Divergent response of aridity index to historical land use and land cover change

Materials and methods

CMIP6 model output

Eleven models (one realization per model) participating in the CMIP6 projects14 are employed in this study. For each model, two experiments are used to quantify the impact of historical LULCC. The first experiment is the standard historical simulation that includes all anthropogenic forcings (e.g., greenhouse gases, aerosols and LULCC) and natural forcings (e.g., solar and volcanic forcings). The second is the hist-noLu simulation, in which all forcings are identical to those in the historical experiment but with land use fixed at the 1850 level15. The LULCC data in all CMIP6 models are prescribed by the Land-Use Harmonization dataset16. Both simulations were run in fully coupled mode from 1850 to 2014, and the period of 1995–2014 is chosen for analyses in this study. The detailed information of each model is listed in Table S1. It is noted that the atmospheric concentrations of greenhouse gases in both experiments are identical and are not influenced by historical LULCC. Differences between the two experiments are the biophysical effects of LULCC only. It is worthing noting that, compared with satellite-based studies using the “space-for-time” strategy, which includes direct effects only, our results accounted for the indirect effects arising from the changes in feedbacks and background climate.

Model performance evaluation

To evaluate the performance of LULCC-induced signal from the model simulations, we compared P, PET, and P/PET from the hist simulation against CRUTS4 data17. The comparison was performed based on 20-year annual mean values over 1995-2014 from observational records and the CMIP6 output (Fig. S5). In general, the models can reproduce the observed climatology reasonably well for both P and PET, with the correlation coefficients (r) between the MMM values and observational values being 0.83 (P) and 0.96 (PET). For P/PET, the r value between the MMM and CRUTS4 data is 0.64, which is a little bit lower than P and PET. However, the models still reproduced the spatial pattern of climate zones reasonably good (Fig. S5g, h). Given this evaluation outcome, it is suitable to utilize these models in our analyses. We also acknowledge that discrepancies exist over the transition zones, such as Central and West North America and West and Central Asia.

Calculation of the aridity index

Aridity index is calculated as the ratio of 20-year mean P over PET, in which P is precipitation and PET is the potential evapotranspiration. The latter is the maximum evapotranspiration given unlimited water, which is estimated by the Food and Agricultural Organization Penman–Monteith method18:

$${PET}=frac{0.408Delta left({R}_{n}-Gright)+gamma frac{900}{T+273}uleft({e}_{s}-{e}_{a}right)}{Delta +gamma left(1+0.34uright)}$$
(1)

where ({PET}) is in mm day-1, (Delta) is the slope of the vapor pressure curve (kPa °C-1), ({R}_{n}) is the surface net radiation (MJ m-1 day-1), (G) is the soil heat flux (MJ m-1 day-1), (gamma) is the psychometric constant (kPa °C-1), (T) is the 2 m air temperature (°C), (u) is the surface wind speed (m s-1), ({e}_{s}) is the near-surface saturation vapor pressure (kPa), and ({e}_{a}) is the actual vapor pressure (kPa). After estimation of the aridity (AI), the climate zones are defined as arid (AI < 0.2), semi-arid (0.2 ≤ AI < 0.5), dry sub-humid (0.5 ≤ AI < 0.65) and humid (AI ≥ 0.65).

Quantification of LULCC impact

The LULCC impact, denoted as Δ or change, was quantified as differences in the same variables between the two simulations in each model. Taking precipitation (P) as an example, the impact of LULCC on P is defined as:

$$Delta P=overline{{P}_{h{ist}}}-overline{{P}_{h{ist}-{noLu}}}$$
(2)

In Equation [2], Δ is the change in P due to LULCC impact, and the overbars represent the annual mean value of 1995-2014. The changes in PET and AI were estimated similarly by replacing P in Equation [2] with the corresponding variables.

These differences were computed for each grid cell in each model and then averaged to obtain the multi-model mean (MMM) values, with an equal weighting factor assigned to each model. All model outputs were resampled to a common spatial resolution of 0.94° × 1.25° in latitude and longitude before data processing. The re-sampling process was carried out by using a bilinear interpolation.

Significance test and confidence interval

A bootstrap technique was used to test whether the MMM values are significantly different from zero at the grid-cell level. The 11 model values were sampled 11 times randomly with replacement to obtain a mean value. The process was repeated 1000 times to construct a 90% confidence interval (CI). The MMM changes are considered significant if zero falls outside the confidence interval. Confidence interval was estimated similarly. After obtaining the 1000 mean values, the 5th and 95th percentile values were considered as the 90% confidence interval.

Regression of changes in AI against LULCC activity

To evaluate the relationship between ∆AI and LULCC activity, as shown in Fig. 1, a linear regression relationship was established. By taking the area-weighted mean value, we binned the changes in AI of all land grids based on the fraction changes in primary and secondary land (psl) with an interval of 10% for each model. Thus, there are 11 values for each bin and 13 bins in total. A linear regression model was subsequently constructed based on the MMM values in each bin. The uncertainty range of the regression was estimated with a bootstrap technique. Specifically, we randomly sampled the 11 data points in each bin and obtained 13 randomly sampled data points in total to construct a linear regression model. This process was repeated 1000 times to obtain the 90% CI (gray shaded region of the regression in Fig. 1).

Decomposition of ∆AI

By using Taylor Series, ∆AI could be approximated as the summation of two terms:

$$Delta {AI}approx frac{Delta P}{{P}_{{hist}-{noLu}}}{{AI}}_{{hist}-{noLu}}-frac{Delta {PET}}{{{PET}}_{{hist}-{noLu}}}{{AI}}_{{hist}-{noLu}}$$
(3)

On the right-hand side of Equation [3], ∆P and ∆PET represent the P and PET changes (hist minus hist-noLu) estimated from Equation [2]. ({P}_{{hist}-{noLu}}), ({{PET}}_{{hist}-{noLu}}), and ({{AI}}_{{hist}-{noLu}}) denote P, PET and AI, respectively, in the hist-noLu simulations. The first term of the right-hand side is therefore the change in AI attributed to ∆P, and the second term of the right-hand side is the change in AI attributed to ∆PET.

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