated the dekad-scale SPI by the followingsteps:Firstly, the multi-decadal precipitations are accumu-lated and denoted by P sequences. Because the wholegrowing periods of winter wheat in Northern and SouthernJiangsu are 24 and 22 dekads, respectively, we selected sixdifferent dekad scales from 1 to 6 to investigate the shorttimescale SPI.Secondly, the parameters of P sequences under gammadistribution are estimated. L-moment of the P sequencesis used to obtain the parameters ing (x) =1βαΓ (α)xα−1e−x/β(1)where g(x) is the probability density function of gammadistribution, fitting to the frequency distribution of Psequence. α and β are the shape and scale parameters, andΓ(α) is the gamma function. The calculation of L-momentsand the parameters is performed with lmomco package ofR software.Once the parameters are determined, SPI values canbe computed under standard normal distribution whichis transformed from the gamma probability distributionfunction. The normalized index obtained temporal andspecial comparability.2.3 Calculations of SPEI with Two MethodsThe calculation of SPEI with dekad scales is similar to thatof SPI, except that the P sequences are replaced by climaticwater balance sequences, which are the differences betweenprecipitations and ET0. In addition to precipitations aswater input, ET0 is incorporated in SPEI to quantify thewater output. However, the calculation of ET0 is so com-plex that it involves numerous parameters. Two widelyused methods, Penman–Monteith method (PM) and Har-greaves method (HG), are applied in our study to obtainET0. The PM method is considered as a standardizedmethod for computing ET0 because of its high accuracy.The calculation is using [24], [25]:ETPM =0.408Δ (Rn − G) + γ 900T +273 U2 (es − ea)Δ + γ (1 + 0.34U2)(2)where ETP M denotes the ET0 calculated by PM method;Δ is the slope of the vapor pressure curve; Rn is the netradiation obtained by difference between net short waveradiation absorbed and net long wave radiation emitted. Gis the soil heat flux density, which is small and negligible.γ is the psychometric constant. T and U2 are the averagedaily temperature and the wind speed at 2 m above ground,respectively. es and ea are the saturated vapor pressureand actual vapor pressure.HG method is another widely used method that re-quires relatively fewer parameters than PM method [25], [26]. The HG equation isETHG = 0.0023Ra(Tmax − Tmin)0.5(Ta + 17.8) (3)where ETHG denotes the ET0 calculated by HG method.Tmax, Tmin, and Ta are the maximum, minimum, and mean480Table 1Key Growing Stages of Winter Wheat in Jiangsu Province. NIC is the North Irrigation Channel in JiangsuRegion Seedling (S1) Over-Wintering (S2) Reviving to Anthesis (S3) After Anthesis (S4)North of the NIC Oct. 11st ∼ Dec. 20th Dec. 21st ∼ Feb. 20th Feb. 21st ∼ Apr.30th May. 1st ∼ Jun. 10thSouth of the NIC Oct. 21st ∼ Dec. 31th Jan. 1st ∼ Feb. 10th Feb. 11th ∼ Apr. 20th Apr. 21st ∼ May. 30thFigure 1. Locations of the meteorological sites in Jiangsu province.air temperature of the day. Ra is the theoretical solarradiation, which is calculated usingRa = (24 × 