Reanalysis and station rainfall data
It is common to employ more than one dataset to assess the robustness of AR detection techniques. Datasets used to identify ARs are the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim (ERA-interim)27 and the most recent reanalysis dataset version from ECMWF, namely the ERA-5 reanalysis project28. Atmospheric reanalysis data between 1979 and 2018 from ERA-interim and ERA-5 at 0.125°×0.125° and 0.25°×0.25° horizontal grid resolution were retrieved, respectively. Data used are 6-hourly specific humidity and zonal wind and meridional wind components at 20 vertical pressure levels (300hPa to 1000hPa), and land-sea mask. The integrated water vapour transport (IVT) vector at each grid cell was calculated in an Eulerian framework13,17 as:
where q, u, ν and are specific humidity (kg kg-1), zonal and meridional vectors (m s‑1), respectively; g is the gravitational acceleration (9.81 m s-2), and dp (Pa) is the pressure difference between two adjacent atmospheric pressure levels. Note that all parameters in equation (2) and (3) were collected at discrete atmospheric pressure levels from the selected datasets. According to Guan and Waliser22, the median length of global 1997-2014 ARs is about 3,665.1km. For the ARs detected in the Southern Hemisphere, ARs commonly have a southeastward direction with a median degree of 120.6°, and the median latitude of the AR equatorward end, centroid, and the poleward end is 28.5°S, 41.1°S, and 49.5°S respectively. Considering that the longitude length of a degree at 49.5°S is approximately 72km and the first eastward meridian line across New Zealand is at about 166°E. Therefore data retrieved over the 0-70°S and 100°E-120°W domain is considered adequate (166°E– 100°E = 66°, 66° × 72km/degree = 4,725km > 3,665.1 km).
Station-based daily rainfall totals were obtained from New Zealand’s national climate database web system hosted by the National Institute of Water and Atmospheric Research (NIWA). Note that the periods of records differ among sites, and the observation times of the day are 2100 UTC (2000UTC) during the wintertime (summertime). Sites with less than 10 years of daily rainfall records between (September–August) 1979 to 2018 and completeness less than 100% were excluded because the lack of daily rainfall data could potentially lead to under- or overestimations in the hydrological impacts of ARs. Given these conditions, a total of 654 stations with a mean length of 19 years were selected over the whole country (see Fig. 5).
AR detection method
The AR detection algorithm introduced in Guan and Waliser22 was used, and ARs were detected based on the ERA-interim and ERA-5 reanalysis dataset, respectively. IVT and IVT threshold (monthly 85th percentile within a 5-month window centred at that month) for each grid cell and the land-sea mask from the two datasets are the inputs. Note that the land-sea mask values were adjusted only to contain grid cells represent New Zeland landmasses (1s represent New Zealand landmasses, 0s refer to others). Briefly, criteria of the AR detection algorithm include the IVT magnitude at each grid cell within a contiguous region being above the IVT threshold and a fixed limit (IVT > 100 kg m-1 s-1) for that grid cell, the apprepicable poleward direction of the AR (IVTy >50 kg m-1 s-1), and the length of an AR greater than 2,000km with a length/width ratio greater or equal to 2. Outputs from the algorithm include the variables of shape, axis, and landfall location of the ARs in netCDF files and detailed characteristics of landfalling ARs in text files. The AR shape variable was used to compute the AR area, the axis was used to calculate the AR length, and the width was calculated as the area divided by the length. The landfall location was marked the first grid cell that the AR axis intersects the coastlines alone the IVT vector direction and that AR was labelled as a landfalling AR. The content in Fig. 2 and Supplementary Fig. 2 is based on the characteristics of landfalling ARs. The detailed description of the AR detection procedure and criteria of this technique are in Guan and Waliser22. Fig. 6 shows one of the strongest detected ARs passing New Zealand.
AR frequency and AR impacts on rainfall
The AR frequency was calculated as the average number of days per year that an AR was detected for each grid cell. The calculation was based on the shape of detected ARs. For example, at least one of the four reanalysis time steps per day meeting the AR detection criteria for it to be counted as an AR day13. Seasonal AR frequency is expressed as the anomalies from the mean seasonal AR days. The coefficients of variation (CV) for annual and seasonal AR days were calculated to evaluate the interannual variation of AR frequency.
Consider a given station with daily rainfall records (measured at 2000 UTC or 2100 UTC) on 15 June 2000. To determine if the rainfall should be associated with an AR, the first step is to search for AR conditions (based on AR shape) at the four grid points that enclosed the station site between 2000 UTC (2100 UTC) 14 June 2000 and 2000 UTC (2100 UTC) 15 June 2000. If any of the four ERA-interim (ERA-5) time steps that AR conditions (based on AR shape) were found in the 4 grid points, the daily rainfall recorded between this period is considered to be AR-generated rainfall, and that day herein considered as a wet AR day. Unlike previous studies that any of the four grid points that AR conditions were present13 and rainfall in the next day10,13,29 (e.g., here the 16 June 2000, if any) considered as AR-precipitation event, only AR conditions presented at 4 grid points and rainfall occurred in the same day were considered as AR-generated rainfall in the present study.
Rainfall intensity under AR and non-AR conditions were compared by the median daily rainfall13 (calculated separately for days with and without AR conditions at each station, and the ratio was subsequently obtained). Further, the fraction of annual and seasonal highest 10% rainfall events that are attributed to ARs were also investigated.