EVALUATION OF WINTER WHEAT YIELDS USING SPI AND SPEI AT 10-DAILY SCALES

Xiangying Xu,∗,∗∗,∗∗∗,∗∗∗∗ Xinkai Zhu,∗,∗∗∗ Yonglong Zhang,∗∗∗∗ Chunyan Li,∗,∗∗∗ Jinfeng Ding,∗,∗∗∗ Junwu Zhu,∗∗∗∗ Bin Li,∗∗∗∗ and Wenshan Guo,∗,∗∗∗

References

  1. [1] M. Zampieri, A. Ceglar, F. Dentener, and A. Toreti, Wheat yield loss attributable to heat waves, drought and water excess at the global, national and subnational scales, Environmental Research Letters, 12(6), 2017, 064008.
  2. [4], [22], [23], we calculated the dekad-scale SPI by the following steps: Firstly, the multi-decadal precipitations are accumulated and denoted by P sequences. Because the whole growing periods of winter wheat in Northern and Southern Jiangsu are 24 and 22 dekads, respectively, we selected six different dekad scales from 1 to 6 to investigate the short timescale SPI. Secondly, the parameters of P sequences under gamma distribution are estimated. L-moment of the P sequences is used to obtain the parameters in g (x) = 1 βαΓ (α) xα−1 e−x/β (1) where g(x) is the probability density function of gamma distribution, fitting to the frequency distribution of P sequence. α and β are the shape and scale parameters, and Γ(α) is the gamma function. The calculation of L-moments and the parameters is performed with lmomco package of R software. Once the parameters are determined, SPI values can be computed under standard normal distribution which is transformed from the gamma probability distribution function. The normalized index obtained temporal and special comparability. 2.3 Calculations of SPEI with Two Methods The calculation of SPEI with dekad scales is similar to that of SPI, except that the P sequences are replaced by climatic water balance sequences, which are the differences between precipitations and ET0. In addition to precipitations as water input, ET0 is incorporated in SPEI to quantify the water output. However, the calculation of ET0 is so complex that it involves numerous parameters. Two widely used methods, Penman–Monteith method (PM) and Hargreaves method (HG), are applied in our study to obtain ET0. The PM method is considered as a standardized method for computing ET0 because of its high accuracy. The calculation is using [24], [25]: ETPM = 0.408Δ (Rn − G) + γ 900 T +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 net radiation obtained by difference between net short wave radiation absorbed and net long wave radiation emitted. G is the soil heat flux density, which is small and negligible. γ is the psychometric constant. T and U2 are the average daily temperature and the wind speed at 2 m above ground, respectively. es and ea are the saturated vapor pressure and actual vapor pressure. HG method is another widely used method that requires relatively fewer parameters than PM method [25], [26]. The HG equation is ETHG = 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 mean 480 Table 1 Key Growing Stages of Winter Wheat in Jiangsu Province. NIC is the North Irrigation Channel in Jiangsu Region 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. 10th South of the NIC Oct. 21st ∼ Dec. 31th Jan. 1st ∼ Feb. 10th Feb. 11th ∼ Apr. 20th Apr. 21st ∼ May. 30th Figure 1. Locations of the meteorological sites in Jiangsu province. air temperature of the day. Ra is the theoretical solar radiation, which is calculated using Ra = (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 distance between the Sun and the Earth. ωs is the hourly angle of Sun rising. ϕ is the latitude, δ is the solar declination, and they are both in radians
  3. [5]. With the values of ET0 computed by two different methods, the differences between precipitation and ET0 could be calculated to obtain the climatic water balance sequences, denoted by D. It is different from SPI that the D sequence is modelled using a three-parameter log-logistic distribution, whose probability density function f(x) is f (x) = β α x − y α β−1 1 + x − y α β −2 (5) where α, β, and γ are the scale, shape, and location parameters. Similar to the procedures used in computing SPI, the parameters of log-logistic distribution are estimated by L-moment, and then the SPEI values are computed as the standardized values of the probability distribution function. 2.4 Yield Data De-trending With the improvement of varieties and cultivation techniques, the yield per unit area of winter wheat increased year by year in the research area. Therefore, in order to analyse the relationships between wheat yields and the water conditions, it is necessary to de-trend the yields. Among several de-trend methods available, the first-order difference method is simple and objective and is able to remove the increasing characteristics of yield series and make it a stationary sequence [3], [27]. With the de-trended wheat yields, the correlation analysis and regression analysis between yields and SPI or SPEI values are carried out to investigate the relationship. 481 4000 5000 6000 7000 2009 2010 2011 2012 2013 2014 Year Originalwheatyield(kg/ha) -600 -300 0 300 600 2010 2011 2012 2013 2014 Year De-trendedwheatyield(kg/ha) Site 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Figure 2. The de-trended wheat yields of 25 sites. 