60/π) × Gsc × dr × (ωs × sin(ϕ) × sin(δ)+ cos(ϕ) × cos(δ) × sin(ωs)) (4)where J is the Julian day. Gsc is the solar constant,Gsc = 0.082 (MJ/(m2· min)). dr is the average distancebetween the Sun and the Earth. ωs is the hourly angle ofSun rising. ϕ is the latitude, δ is the solar declination, andthey are both in radians [5].With the values of ET0 computed by two differentmethods, the differences between precipitation and ET0could be calculated to obtain the climatic water balancesequences, denoted by D. It is different from SPI that theD sequence is modelled using a three-parameter log-logisticdistribution, whose probability density function f(x) isf (x) =βαx − yαβ−11 +x − yαβ −2(5)where α, β, and γ are the scale, shape, and location param-eters. Similar to the procedures used in computing SPI,the parameters of log-logistic distribution are estimatedby L-moment, and then the SPEI values are computedas the standardized values of the probability distributionfunction.2.4 Yield Data De-trendingWith the improvement of varieties and cultivation tech-niques, the yield per unit area of winter wheat increasedyear by year in the research area. Therefore, in orderto analyse the relationships between wheat yields and thewater conditions, it is necessary to de-trend the yields.Among several de-trend methods available, the first-orderdifference method is simple and objective and is able to re-move the increasing characteristics of yield series and makeit a stationary sequence [3], [27]. With the de-trendedwheat yields, the correlation analysis and regression anal-ysis between yields and SPI or SPEI values are carried outto investigate the relationship.48140005000600070002009 2010 2011 2012 2013 2014YearOriginalwheatyield(kg/ha)-600-30003006002010 2011 2012 2013 2014YearDe-trendedwheatyield(kg/ha)Site12345678910111213141516171819202122232425Figure 2. The de-trended wheat yields of 25 sites.2009 2010 2011 2012 2013 2014yearTotalprecipitiations0100200300400500600Northern JiangsuSouthern Jiangsua2009 2010 2011 2012 2013 2014yearTotalprecipitiations050100150200250300S1S2S3S4S1S2S3S4Northern Jiangsu2009 2010 2011 2012 2013 2014yearTotalprecipitiations050100150200250300S1S2S3S4Southern JiangsuFigure 3. Site-averaged total precipitations of Northern and Southern Jiangsu during the whole growing stages (a) and fourkey growth stages of winter wheat in Jiangsu.3. Results3.1 De-trended Wheat YieldsThe de-trended wheat yields of 25 sites between 2010 and2014 are shown in Fig. 2. Although the year span of originalyield sequences is too small to show obvious upward trends,the first-order difference of yields weakens the effects oftechnology and reflects much more influences of randomfactors including water conditions. The de-trended yieldsfor all sites range from −600 to 600 kg/ha, exhibitingrandom fluctuations.3.2 Moisture Conditions of the Wheat-GrowingStagesThe site-averaged total precipitations of Northern andSouthern Jiangsu during the whole growing stages andfour key growth stages of the winter wheat are displayedin Fig. 3. It shows that the precipitations of the wholegrowing