Three variants of synthetic benchmarks time series of GPS and ERA-Interim IWV differences

<b>Description of the synthetic datasets</b><br>Daily synthetic series of 6000 samples (i.e. length of 16y*365d) for 120 IGS sites for GPS-retrieved (IGS repro1) Integrated Water Vapour (IWV) values, and IWV differences between ERA-Interim model and GPS (IGS repro1) were simulated based on the characterisation (signal and noises) derived from the real datasets. The real ERAI-GPS IWV differences were firstly homogenized with a manual detection of breaks to provide the most consistent series. All manually detected epochs of breaks were cross-validated with information included in the log-files of the stations. If manually detected breaks were not reported as change in a log-file, then they were not corrected for, unless the offset is clearly seen in differences (ERAI-GPS). We assume the ERA-Interim model as an absolute reference with no artificial breaks. Under this assumption, only climate signals should be responsible for jumps in the time series.<br><br>We tested different approaches, as we generated synthetic datasets for the IGS repro1, the ERA-Interim, and their differences. We found that generating directly the synthetic differences is closer to the real differences than building the differences afterwards based on generated synthetic ERA-Interim and the generated synthetic IGS repro1 IWV time series separately, so we proceeded with the synthetic differences. <br><br><b>Specifications of the synthetic datasets available</b><br>Three different variants of those synthetic datasets were constructed:<br>Variant 1: <i>The ‘Easy’ dataset</i>: it includes seasonal signals (annual, semi-annual, 3 &amp; 4 months if present for a particular station) + offsets + white noise.<br>Variant 2: <i>The ‘Moderate’ dataset</i>: seasonal signals (annual, semi-annual, 3 &amp; 4 months) + offsets + autoregressive process of the first order + white noise (AR(1)+WH).<br>Variant 3: The <i>‘Complex’ dataset</i>: trend + seasonal signals (annual, semi-annual, 3 &amp; 4 months) + offsets + AR(1)+WH + gaps.<br><br>Variant 1 was created only for the ERA-Interim - GPS differences while Variants 2 and 3 were created both for 1) differences of IWV between ERAI and GPS (ERAI-GPS), and 2) GPS itself. The values of trends, amplitudes of seasonal signals, noise process and percentage of gaps were directly modelled taking into account the derived characteristics from the real datasets. The epochs of offsets were simulated randomly, separately for each variant, but the number and amplitudes of the offsets are characteristic for the real datasets. <br><b>File format of the synthetic datasets </b><br>Each of the simulated series are stored in a separated file. As for the real dataset, each file includes three columns: “year, y-x, x”. “Year” is a date formatted as YYMMDD.HHMMSS (e.g. 950101.120000 for 1st January 1995 at 12:00 UTC), column “y-x” includes differences between the ERAI and GPS synthetic values (in that order), and “x” means the ‘GPS-retrieved’ IWV synthetic values.