The scale-specific and localized bivariate relationships in geosciences can be revealed using bivariate wavelet coherence. The objective of this study was to develop a multiple wavelet coherence method for examining scale-specific and localized multivariate relationships. Stationary and non-stationary artificial data sets, generated with the response variable as the summation of five predictor variables (cosine waves) with different scales, were used to test the new method. Comparisons were also conducted using existing multivariate methods, including multiple spectral coherence and multivariate empirical mode decomposition (MEMD). Results show that multiple spectral coherence is unable to identify localized multivariate relationships, and underestimates the scale-specific multivariate relationships for non-stationary processes. The MEMD method was able to separate all variables into components at the same set of scales, revealing scale-specific relationships when combined with multiple correlation coefficients, but has the same weakness as multiple spectral coherence. However, multiple wavelet coherences are able to identify scale-specific and localized multivariate relationships, as they are close to 1 at multiple scales and locations corresponding to those of predictor variables. Therefore, multiple wavelet coherence outperforms other common multivariate methods. Multiple wavelet coherence was applied to a real data set and revealed the optimal combination of factors for explaining temporal variation of free water evaporation at the Changwu site in China at multiple scale-location domains. Matlab codes for multiple wavelet coherence were developed and are provided in the Supplement.

Biochar amendments have been used in agriculture to improve soil fertility and enhance crop productivity. A greenhouse experiment was conducted to test the hypothesis that biochar amendment could also enhance the productivity of salt-affected soils. The trial was conducted over two consecutive growing seasons to investigate the effect of biochar amendment (four application rates as: B₁ = 0%, B₂ = 2%, B₃ = 4%, and B₄ = 8% by mass of soil) on yield and quality of tomatoes grown in a silt loam soil using non-saline water (I₀ = 0.7 dS m⁻¹) and saline water (I₁ = 1 dS m⁻¹; I₂ = 3 dS m⁻¹) irrigation. Furthermore, the study investigated the mechanism by which biochar addresses the salt stress on plant. The results showed that soil productivity as indicated by the vegetative growth and tomato yield components was adversely and significantly affected by saline water irrigation (P < 0.05). Tomato yield decreased from 689 ± 35.6 to 533 ± 79.0 g per plant as salinity of irrigation water increased from I₀ to I₂. Then, biochar amendment increased vegetative growth, yield, and quality parameters under saline irrigation water regimes, and ameliorated the salt stresses on crop growth. The highest (8.73 ± 0.15 and 4.10 ± 0.82 g kg⁻¹) and the lowest (8.33 ± 0.08 and 2.42 ± 0.76 g kg⁻¹) values of soil pH and soil organic matter were measured at B₄I₀ and B₁I₂ treatments, respectively. Also, the highest rate of biochar amendment combining with non-saline water irrigation (B₄I₀) produced tomato with the highest plant photosynthetic (17.08 ± 0.19 μmol m⁻² s⁻¹) and transpiration rate (8.16 ± 0.18 mmol H₂O m⁻² s⁻¹). Mechanically, biochar amendment reduced transient sodium ions by adsorption and released mineral nutrients such as potassium, calcium, and magnesium into the soil solution. Therefore, biochar amendments have the potential in ameliorating salt stress and enhancing tomato production.