stages are higher in the southern sites than in thenorthern sites within all 6 years. In 2011, both regions hada low rainfall. Comparing four key growing stages, rainfallin S4 of the north and in S3 of the south is more prominentthan other periods during these years.482-2-10122008 2009 2010 2011 2012 2013 2014Northern Jiangsu SPI-1-2-10122008 2009 2010 2011 2012 2013 2014Southern Jiangsu SPI-1-2-10122008 2009 2010 2011 2012 2013 2014Northern Jiangsu SPEIHG-1-2-10122008 2009 2010 2011 2012 2013 2014Southern Jiangsu SPEIHG-1-2-10122008 2009 2010 2011 2012 2013 2014Northern Jiangsu SPEIPM-1-2-10122008 2009 2010 2011 2012 2013 2014Southern Jiangsu SPEIPM-1Figure 4. SPI and SPEI of 1-dekad scale in Northern and Southern Jiangsu.The site-averaged SPI and SPEI of 1-dekad scale arecalculated and shown in Fig. 4. It is obvious that the SPI-1has more negative values than SPEIHG-1 and SPEIP M -1 both in the north and in the south. When there isa lack of precipitation, SPI will be calculated negative,and if the value is less than −0.5, drought is indicated.However, when considering the evapotranspiration, thelow precipitation and low evapotranspiration may lead toan opposite wet condition in SPEI. Therefore, in severalcases, such as in 2011, the values of SPI-1 and SPEI-1 areopposite in positive and negative symbols.3.3 Correlations between Wheat Yields and SPI orSPEISix different dekad-scale SPI sequences have been calcu-lated. To analyse the relationships between the SPI andthe wheat yields, the first-order differences of SPI valuesshould be obtained. Then the Spearman correlation coef-ficients between de-trended wheat yields and SPI are com-puted and shown in Fig. 5. The northern and southernstations are calculated separately because of the differentlengths of wheat growth periods. In Northern Jiangsu,the negative correlation coefficients of 3-dekad scale SPI inthe first dekad of January (Jan-1) are the most remark-able (−0.77), while the positive correlation coefficients of3-dekad scale SPI in the third dekads of October are thehighest (0.68). In southern Jiangsu, the maximum is 0.24and the minimum is −0.35, which appeared in March andNovember, respectively.Similarly, SPEI values using HG method are computedwith six different scales. The correlation coefficients areshown in Fig. 6. In the north, the highest (0.73) and thelowest (−0.68) correlation coefficients appear in the lastdekad of October, the second dekad of November, and thefirst dekad of February. In the south, the maximum valueis 0.29 in October and the minimum value is −0.37 in thesecond dekad of November.In parallel with HG method, SPEI values are computedwith PM method. The results of correlation analysisare shown in Fig. 7, where the maximum and minimumcoefficients are 0.76 and −0.73 for the north in Octoberand January, as well as 0.27 and −0.39 for the south inOctober and November, respectively.The correlation analysis suggests that correlations ofwheat yields and SPI or SPEI in the northern sites aremore significant than that in the southern sites. The rela-tionships show consistent periodic changes