2009 2010 2011 2012 2013 2014 year Totalprecipitiations 0100200300400500600 Northern Jiangsu Southern Jiangsu a 2009 2010 2011 2012 2013 2014 year Totalprecipitiations 050100150200250300 S1 S2 S3 S4 S1 S2 S3 S4 Northern Jiangsu 2009 2010 2011 2012 2013 2014 year Totalprecipitiations 050100150200250300 S1 S2 S3 S4 Southern Jiangsu Figure 3. Site-averaged total precipitations of Northern and Southern Jiangsu during the whole growing stages (a) and four key growth stages of winter wheat in Jiangsu. 3. Results 3.1 De-trended Wheat Yields The de-trended wheat yields of 25 sites between 2010 and 2014 are shown in Fig. 2. Although the year span of original yield sequences is too small to show obvious upward trends, the first-order difference of yields weakens the effects of technology and reflects much more influences of random factors including water conditions. The de-trended yields for all sites range from −600 to 600 kg/ha, exhibiting random fluctuations. 3.2 Moisture Conditions of the Wheat-Growing Stages The site-averaged total precipitations of Northern and Southern Jiangsu during the whole growing stages and four key growth stages of the winter wheat are displayed in Fig. 3. It shows that the precipitations of the whole growing stages are higher in the southern sites than in the northern sites within all 6 years. In 2011, both regions had a low rainfall. Comparing four key growing stages, rainfall in S4 of the north and in S3 of the south is more prominent than other periods during these years. 482 -2-1012 2008 2009 2010 2011 2012 2013 2014 Northern Jiangsu SPI-1 -2-1012 2008 2009 2010 2011 2012 2013 2014 Southern Jiangsu SPI-1 -2-1012 2008 2009 2010 2011 2012 2013 2014 Northern Jiangsu SPEIHG-1 -2-1012 2008 2009 2010 2011 2012 2013 2014 Southern Jiangsu SPEIHG-1 -2-1012 2008 2009 2010 2011 2012 2013 2014 Northern Jiangsu SPEIPM-1 -2-1012 2008 2009 2010 2011 2012 2013 2014 Southern Jiangsu SPEIPM-1 Figure 4. SPI and SPEI of 1-dekad scale in Northern and Southern Jiangsu. The site-averaged SPI and SPEI of 1-dekad scale are calculated and shown in Fig. 4. It is obvious that the SPI-1 has more negative values than SPEIHG-1 and SPEIP M 1 both in the north and in the south. When there is a 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, the low precipitation and low evapotranspiration may lead to an opposite wet condition in SPEI. Therefore, in several cases, such as in 2011, the values of SPI-1 and SPEI-1 are opposite in positive and negative symbols. 3.3 Correlations between Wheat Yields and SPI or SPEI Six different dekad-scale SPI sequences have been calculated. To analyse the relationships between the SPI and the wheat yields, the first-order differences of SPI values should be obtained. Then the Spearman correlation coefficients between de-trended wheat yields and SPI are computed and shown in Fig. 5. The northern and southern stations are calculated separately because of the different lengths of wheat growth periods. In Northern Jiangsu, the negative correlation coefficients of 3-dekad scale SPI in the first dekad of January (Jan-1) are the most remarkable (−0.77), while the positive correlation coefficients of 3-dekad scale SPI in the third dekads of October are the highest (0.68). In southern Jiangsu, the maximum is 0.24 and the minimum is −0.35, which appeared in March and November, respectively. Similarly, SPEI values using HG method are computed with six different scales. The correlation coefficients are shown in Fig. 6. In the north, the highest (0.73) and the lowest (−0.68) correlation coefficients appear in the last dekad of October, the second dekad of November, and the first dekad of February. In the south, the maximum value is 0.29 in October and the minimum value is −0.37 in the second dekad of November. In parallel with HG method, SPEI values are computed with PM method. The results of correlation analysis are shown in Fig. 7, where the maximum and minimum coefficients are 0.76 and −0.73 for the north in October and January, as well as 0.27 and −0.39 for the south in October and November, respectively. The correlation analysis suggests that correlations of wheat yields and SPI or SPEI in the northern sites are more significant than that in the southern sites. The relationships show consistent periodic changes during wheatgrowing stages, especially in the north, where there are two dry (red) periods when wheat is at the seedling and the reviving to anthesis stages, and two wet (blue) periods when the 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 accordant with each other on the positive or negative relations with wheat yields, except that in the second dekad of March of the southern sites, 1-dekad scale of SPI sequence is positively correlated to yields significantly (r = 0.24, P = 0.03), but the SPEIHG sequence is negatively correlated (r = −0.22, P = 0.05), and the SPEIPM sequence is not significantly correlated (r = 0.07, P = 0.51). However, the other timescales of all three indices at this dekad show remarkable negative correlation with wheat yields. 