Reconstruction method of regional precipitation

From the growth-climate response analysis, the primary growth limiting climatic factor was identified. Then, the significant response was used to develop a growth-climate model which was subsequently used to reconstruct the past climate of target variable and target season. From the growth-climate relationship analysis between the regional composite chronology and climatic data, it was found that spring season (February–June, FJ) precipitation reconstruction is theoretically possible; so, it was targeted for reconstruction. The transfer function explained by Blasing and Fritts ³³ was used to reconstruct the climatic variable (Precipitation). Finally, one reconstruction model was built using simple linear regression using spring season (February–June) precipitation (1965–2018 CE) as the predictant (dependent variable), and the regional composite tree-ring chronology as the independent variable (predictor). The time-stability of the model was tested using calibration and verification methods i.e., split-sample-half validation⁵² and leave-one-out cross-validation⁵³. Pearson’s correlation coefficient (r), the coefficient of determination (R²), adjusted coefficient of determination (R²_adj), reduction of error (RE), and coefficient of efficiency (CE) were used to evaluate model skill. We also calculated root-mean squared-error (RMSE) from the model as an indicator of variability in the reconstruction. Linear regression model assumptions were evaluated by inspection of residual plots to ensure that there was no pattern in error variance. The autocorrelation function of the residuals was examined visually, and the Durbin–Watson statistic was used to evaluate the assumption of independence in the predictor variable. We also conducted a sign test to evaluate the fidelity of year-to-year changes in the reconstructed precipitation to the tree-ring predictor⁴¹. The RE and CE positive values of climate-growth models was taken as a basis for the validity and reliability of the regression model³⁷. Once the model was judged to be effective and stable, it was then applied to reconstruct past spring season precipitation for the period covered by regional composite tree-ring width chronology. The reconstruction was truncated at the point at which the EPS value became less than the arbitrary but commonly used threshold value of 0.85⁴⁵. Spatial representation of the reconstruction was checked in the KNMI climate explorer^33,54 by performing spatial correlation between the observed and reconstructed precipitation with CRU grid precipitation and sea surface temperature. To check the teleconnection and identify the influence of broader scale climatic modes and phases, relationship (Pearson’s correlation) between the reconstructed climate and different climatic indices (ENSO, AMO, SOI, ONI, NAO, PDO, etc.) was analyzed (Supplementary Table S3). Similarly, we also compared climatic trends in our reconstructed precipitation from Pakistan with other independent and available reconstructions reported from the Himalayas to check the coherencies in the reconstructions. Furthermore, a power spectrum analysis was performed by using the Multi Taper method to check the periodicities in spring precipitation⁵⁵. Similarly, Morlet Wavelet analysis was also performed to check the temporal pattern in the periodicity of the precipitation⁵⁶.