during wheat-growing stages, especially in the north, where there are twodry (red) periods when wheat is at the seedling and the re-viving to anthesis stages, and two wet (blue) periods whenthe stages are about over-wintering and after anthesis.In terms of the coefficients at the significant level(P ≤ 0.05), the SPI, SPEIHG, and SPEIPM are accor-dant with each other on the positive or negative relationswith wheat yields, except that in the second dekad ofMarch of the southern sites, 1-dekad scale of SPI sequenceis positively correlated to yields significantly (r = 0.24,P = 0.03), but the SPEIHG sequence is negatively cor-related (r = −0.22, P = 0.05), and the SPEIPM se-quence is not significantly correlated (r = 0.07, P = 0.51).However, the other timescales of all three indices at thisdekad show remarkable negative correlation with wheatyields.4830.48 0.37 0.06 -0.05 0.62 0.48 -0.7 -0.46 0.45 -0.18 -0.44 -0.41 0.67 -0.14 0.39 0.17 0.67 0.09 0.44 0.28 -0.54 -0.2 -0.49 0.460.17 0.45 0.21 0.14 0.45 0.55 -0.24 -0.74 -0.22 0.2 -0.3 -0.38 0.27 0.44 0.22 0.01 0.57 0.66 0.46 0.46 -0.34 -0.45 -0.31 -0.180.15 0.68 0.23 0.23 0.28 0.46 0.04 -0.23 -0.77 -0.13 -0.2 -0.36 0.05 0.05 0.47 -0.17 0.49 0.51 0.54 0.46 0.07 -0.21 -0.5 -0.070.17 0.44 0.2 0.22 0.32 0.35 0.1 0 -0.2 -0.75 -0.23 -0.34 0.06 -0.27 0.12 0.42 0.47 0.51 0.48 0.5 0.14 -0.02 -0.4 -0.33-0.53 0.36 0.3 0.19 0.33 0.37 0.14 0.05 0.07 -0.18 -0.72 -0.4 0.11 -0.27 -0.24 0.1 0.6 0.48 0.47 0.49 0.31 0.06 -0.32 -0.27-0.36 -0.47 0.27 0.32 0.33 0.37 0.2 0.11 0.12 0.07 -0.23 -0.7 0.08 -0.26 -0.25 -0.12 0.53 0.61 0.42 0.47 0.36 0.48 -0.3 -0.231-dekad2-dekads3-dekads4-dekads5-dekads6-dekadsOct-2Oct-3Nor-1Nov-2Nov-3Dec-1Dec-2Dec-3Jan-1Jan-2Jan-3Feb-1Feb-2Feb-3Mar-1Mar-2Mar-3Apr-1Apr-2Apr-3May-1May-2May-3Jun-1-1.0-0.50.00.51.0Correlation0.23 -0.28 -0.31 0.02 -0.22 -0.18 0.1 -0.13 0.14 -0.06 -0.28 -0.07 -0.08 -0.25 0.24 -0.12 -0.22 -0.2 0.08 -0.16 0.02 00.23 -0.06 -0.33 -0.23 -0.15 -0.28 -0.13 -0.09 0.02 -0.07 -0.22 -0.27 -0.1 -0.26 -0.28 -0.21 -0.24 -0.26 -0.16 -0.2 -0.01 0.040.22 -0.05 -0.19 -0.27 -0.24 -0.17 -0.17 -0.11 0.09 -0.12 -0.19 -0.22 -0.24 -0.22 -0.3 -0.27 -0.24 -0.24 -0.22 -0.18 -0.02 -0.020.12 -0.16 -0.19 -0.16 -0.27 -0.25 -0.15 -0.19 -0.09 -0.03 -0.19 -0.19 -0.24 -0.29 -0.24 -0.29 -0.26 -0.25 -0.22 -0.2 -0.08 -0.040.12 -0.14 -0.35 -0.16 -0.17 -0.32 -0.18 -0.15 -0.13 -0.09 -0.15 -0.17 -0.24 -0.31 -0.3 -0.23 -0.28 -0.27 -0.23 -0.2 -0.13 -0.030.05 -0.07 -0.28 -0.31 -0.16 -0.2 -0.26 -0.21 -0.09 -0.11 -0.21 -0.18 -0.23 -0.31 -0.3 -0.26 -0.24 -0.26 -0.27 -0.23 -0.17 -0.091-dekad2-dekads3-dekads4-dekads5-dekads6-dekadsOct-3Nor-1Nov-2Nov-3Dec-1Dec-2Dec-3Jan-1Jan-2Jan-3Feb-1Feb-2Feb-3Mar-1Mar-2Mar-3Apr-1Apr-2Apr-3May-1May-2May-3-1.0-0.50.00.51.0CorrelationFigure 5. The Spearman correlation coefficients between wheat yields and SPI. The upper part of the figure exhibits thecorrelation coefficients in the north over 24 dekads of wheat growth periods (In x axis, 1, 2, 3 represent the first, second, andthird dekad of the month, respectively.) for six scales of SPI (In y axis, 1, 2, 3, 4, 5, 6 represent the six dekad