483 0.48 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 0.46 0.17 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 -0.18 0.15 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 -0.07 0.17 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 -0.23 1-dekad 2-dekads 3-dekads 4-dekads 5-dekads 6-dekads O ct-2 O ct-3 N or-1 N ov-2 N ov-3 D ec-1 D ec-2 D ec-3 Jan-1 Jan-2 Jan-3 Feb-1 Feb-2 Feb-3 M ar-1 M ar-2 M ar-3 Apr-1 Apr-2 Apr-3 M ay-1 M ay-2 M ay-3 Jun-1 -1.0 -0.5 0.0 0.5 1.0 Correlation 0.23 -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 0 0.23 -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 0.04 0.22 -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 -0.02 0.12 -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 -0.04 0.12 -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 -0.03 0.05 -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 -0.09 1-dekad 2-dekads 3-dekads 4-dekads 5-dekads 6-dekads O ct-3 N or-1 N ov-2 N ov-3 D ec-1 D ec-2 D ec-3 Jan-1 Jan-2 Jan-3 Feb-1 Feb-2 Feb-3 M ar-1 M ar-2 M ar-3 Apr-1 Apr-2 Apr-3 M ay-1 M ay-2 M ay-3 -1.0 -0.5 0.0 0.5 1.0 Correlation Figure 5. The Spearman correlation coefficients between wheat yields and SPI. The upper part of the figure exhibits the correlation coefficients in the north over 24 dekads of wheat growth periods (In x axis, 1, 2, 3 represent the first, second, and third dekad of the month, respectively.) for six scales of SPI (In y axis, 1, 2, 3, 4, 5, 6 represent the six dekad scales). The lower part of the figure exhibits the correlations in southern sites over 22 dekads of wheat growth periods (x axis) for six scales 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 0.26 0.45 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 -0.34 0.37 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 -0.2 0.34 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 -0.32 1-dekad 2-dekads 3-dekads 4-dekads 5-dekads 6-dekads O ct-2 O ct-3 N or-1 N ov-2 N ov-3 D ec-1 D ec-2 D ec-3 Jan-1 Jan-2 Jan-3 Feb-1 Feb-2 Feb-3 M ar-1 M ar-2 M ar-3 Apr-1 Apr-2 Apr-3 M ay-1 M ay-2 M ay-3 Jun-1 -1.0 -0.5 0.0 0.5 1.0 Correlation 0.29 -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 -0.17 0.28 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 -0.06 0.19 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 -0.13 0.09 -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 -0.13 0.07 -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 -0.17 0 -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 -0.2 1-dekad 2-dekads 3-dekads 4-dekads 5-dekads 6-dekads O ct-3 N or-1 N ov-2 N ov-3 D ec-1 D ec-2 D ec-3 Jan-1 Jan-2 Jan-3 Feb-1 Feb-2 Feb-3 M ar-1 M ar-2 M ar-3 Apr-1 Apr-2 Apr-3 M ay-1 M ay-2 M ay-3 -1.0 -0.5 0.0 0.5 1.0 Correlation Figure 6. The Spearman correlation coefficients between wheat yields and SPEIHG. 484 0.64 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 0.38 0.57 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 -0.24 0.21 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 -0.1 0.21 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 -0.24 1-dekad 2-dekads 3-dekads 4-dekads 5-dekads 6-dekads O ct-2 O ct-3 N or-1 N ov-2 N ov-3 D ec-1 D ec-2 D ec-3 Jan-1 Jan-2 Jan-3 Feb-1 Feb-2 Feb-3 M ar-1 M ar-2 M ar-3 Apr-1 Apr-2 Apr-3 M ay-1 M ay-2 M ay-3 Jun-1 -1.0 -0.5 0.0 0.5 1.0 Correlation 0.27 -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 -0.12 0.27 -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 0.01 0.2 -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 -0.07 0.07 -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 -0.05 0.06 -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 -0.09 1-dekad 2-dekads 3-dekads 4-dekads 5-dekads 6-dekads O ct-3 N or-1 N ov-2 N ov-3 D ec-1 D ec-2 D ec-3 Jan-1 Jan-2 Jan-3 Feb-1 Feb-2 Feb-3 M ar-1 M ar-2 M ar-3 Apr-1 Apr-2 Apr-3 M ay-1 M ay-2 M ay-3 -1.0 -0.5 0.0 0.5 1.0 Correlation Figure 7. The Spearman correlation coefficients between wheat yields and SPEIP M . 3.4 Regression of De-trended Wheat Yields with SPI and SPEI Two sequences of SPI, SPEIHG, and SPEIPM with the highest positive or lowest negative correlations to wheat yields are selected to build the regression formulas in Northern and Southern Jiangsu. The relations of the index values and de-trended wheat yields are shown in Fig. 8. In each formula displayed, dependent variable y represents the de-trended wheat yields and independent variables x1 and x2 represent the moisture conditions with the greatest positive or negative impact on wheat yields. The R2 of regression formulas indicates that wheat yields can be well explained by the indices in northern sites (R2 between 0.53 and 0.66). However, in the southern sites, the performances of all indices are poor (R2 between 0.07 and 0.09). In addition, the results of SPI, SPEIPM, and SPEIHG are very close to each other. 4. Conclusion According to the high correlations and goodness of fits obtained in the northern sites, we can conclude that all three indices with dekad scales in particular growth stages are able to effectively reflect the water conditions that influence wheat yield fluctuations in the study period. On the other hand, it is less effective in the southern sites to use these short-term indices to evaluate wheat yields. The reason may lie in the different climatic conditions of the two regions. In Northern Jiangsu, lower precipitations lead to more sensitive yield responses to short-term water supply, but in Southern Jiangsu, abundant water resources make it insensitive for wheat yields to short-term moisture variations. The negative correlations between wheat yields and indices in most dekads of the southern sites are in line with several previous studies [3], [17] reflecting the sufficient water supply and un-negligible risk of waterlogging for wheat production in this area. Furthermore, the most relevant growth stages are different in this study from those with a long research periods [3], whose conclusion is that the late growth stages of