Diagnostics and metrics

The performance of the CMIP6 MME is evaluated against the in-situ measurements collected at the GSOD stations using the verification diagnostics proposed by¹⁰⁶. In particular, the bias, the correlation ρ, the variance similarity η and the normalized error variance α are considered. They are defined in Eqs. (1–4) below, where F is the forecast or simulation, O is the observations, D is the discrepancy between the two, and <X> and X are the mean and standard deviation of X, respectively. The bias is given by the mean discrepancy between the model simulations and observations. The correlation ρ is a measure of the phase agreement between the model simulations and observations, while the variance similarity η indicates the amplitude agreement between the two. The normalized error variance α is the variance of the error arising from discrepancies between the observed and modeled phase and amplitude, normalized by the combined modeled and observed signal variances. The best performance corresponds to a bias of 0, ρ = η = 1 and α = 0. For a random simulation α = 1, and hence for a model simulation to be deemed useful α < 1. The diagnostics ρ, η and α are non-dimensional, symmetric with respect to simulations and observations, and can be extracted for scalar and vector variables. These diagnostics are computed both over time and space. In the first approach, and at the location of each station and for a given season, the skill scores are extracted using all the days in the historical period (1980–2014). In the second approach, and for a given season and each day, the skill scores are computed using data from all the stations. Box plots are then constructed to highlight the range of values obtained for the stations and time-period considered, respectively, for a given season.

The trend and intercept of the linear regression are obtained with the Theil-Sen estimator, which is a non-parametric test that is insensitive to outliers and more robust than the ordinary least square regression technique ^107,108. The statistical significance is assessed with the Mann–Kendall test¹⁰⁹ considering a confidence level of 95%.

Changes in the length of the seasons are inferred with the percentile metric described in¹¹⁰ applied to the daily-mean air temperature. First, the 29 February is excluded in leap years so all years have 365 days, and the number of years selected for the historical (1980–2014) and climate change (2066–2100) periods is also the same, 35-years in each, in order to ensure a fair comparison. For each year, summer is defined as the period when the daily-mean air temperature is above the 75th percentile for that year, and winter when it is below the 25th percentile. Spring and autumn are the transition seasons with the temperature increasing in the former and decreasing in the latter. As in¹¹⁰, and in order to smooth the high frequency variability in the daily-mean temperature data and avoid more than two intersections with each temperature threshold, a third-degree polynomial function is fitted to the raw data. This methodology, applied here to each grid-point in the domain (i.e. the temperature thresholds are spatially varying), has the advantage of being insensitive to the background warming, which would have resulted in a shorter winter and longer summer season in a future climate. This is not true for other techniques such as the seasonal shift metric proposed by¹¹¹. Furthermore, the statistical significance of the projected changes in the seasons’ lengths is assessed with the bootstrap technique considering 1000 samples¹¹².

An important feature of the large-scale circulation in the target region is the subtropical high, which is typically diagnosed based on the maximum geopotential height at a selected pressure level such as 850 hPa, 500 hPa or 300 hPa^113,114. Here, the position of the subtropical high over North Africa (0°–35° N; 15° W–30° E) and Arabian Peninsula (5°–35° N; 35°–60° E) is identified based on the maximum of the 500 hPa geopotential height over each area, as this standard pressure level is above the complex topography in both regions. The bootstrapping technique¹¹² is used to assess whether the projected changes in the position of each subtropical high from the historical to the climate change period are statistically significant at 95% confidence level considering 1000 samples.

The position and strength of the Saharan Heat Low (SHL¹¹⁵) and Arabian Heat Low (AHL¹¹⁶) are characterized using the low-level atmospheric thickness (LLAT) metric, given by the difference between the 700 hPa and 925 hPa geopotential height values. In particular, the SHL corresponds to the area with the 10% highest LLAT in the region 20° W–30 °E and 0°–40° N at 06 UTC, just before local sunrise, as during daytime this field is impacted by the complex surface albedo pattern¹¹⁵. For the AHL, the LLAT is taken at 03 UTC and in the region 40°–60° E and 10°–35° N, excluding both water bodies and areas where the 925 hPa pressure surface is below topography¹¹⁶. For each heat low, the intensity is given by the average LLAT value over the defined heat low regions, while the latitude/longitude is defined as the LLAT-weighted latitude/longitude. Following¹¹⁶, the Intertropical Discontinuity (ITD), which is the boundary between the hotter and drier desert air and the cooler and more moist air over the Gulf of Guinea/Arabian Sea, is diagnosed using the 15 °C isoline of dewpoint temperature over West Africa (10°W–20° E) and the Arabian Peninsula (43°–60° E).