scales). Thelower part of the figure exhibits the correlations in southern sites over 22 dekads of wheat growth periods (x axis) for sixscales of SPI (y axis).0.52 0.73 -0.14 0.24 0.52 0.49 -0.55 -0.23 0.14 -0.59 -0.66 -0.6 0.46 -0.01 0.21 0.08 0.62 0.64 0.18 -0.23 -0.32 -0.12 -0.32 0.260.45 0.68 0.22 -0.01 0.46 0.53 -0.1 -0.55 -0.22 -0.27 -0.62 -0.68 -0.2 0.2 0.03 -0.01 0.53 0.68 0.26 0.02 -0.25 -0.35 -0.23 -0.340.37 0.62 0.28 0.28 0.3 0.47 0.2 -0.15 -0.51 -0.3 -0.41 -0.67 -0.4 -0.21 0.23 -0.01 0.52 0.55 0.43 0.17 -0.17 -0.33 -0.34 -0.20.34 0.56 0.31 0.38 0.48 0.39 0.21 0.1 -0.07 -0.54 -0.31 -0.61 -0.45 -0.32 -0.17 0.22 0.48 0.57 0.39 0.27 0.14 -0.33 -0.34 -0.34-0.63 0.53 0.51 0.38 0.55 0.51 0.11 0.13 0.1 -0.14 -0.52 -0.46 -0.39 -0.41 -0.35 -0.04 0.46 0.51 0.4 0.29 0.21 -0.2 -0.32 -0.33-0.5 -0.55 0.48 0.73 0.59 0.56 0.17 0.07 0.13 0.06 -0.3 -0.55 -0.36 -0.4 -0.44 -0.35 0.4 0.51 0.34 0.33 0.21 0.18 -0.31 -0.321-dekad2-dekads3-dekads4-dekads5-dekads6-dekadsOct-2Oct-3Nor-1Nov-2Nov-3Dec-1Dec-2Dec-3Jan-1Jan-2Jan-3Feb-1Feb-2Feb-3Mar-1Mar-2Mar-3Apr-1Apr-2Apr-3May-1May-2May-3Jun-1-1.0-0.50.00.51.0Correlation0.29 -0.24 -0.29 -0.09 -0.14 -0.26 -0.07 -0.15 0.15 -0.13 -0.29 -0.19 -0.11 -0.25 -0.22 -0.18 -0.2 -0.31 -0.18 -0.18 0.03 -0.170.28 0.05 -0.37 -0.26 -0.11 -0.26 -0.18 -0.09 -0.04 -0.09 -0.24 -0.31 -0.16 -0.29 -0.28 -0.21 -0.19 -0.3 -0.26 -0.19 -0.12 -0.060.19 0.1 -0.21 -0.28 -0.25 -0.19 -0.17 -0.21 -0.02 -0.1 -0.2 -0.26 -0.29 -0.28 -0.31 -0.28 -0.19 -0.29 -0.29 -0.26 -0.17 -0.130.09 -0.02 -0.13 -0.17 -0.28 -0.28 -0.14 -0.2 -0.18 -0.08 -0.2 -0.23 -0.28 -0.32 -0.3 -0.27 -0.25 -0.29 -0.32 -0.28 -0.25 -0.130.07 -0.03 -0.26 -0.12 -0.18 -0.29 -0.23 -0.16 -0.14 -0.16 -0.14 -0.24 -0.25 -0.32 -0.33 -0.29 -0.26 -0.3 -0.29 -0.31 -0.28 -0.170 -0.04 -0.22 -0.28 -0.13 -0.23 -0.26 -0.25 -0.12 -0.12 -0.19 -0.2 -0.26 -0.3 -0.32 -0.3 -0.28 -0.31 -0.29 -0.3 -0.25 -0.21-dekad2-dekads3-dekads4-dekads5-dekads6-dekadsOct-3Nor-1Nov-2Nov-3Dec-1Dec-2Dec-3Jan-1Jan-2Jan-3Feb-1Feb-2Feb-3Mar-1Mar-2Mar-3Apr-1Apr-2Apr-3May-1May-2May-3-1.0-0.50.00.51.0CorrelationFigure 6. The Spearman correlation coefficients between wheat yields and SPEIHG.4840.64 0.69 -0.22 0 0.54 0.53 -0.72 -0.5 0.21 -0.62 -0.63 -0.35 0.65 -0.17 0.41 0 0.65 0.49 0.41 0.18 -0.36 -0.05 -0.38 0.380.57 0.73 0.09 -0.16 0.47 0.51 -0.19 -0.72 -0.46 -0.18 -0.62 -0.48 0.26 0.32 0.11 0.04 0.51 0.64 0.41 0.37 -0.08 -0.27 -0.19 -0.240.21 0.76 0.16 0.12 0.17 0.52 0.14 -0.24 -0.72 -0.5 -0.59 -0.54 -0.06 0.07 0.35 -0.05 0.53 0.57 0.47 0.36 0.11 -0.17 -0.37 -0.10.21 0.5 0.21 0.19 0.31 0.38 0.15 0.03 -0.25 -0.73 -0.5 -0.52 -0.07 -0.26 0.12 0.4 0.48 0.56 0.45 0.46 0.22 0 -0.33 -0.28-0.61 0.44 0.51 0.22 0.37 0.45 0.01 0 0.04 -0.31 -0.7 -0.56 -0.06 -0.28 -0.22 0.13 0.57 0.5 0.42 0.46 0.26 0.11 -0.28 -0.26-0.45 -0.57 0.43 0.5 0.43 0.46 0.11 -0.01 0.02 0.04 -0.39 -0.69 -0.14 -0.26 -0.24 -0.14 0.5 0.59 0.38 0.45 0.31 0.4 -0.26 -0.241-dekad2-dekads3-dekads4-dekads5-dekads6-dekadsOct-2Oct-3Nor-1Nov-2Nov-3Dec-1Dec-2Dec-3Jan-1Jan-2Jan-3Feb-1Feb-2Feb-3Mar-1Mar-2Mar-3Apr-1Apr-2Apr-3May-1May-2May-3Jun-1-1.0-0.50.00.51.0Correlation0.27 -0.31 -0.3 0.04 -0.15 -0.2 0.11 -0.16 0.15 -0.1 -0.3 -0.08 -0.09 -0.28 0.07 -0.19 -0.22 -0.22 -0.11 -0.19 0.05 -0.120.27 -0.07 -0.39 -0.25 -0.07 -0.27 -0.11 -0.02 -0.02 -0.09 -0.24 -0.28 -0.1 -0.27 -0.27 -0.21 -0.24 -0.27 -0.2 -0.2 -0.1 0.010.2 -0.02 -0.24 -0.28 -0.22 -0.17 -0.17 -0.15 0.05 -0.13 -0.23 -0.24 -0.23 -0.22 -0.29 -0.26 -0.22 -0.27 -0.22 -0.22 -0.1 -0.070.07 -0.14 -0.23 -0.16 -0.28 -0.27 -0.15 -0.18 -0.12 -0.04 -0.22 -0.24 -0.24 -0.29 -0.24 -0.27 -0.26 -0.25 -0.25 -0.22 -0.12 -0.050.06 -0.14 -0.35 -0.16 -0.19 -0.3 -0.18 -0.15 -0.14 -0.16 -0.18 -0.23 -0.24 -0.31 -0.29 -0.24 -0.26 -0.26 -0.23 -0.23 -0.18 -0.08-0.04 -0.09 -0.28 -0.32 -0.16 -0.21 -0.24 -0.19 -0.1 -0.13 -0.24 -0.17 -0.24 -0.3 -0.31 -0.26 -0.25 -0.26 -0.27 -0.24 -0.21 -0.091-dekad2-dekads3-dekads4-dekads5-dekads6-dekadsOct-3Nor-1Nov-2Nov-3Dec-1Dec-2Dec-3Jan-1Jan-2Jan-3Feb-1Feb-2Feb-3Mar-1Mar-2Mar-3Apr-1Apr-2Apr-3May-1May-2May-3-1.0-0.50.00.51.0CorrelationFigure 7. The Spearman correlation coefficients between wheat yields and SPEIP M .3.4 Regression of De-trended Wheat Yields withSPI and SPEITwo sequences of SPI, SPEIHG, and SPEIPM with thehighest positive or lowest negative correlations to wheatyields are selected to build the regression formulas inNorthern and Southern Jiangsu. The relations of the indexvalues and de-trended wheat yields are shown in Fig. 8.In each formula displayed, dependent variable y representsthe de-trended wheat yields and independent variables x1and x2 represent the moisture conditions with the greatestpositive or negative impact on wheat yields. The R2ofregression formulas indicates that wheat yields can be wellexplained by the indices in northern sites (R2between 0.53and 0.66). However, in the southern sites, the performancesof all indices are poor (R2between 0.07 and 0.09). Inaddition, the results of SPI, SPEIPM, and SPEIHG are veryclose to each other.4. ConclusionAccording to the high correlations and goodness of fitsobtained in the northern sites, we can conclude that allthree indices with dekad scales in particular growth stagesare able to effectively reflect the water conditions that in-fluence wheat yield fluctuations in the study period. Onthe other hand, it is less effective in the southern sitesto use these short-term indices to evaluate wheat yields.The reason may lie in the different climatic conditions ofthe two regions. In Northern Jiangsu, lower precipitationslead to more sensitive yield responses to short-term watersupply, but in Southern Jiangsu, abundant water resourcesmake it insensitive for wheat yields to short-term moisturevariations. The negative correlations between wheat yieldsand indices in most dekads of the southern sites are in linewith several previous studies [3], [17] reflecting the suffi-cient water supply and un-negligible risk of waterloggingfor wheat production in this area. Furthermore, the mostrelevant growth stages are different in this study from thosewith a long research periods [3], whose conclusion is thatthe late growth stages of winter wheat are most sensitiveperiods of moisture for wheat yields. In this study, therelated periods