winter wheat are most sensitive periods of moisture for wheat yields. In this study, the related periods are mainly in the vegetative growth stages because the time span of this research is different from the previous study, and it reflects the climatic features of the recent six years. Comparing the maximum and minimum correlation coefficients and the R2 of regression formulas in the north and south, the performance of SPEIPM is close to that of SPI, though SPI does not take evapotranspiration into account. This may be due to the temperature during wheat growth stages, which results in a small amount of evapotranspiration and thus has little effects on water balance. Moreover, the calculation of ET0 cannot be so accurate as to avoid errors, thereby affecting the accuracy of SPEIPM. Similarly, using a simplified ET0 calculation method, SPEIHG may have some deviations. Among the six timescales, performances of indices with short scales such as 1–3 dekads are not inferior to those of long-scale indices, in addition, 10 of the 12 selected input indices in the regression formulas belong to 1–3-dekad scales. Although longer timescales have cumulative effects, 485 -1 0 1 2 -400-2000200400600800 SPI value De-trendedwheatyield(kg/ha) spi_Oct(3)_3: x1 spi_Jan(1)_3: x2y=62.20+223.78x1-113.65x2 R 2 =0.66 Northern Jiangsu -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 -5000500 SPI value De-trendedwheatyield(kg/ha) spi_Mar(2)_1: x1 spi_Nov(2)_5: x2y=74.16+20.19x1-68.38x2 R 2 =0.07 Southern Jiangsu -2.0 -1.5 -1.0 -0.5 0.0 0.5 -400-2000200400600800 SPEIHG value De-trendedwheatyield(kg/ha) spei_Oct(3)_1: x1 spei_Feb(1)_2: x2y=85.68+220.06x1-293.48x2 R 2 =0.53 Northern Jiangsu -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 -5000500 SPEIHG value De-trendedwheatyield(kg/ha) spei_Oct(3)_1: x1 spei_Nov(2)_2: x2y=58.63+37.22x1-82.42x2 R 2 =0.09 -1.0 -0.5 0.0 0.5 -400-2000200400600800 SPEIPM value De-trendedwheatyield(kg/ha) spei_Oct(3)_3: x1 spei_Jan(2)_4: x2y=101.76+349.46x1-283.59x2 R 2 =0.63 Northern Jiangsu -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -5000500 SPEIPM value De-trendedwheatyield(kg/ha) spei_Oct(3)_1: x1 spei_Nov(2)_2: x2y=69.70+57.97x1-51.38x2 R 2 =0.09 Southern Jiangsu Figure 8. The relations of index values and de-trended wheat yields. The dependent variable y in regression formulas represents the de-trended wheat yields and the independent variables x1 and x2 are index values with the highest positive or 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. 486 the coefficients of long-scale indices are not better than that of the short ones in most cases of the study, indicating that smoothing effects of long scales may weaken the sensitivity of indices in moisture assessment. Therefore short-scale indices may be more sensitive to reflect the water conditions for wheat production, especially in Northern Jiangsu, and they can be used as an alternative method to evaluate the wheat yields in this area. Our next work is to add other technologies such as remote sensing in accurate wheat yield evaluations [28]. References [1] M. Zampieri, A. Ceglar, F. Dentener, and A. Toreti, Wheat yield loss attributable to heat waves, drought and water excess at the global, national and subnational scales, Environmental Research Letters, 12(6), 2017, 064008. [2] S.Wang, X. Mo, S. Hu, S. Liu, and Z. Liu, Assessment of droughts and wheat yield loss on the north China plain with an aggregate drought index (ADI) approach, Ecological Indicators, 87, 2018,107–116. [3] X. Xu, P. Gao, X. Zhu, W. Guo, and C. Li, Estimating the responses of winter wheat yields to moisture variations in the past 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 of drought frequency and duration to time scales, Proc. Eighth Conference on Applied Climatology, Anaheim, California, 1993, 179–184. [5] S.M. Vicente-Serrano, S. Beguer´ıa, and J.I. L´opez-Moreno, A multiscalar drought index sensitive to global warming: The standardized precipitation evapotranspiration index, Journal of Climate, 23(7), 2010, 1696–1718.
  4. [6] R.A. Seiler, M. Hayes, and L. Bressan, Using the standardized precipitation index for flood risk monitoring, International Journal of Climatology, 22(11), 2002, 1365–1376.
  5. [7] K. Yildirak, and A.S. Selcuk-Kestel, Adjusting SPI for crop specific agricultural drought, Environmental and Ecological Statistics, 22(4), 2015, 681–691.
  6. [8] M. Yu, Q. Li., M.J. Hayes, M.D. Svoboda, and R.R. Heim, Are droughts becoming more frequent or severe in China based on SPEI: 1951–2010? International Journal of Climatology, 34(3), 2014, 545–558.
  7. [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. Morán-Tejeda, and A. Sanchez-Lorenzo, Performance of drought indices for ecological, agricultural, and hydrological applications, Earth Interactions, 16(10), 2012, 1–27.
  8. [10] E. Lu, Determining the start, duration, and strength of flood and drought with daily precipitation: rationale, Geophysical Research Letters, 36(12), 2009, L12707.
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  11. [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 in north China plain, Journal of Integrative Agriculture, 14(4), 2015, 660–669.
  12. [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 of Climatology, 34(10), 2014, 3001–3023.
  13. [15] G. Zhao, Study on chinese wheat planting regionalization (I), Journal of Triticeae Crops, 30(5), 2010, 886–895.
  14. [17] reflecting the sufficient water supply and un-negligible risk of waterlogging for wheat production in this area. Furthermore, the most relevant growth stages are different in this study from those with a long research periods [3], whose conclusion is that the late growth stages of winter wheat are most sensitive periods of moisture for wheat yields. In this study, the related periods are mainly in the vegetative growth stages because the time span of this research is different from the previous study, and it reflects the climatic features of the recent six years. Comparing the maximum and minimum correlation coefficients and the R2 of regression formulas in the north and south, the performance of SPEIPM is close to that of SPI, though SPI does not take evapotranspiration into account. This may be due to the temperature during wheat growth stages, which results in a small amount of evapotranspiration and thus has little effects on water balance. Moreover, the calculation of ET0 cannot be so accurate as to avoid errors, thereby affecting the accuracy of SPEIPM. Similarly, using a simplified ET0 calculation method, SPEIHG may have some deviations. Among the six timescales, performances of indices with short scales such as 1–3 dekads are not inferior to those of long-scale indices, in addition, 10 of the 12 selected input indices in the regression formulas belong to 1–3-dekad scales. Although longer timescales have cumulative effects, 485 -1 0 1 2 -400-2000200400600800 SPI value De-trendedwheatyield(kg/ha) spi_Oct(3)_3: x1 spi_Jan(1)_3: x2y=62.20+223.78x1-113.65x2 R 2 =0.66 Northern Jiangsu -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 -5000500 SPI value De-trendedwheatyield(kg/ha) spi_Mar(2)_1: x1 spi_Nov(2)_5: x2y=74.16+20.19x1-68.38x2 R 2 =0.07 Southern Jiangsu -2.0 -1.5 -1.0 -0.5 0.0 0.5 -400-2000200400600800 SPEIHG value De-trendedwheatyield(kg/ha) spei_Oct(3)_1: x1 spei_Feb(1)_2: x2y=85.68+220.06x1-293.48x2 R 2 =0.53 Northern Jiangsu -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 -5000500 SPEIHG value De-trendedwheatyield(kg/ha) spei_Oct(3)_1: x1 spei_Nov(2)_2: x2y=58.63+37.22x1-82.42x2 R 2 =0.09 -1.0 -0.5 0.0 0.5 -400-2000200400600800 SPEIPM value De-trendedwheatyield(kg/ha) spei_Oct(3)_3: x1 spei_Jan(2)_4: x2y=101.76+349.46x1-283.59x2 R 2 =0.63 Northern Jiangsu -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -5000500 SPEIPM value De-trendedwheatyield(kg/ha) spei_Oct(3)_1: x1 spei_Nov(2)_2: x2y=69.70+57.97x1-51.38x2 R 2 =0.09 Southern Jiangsu Figure 8. The relations of index values and de-trended wheat yields. The dependent variable y in regression formulas represents the de-trended wheat yields and the independent variables x1 and x2 are index values with the highest positive or 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. 486 the coefficients of long-scale indices are not better than that of the short ones in most cases of the study, indicating that smoothing effects of long scales may weaken the sensitivity of indices in moisture assessment. Therefore short-scale indices may be more sensitive to reflect the water conditions for wheat production, especially in Northern Jiangsu, and they can be used as an alternative method to evaluate the wheat yields in this area. Our next work is to add other technologies such as remote sensing in accurate wheat yield evaluations [28]. References [1] M. Zampieri, A. Ceglar, F. Dentener, and A. Toreti, Wheat yield loss attributable to heat waves, drought and water excess at the global, national and subnational scales, Environmental Research Letters, 12(6), 2017, 064008. [2] S.Wang, X. Mo, S. Hu, S. Liu, and Z. Liu, Assessment of droughts and wheat yield loss on the north China plain with an aggregate drought index (ADI) approach, Ecological Indicators, 87, 2018,107–116. [3] X. Xu, P. Gao, X. Zhu, W. Guo, and C. Li, Estimating the responses of winter wheat yields to moisture variations in the past 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 of drought frequency and duration to time scales, Proc. Eighth Conference on Applied Climatology, Anaheim, California, 1993, 179–184. [5] S.M. Vicente-Serrano, S. Beguer´ıa, and J.I. L´opez-Moreno, A multiscalar drought index sensitive to global warming: The standardized precipitation evapotranspiration index, Journal of Climate, 23(7), 2010, 1696–1718. [6] R.A. Seiler, M. Hayes, and L. Bressan, Using the standardized precipitation index for flood risk monitoring, International Journal of Climatology, 22(11), 2002, 1365–1376. [7] K. Yildirak, and A.S. Selcuk-Kestel, Adjusting SPI for crop specific agricultural drought, Environmental and Ecological Statistics, 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 based on 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. Morán-Tejeda, and A. Sanchez-Lorenzo, Performance of drought indices for ecological, agricultural, and hydrological applications, Earth Interactions, 16(10), 2012, 1–27. [10] E. Lu, Determining the start, duration, and strength of flood and drought with daily precipitation: rationale, Geophysical Research Letters, 36(12), 2009, L12707. [11] V. Potopová, P. ˇSt`ıpánek, M. Moˇznı, L. Türkott, and J. Soukup, Performance of the standardised precipitation evapotranspiration index at various lags for agricultural drought risk assessment in the Czech Republic, Agricultural and Forest Meteorology, 202, 2015, 26–38. [12] V. Potopová, C. Boroneant, B. Boincean, and J. Souokup, Impact of agricultural drought on main crop yieldsin the Republic 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 in north 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 of Climatology, 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, and Z. Liang, Impact of the changing area sown to winter wheat on crop water footprint in the North China Plain, Ecological Indicators, 57, 2015, 100–109. [17] J. Ding, S. Su, Y. Zhang, C. Li, and W. Guo, Seedling growth and recovery in response to waterlogging of wheat cultivars grown in the Yangtze River Basin of China from three different decades, Journal of Agricultural Science, 9(4), 2017, 128.
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  16. [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 and water assessment tool driven by CMADS, Tehnicki vjesnik Technical Gazette, 24(2), 2017, 525–534.
  17. [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 in watershed hydrological simulation: a case study of the Heihe River Basin, Pearl River, 37(7), 2016, 1–19.