are mainly in the vegetative growth stagesbecause the time span of this research is different from theprevious study, and it reflects the climatic features of therecent six years.Comparing the maximum and minimum correlationcoefficients and the R2of regression formulas in the northand south, the performance of SPEIPM is close to thatof SPI, though SPI does not take evapotranspiration intoaccount. This may be due to the temperature duringwheat growth stages, which results in a small amountof evapotranspiration and thus has little effects on waterbalance. Moreover, the calculation of ET0 cannot be soaccurate as to avoid errors, thereby affecting the accuracyof SPEIPM. Similarly, using a simplified ET0 calculationmethod, SPEIHG may have some deviations.Among the six timescales, performances of indices withshort scales such as 1–3 dekads are not inferior to those oflong-scale indices, in addition, 10 of the 12 selected inputindices in the regression formulas belong to 1–3-dekadscales. Although longer timescales have cumulative effects,485-1 0 1 2-400-2000200400600800SPI valueDe-trendedwheatyield(kg/ha)spi_Oct(3)_3: x1spi_Jan(1)_3: x2y=62.20+223.78x1-113.65x2R2=0.66Northern Jiangsu-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0-5000500SPI valueDe-trendedwheatyield(kg/ha)spi_Mar(2)_1: x1spi_Nov(2)_5: x2y=74.16+20.19x1-68.38x2R2=0.07Southern Jiangsu-2.0 -1.5 -1.0 -0.5 0.0 0.5-400-2000200400600800SPEIHG valueDe-trendedwheatyield(kg/ha)spei_Oct(3)_1: x1spei_Feb(1)_2: x2y=85.68+220.06x1-293.48x2R2=0.53Northern Jiangsu-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-5000500SPEIHG valueDe-trendedwheatyield(kg/ha)spei_Oct(3)_1: x1spei_Nov(2)_2: x2y=58.63+37.22x1-82.42x2R2=0.09-1.0 -0.5 0.0 0.5-400-2000200400600800SPEIPM valueDe-trendedwheatyield(kg/ha)spei_Oct(3)_3: x1spei_Jan(2)_4: x2y=101.76+349.46x1-283.59x2R2=0.63Northern Jiangsu-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-5000500SPEIPM valueDe-trendedwheatyield(kg/ha)spei_Oct(3)_1: x1spei_Nov(2)_2: x2y=69.70+57.97x1-51.38x2R2=0.09Southern JiangsuFigure 8. The relations of index values and de-trended wheat yields. The dependent variable y in regression formulasrepresents the de-trended wheat yields and the independent variables x1 and x2 are index values with the highest positiveor lowest negative correlations to wheat yields. Each index is denoted by the name, dekad, and timescale, for example,spi Oct(3) 3 means the index of spi in the third dekad of October with a 3-dekad scale.486the coefficients of long-scale indices are not better than thatof the short ones in most cases of the study, indicating thatsmoothing effects of long scales may weaken the sensitivityof indices in moisture assessment. Therefore short-scaleindices may be more sensitive to reflect the water conditionsfor wheat production, especially in Northern Jiangsu, andthey can be used as an alternative method to evaluate thewheat yields in this area. Our next work is to add othertechnologies such as remote sensing in accurate wheat yieldevaluations [28].References[1] M. 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