  18. [22],
  19. [23], we calculated the dekad-scale SPI by the following steps: Firstly, the multi-decadal precipitations are accumulated and denoted by P sequences. Because the whole growing periods of winter wheat in Northern and Southern Jiangsu are 24 and 22 dekads, respectively, we selected six different dekad scales from 1 to 6 to investigate the short timescale SPI. Secondly, the parameters of P sequences under gamma distribution are estimated. L-moment of the P sequences is used to obtain the parameters in g (x) = 1 βαΓ (α) xα−1 e−x/β (1) where g(x) is the probability density function of gamma distribution, fitting to the frequency distribution of P sequence. α and β are the shape and scale parameters, and Γ(α) is the gamma function. The calculation of L-moments and the parameters is performed with lmomco package of R software. Once the parameters are determined, SPI values can be computed under standard normal distribution which is transformed from the gamma probability distribution function. The normalized index obtained temporal and special comparability. 2.3 Calculations of SPEI with Two Methods The calculation of SPEI with dekad scales is similar to that of SPI, except that the P sequences are replaced by climatic water balance sequences, which are the differences between precipitations and ET0. In addition to precipitations as water input, ET0 is incorporated in SPEI to quantify the water output. However, the calculation of ET0 is so complex that it involves numerous parameters. Two widely used methods, Penman–Monteith method (PM) and Hargreaves method (HG), are applied in our study to obtain ET0. The PM method is considered as a standardized method for computing ET0 because of its high accuracy. The calculation is using
  20. [24],
  21. [25]: ETPM = 0.408Δ (Rn − G) + γ 900 T +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 net radiation obtained by difference between net short wave radiation absorbed and net long wave radiation emitted. G is the soil heat flux density, which is small and negligible. γ is the psychometric constant. T and U2 are the average daily temperature and the wind speed at 2 m above ground, respectively. es and ea are the saturated vapor pressure and actual vapor pressure. HG method is another widely used method that requires relatively fewer parameters than PM method [25],
  22. [26]. The HG equation is ETHG = 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 mean 480 Table 1 Key Growing Stages of Winter Wheat in Jiangsu Province. NIC is the North Irrigation Channel in Jiangsu Region 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. 10th South of the NIC Oct. 21st ∼ Dec. 31th Jan. 1st ∼ Feb. 10th Feb. 11th ∼ Apr. 20th Apr. 21st ∼ May. 30th Figure 1. Locations of the meteorological sites in Jiangsu province. air temperature of the day. Ra is the theoretical solar radiation, which is calculated using Ra = (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 distance between the Sun and the Earth. ωs is the hourly angle of Sun rising. ϕ is the latitude, δ is the solar declination, and they are both in radians [5]. With the values of ET0 computed by two different methods, the differences between precipitation and ET0 could be calculated to obtain the climatic water balance sequences, denoted by D. It is different from SPI that the D sequence is modelled using a three-parameter log-logistic distribution, whose probability density function f(x) is f (x) = β α x − y α β−1 1 + x − y α β −2 (5) where α, β, and γ are the scale, shape, and location parameters. Similar to the procedures used in computing SPI, the parameters of log-logistic distribution are estimated by L-moment, and then the SPEI values are computed as the standardized values of the probability distribution function. 2.4 Yield Data De-trending With the improvement of varieties and cultivation techniques, the yield per unit area of winter wheat increased year by year in the research area. Therefore, in order to analyse the relationships between wheat yields and the water conditions, it is necessary to de-trend the yields. Among several de-trend methods available, the first-order difference method is simple and objective and is able to remove the increasing characteristics of yield series and make it a stationary sequence [3],
  23. [27]. With the de-trended wheat yields, the correlation analysis and regression analysis between yields and SPI or SPEI values are carried out to investigate the relationship. 481 4000 5000 6000 7000 2009 2010 2011 2012 2013 2014 Year Originalwheatyield(kg/ha) -600 -300 0 300 600 2010 2011 2012 2013 2014 Year De-trendedwheatyield(kg/ha) Site 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Figure 2. The de-trended wheat yields of 25 sites. 2009 2010 2011 2012 2013 2014 year Totalprecipitiations 0100200300400500600 Northern Jiangsu Southern Jiangsu a 2009 2010 2011 2012 2013 2014 year Totalprecipitiations 050100150200250300 S1 S2 S3 S4 S1 S2 S3 S4 Northern Jiangsu 2009 2010 2011 2012 2013 2014 year Totalprecipitiations 050100150200250300 S1 S2 S3 S4 Southern Jiangsu Figure 3. Site-averaged total precipitations of Northern and Southern Jiangsu during the whole growing stages (a) and four key growth stages of winter wheat in Jiangsu. 3. Results 3.1 De-trended Wheat Yields The de-trended wheat yields of 25 sites between 2010 and 2014 are shown in Fig. 2. Although the year span of original yield sequences is too small to show obvious upward trends, the first-order difference of yields weakens the effects of technology and reflects much more influences of random factors including water conditions. The de-trended yields for all sites range from −600 to 600 kg/ha, exhibiting random fluctuations. 3.2 Moisture Conditions of the Wheat-Growing Stages The site-averaged total precipitations of Northern and Southern Jiangsu during the whole growing stages and four key growth stages of the winter wheat are displayed in Fig. 3. It shows that the precipitations of the whole growing stages are higher in the southern sites than in the northern sites within all 6 years. In 2011, both regions had a low rainfall. Comparing four key growing stages, rainfall in S4 of the north and in S3 of the south is more prominent than other periods during these years. 482 -2-1012 2008 2009 2010 2011 2012 2013 2014 Northern Jiangsu SPI-1 -2-1012 2008 2009 2010 2011 2012 2013 2014 Southern Jiangsu SPI-1 -2-1012 2008 2009 2010 2011 2012 2013 2014 Northern Jiangsu SPEIHG-1 -2-1012 2008 2009 2010 2011 2012 2013 2014 Southern Jiangsu SPEIHG-1 -2-1012 2008 2009 2010 2011 2012 2013 2014 Northern Jiangsu SPEIPM-1 -2-1012 2008 2009 2010 2011 2012 2013 2014 Southern Jiangsu SPEIPM-1 Figure 4. SPI and SPEI of 1-dekad scale in Northern and Southern Jiangsu. The site-averaged SPI and SPEI of 1-dekad scale are calculated and shown in Fig. 4. It is obvious that the SPI-1 has more negative values than SPEIHG-1 and SPEIP M 1 both in the north and in the south. When there is a 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, the low precipitation and low evapotranspiration may lead to an opposite wet condition in SPEI. Therefore, in several cases, such as in 2011, the values of SPI-1 and SPEI-1 are opposite in positive and negative symbols. 3.3 Correlations between Wheat Yields and SPI or SPEI Six different dekad-scale SPI sequences have been calculated. To analyse the relationships between the SPI and the wheat yields, the first-order differences of SPI values should be obtained. Then the Spearman correlation coefficients between de-trended wheat yields and SPI are computed and shown in Fig. 5. The northern and southern stations are calculated separately because of the different lengths of wheat growth periods. In Northern Jiangsu, the negative correlation coefficients of 3-dekad scale SPI in the first dekad of January (Jan-1) are the most remarkable (−0.77), while the positive correlation coefficients of 3-dekad scale SPI in the third dekads of October are the highest (0.68). In southern Jiangsu, the maximum is 0.24 and the minimum is −0.35, which appeared in March and November, respectively. Similarly, SPEI values using HG method are computed with six different scales. The correlation coefficients are shown in Fig. 6. In the north, the highest (0.73) and the lowest (−0.68) correlation coefficients appear in the last dekad of October, the second dekad of November, and the first dekad of February. In the south, the maximum value is 0.29 in October and the minimum value is −0.37 in the second dekad of November. In parallel with HG method, SPEI values are computed with PM method. The results of correlation analysis are shown in Fig. 7, where the maximum and minimum coefficients are 0.76 and −0.73 for the north in October and January, as well as 0.27 and −0.39 for the south in October and November, respectively. The correlation analysis suggests that correlations of wheat yields and SPI or SPEI in the northern sites are more significant than that in the southern sites. The relationships show consistent periodic changes during wheatgrowing stages, especially in the north, where there are two dry (red) periods when wheat is at the seedling and the reviving to anthesis stages, and two wet (blue) periods when the 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 accordant with each other on the positive or negative relations with wheat yields, except that in the second dekad of March of the southern sites, 1-dekad scale of SPI sequence is positively correlated to yields significantly (r = 0.24, P = 0.03), but the SPEIHG sequence is negatively correlated (r = −0.22, P = 0.05), and the SPEIPM sequence is not significantly correlated (r = 0.07, P = 0.51). However, the other timescales of all three indices at this dekad show remarkable negative correlation with wheat yields. 483 0.48 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 0.46 0.17 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 -0.18 0.15 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 -0.07 0.17 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 -0.23 1-dekad 2-dekads 3-dekads 4-dekads 5-dekads 6-dekads O ct-2 O ct-3 N or-1 N ov-2 N ov-3 D ec-1 D ec-2 D ec-3 Jan-1 Jan-2 Jan-3 Feb-1 Feb-2 Feb-3 M ar-1 M ar-2 M ar-3 Apr-1 Apr-2 Apr-3 M ay-1 M ay-2 M ay-3 Jun-1 -1.0 -0.5 0.0 0.5 1.0 Correlation 0.23 -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 0 0.23 -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 0.04 0.22 -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 -0.02 0.12 -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 -0.04 0.12 -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 -0.03 0.05 -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 -0.09 1-dekad 2-dekads 3-dekads 4-dekads 5-dekads 6-dekads O ct-3 N or-1 N ov-2 N ov-3 D ec-1 D ec-2 D ec-3 Jan-1 Jan-2 Jan-3 Feb-1 Feb-2 Feb-3 M ar-1 M ar-2 M ar-3 Apr-1 Apr-2 Apr-3 M ay-1 M ay-2 M ay-3 -1.0 -0.5 0.0 0.5 1.0 Correlation Figure 5. The Spearman correlation coefficients between wheat yields and SPI. The upper part of the figure exhibits the correlation coefficients in the north over 24 dekads of wheat growth periods (In x axis, 1, 2, 3 represent the first, second, and third dekad of the month, respectively.) for six scales of SPI (In y axis, 1, 2, 3, 4, 5, 6 represent the six dekad scales). The lower part of the figure exhibits the correlations in southern sites over 22 dekads of wheat growth periods (x axis) for six scales 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 0.26 0.45 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 -0.34 0.37 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 -0.2 0.34 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 -0.32 1-dekad 2-dekads 3-dekads 4-dekads 5-dekads 6-dekads O ct-2 O ct-3 N or-1 N ov-2 N ov-3 D ec-1 D ec-2 D ec-3 Jan-1 Jan-2 Jan-3 Feb-1 Feb-2 Feb-3 M ar-1 M ar-2 M ar-3 Apr-1 Apr-2 Apr-3 M ay-1 M ay-2 M ay-3 Jun-1 -1.0 -0.5 0.0 0.5 1.0 Correlation 0.29 -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 -0.17 0.28 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 -0.06 0.19 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 -0.13 0.09 -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 -0.13 0.07 -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 -0.17 0 -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 -0.2 1-dekad 2-dekads 3-dekads 4-dekads 5-dekads 6-dekads O ct-3 N or-1 N ov-2 N ov-3 D ec-1 D ec-2 D ec-3 Jan-1 Jan-2 Jan-3 Feb-1 Feb-2 Feb-3 M ar-1 M ar-2 M ar-3 Apr-1 Apr-2 Apr-3 M ay-1 M ay-2 M ay-3 -1.0 -0.5 0.0 0.5 1.0 Correlation Figure 6. The Spearman correlation coefficients between wheat yields and SPEIHG. 484 0.64 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 0.38 0.57 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 -0.24 0.21 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 -0.1 0.21 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 -0.24 1-dekad 2-dekads 3-dekads 4-dekads 5-dekads 6-dekads O ct-2 O ct-3 N or-1 N ov-2 N ov-3 D ec-1 D ec-2 D ec-3 Jan-1 Jan-2 Jan-3 Feb-1 Feb-2 Feb-3 M ar-1 M ar-2 M ar-3 Apr-1 Apr-2 Apr-3 M ay-1 M ay-2 M ay-3 Jun-1 -1.0 -0.5 0.0 0.5 1.0 Correlation 0.27 -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 -0.12 0.27 -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 0.01 0.2 -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 -0.07 0.07 -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 -0.05 0.06 -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 -0.09 1-dekad 2-dekads 3-dekads 4-dekads 5-dekads 6-dekads O ct-3 N or-1 N ov-2 N ov-3 D ec-1 D ec-2 D ec-3 Jan-1 Jan-2 Jan-3 Feb-1 Feb-2 Feb-3 M ar-1 M ar-2 M ar-3 Apr-1 Apr-2 Apr-3 M ay-1 M ay-2 M ay-3 -1.0 -0.5 0.0 0.5 1.0 Correlation Figure 7. The Spearman correlation coefficients between wheat yields and SPEIP M . 3.4 Regression of De-trended Wheat Yields with SPI and SPEI Two sequences of SPI, SPEIHG, and SPEIPM with the highest positive or lowest negative correlations to wheat yields are selected to build the regression formulas in Northern and Southern Jiangsu. The relations of the index values and de-trended wheat yields are shown in Fig. 8. In each formula displayed, dependent variable y represents the de-trended wheat yields and independent variables x1 and x2 represent the moisture conditions with the greatest positive or negative impact on wheat yields. The R2 of regression formulas indicates that wheat yields can be well explained by the indices in northern sites (R2 between 0.53 and 0.66). However, in the southern sites, the performances of all indices are poor (R2 between 0.07 and 0.09). In addition, the results of SPI, SPEIPM, and SPEIHG are very close to each other. 4. Conclusion According to the high correlations and goodness of fits obtained in the northern sites, we can conclude that all three indices with dekad scales in particular growth stages are able to effectively reflect the water conditions that influence wheat yield fluctuations in the study period. On the other hand, it is less effective in the southern sites to use these short-term indices to evaluate wheat yields. The reason may lie in the different climatic conditions of the two regions. In Northern Jiangsu, lower precipitations lead to more sensitive yield responses to short-term water supply, but in Southern Jiangsu, abundant water resources make it insensitive for wheat yields to short-term moisture variations. The negative correlations between wheat yields and indices in most dekads of the southern sites are in line with several previous studies [3], [17] reflecting the sufficient water supply and un-negligible risk of waterlogging for wheat production in this area. Furthermore, the most relevant growth stages are different in this study from those with a long research periods [3], whose conclusion is that the late growth stages of winter wheat are most sensitive periods of moisture for wheat yields. In this study, the related periods are mainly in the vegetative growth stages because the time span of this research is different from the previous study, and it reflects the climatic features of the recent six years. Comparing the maximum and minimum correlation coefficients and the R2 of regression formulas in the north and south, the performance of SPEIPM is close to that of SPI, though SPI does not take evapotranspiration into account. This may be due to the temperature during wheat growth stages, which results in a small amount of evapotranspiration and thus has little effects on water balance. Moreover, the calculation of ET0 cannot be so accurate as to avoid errors, thereby affecting the accuracy of SPEIPM. Similarly, using a simplified ET0 calculation method, SPEIHG may have some deviations. Among the six timescales, performances of indices with short scales such as 1–3 dekads are not inferior to those of long-scale indices, in addition, 10 of the 12 selected input indices in the regression formulas belong to 1–3-dekad scales. Although longer timescales have cumulative effects, 485 -1 0 1 2 -400-2000200400600800 SPI value De-trendedwheatyield(kg/ha) spi_Oct(3)_3: x1 spi_Jan(1)_3: x2y=62.20+223.78x1-113.65x2 R 2 =0.66 Northern Jiangsu -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 -5000500 SPI value De-trendedwheatyield(kg/ha) spi_Mar(2)_1: x1 spi_Nov(2)_5: x2y=74.16+20.19x1-68.38x2 R 2 =0.07 Southern Jiangsu -2.0 -1.5 -1.0 -0.5 0.0 0.5 -400-2000200400600800 SPEIHG value De-trendedwheatyield(kg/ha) spei_Oct(3)_1: x1 spei_Feb(1)_2: x2y=85.68+220.06x1-293.48x2 R 2 =0.53 Northern Jiangsu -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 -5000500 SPEIHG value De-trendedwheatyield(kg/ha) spei_Oct(3)_1: x1 spei_Nov(2)_2: x2y=58.63+37.22x1-82.42x2 R 2 =0.09 -1.0 -0.5 0.0 0.5 -400-2000200400600800 SPEIPM value De-trendedwheatyield(kg/ha) spei_Oct(3)_3: x1 spei_Jan(2)_4: x2y=101.76+349.46x1-283.59x2 R 2 =0.63 Northern Jiangsu -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -5000500 SPEIPM value De-trendedwheatyield(kg/ha) spei_Oct(3)_1: x1 spei_Nov(2)_2: x2y=69.70+57.97x1-51.38x2 R 2 =0.09 Southern Jiangsu Figure 8. The relations of index values and de-trended wheat yields. The dependent variable y in regression formulas represents the de-trended wheat yields and the independent variables x1 and x2 are index values with the highest positive or 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. 486 the coefficients of long-scale indices are not better than that of the short ones in most cases of the study, indicating that smoothing effects of long scales may weaken the sensitivity of indices in moisture assessment. Therefore short-scale indices may be more sensitive to reflect the water conditions for wheat production, especially in Northern Jiangsu, and they can be used as an alternative method to evaluate the wheat yields in this area. Our next work is to add other technologies such as remote sensing in accurate wheat yield evaluations
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