Vol. 128, No. 2 * Pages 143–286 * April - June 2024

Our method MISH (Meteorological Interpolation based on Surface Homogenized Data Basis; Szentimrey and Bihari) was developed for spatial interpolation of meteorological elements. According to mathematical theorems, the optimal interpolation parameters are known functions of certain climate statistical parameters, which fact means we could interpolate optimally if we knew the climate. Furthermore, the data assimilation methods also need to know the climate if Bayesian estimation theory is to be correctly applied. Therefore, we have developed the MISH system also to model the climate statistical parameters, i.e. present climate, by using long data series. It is a nonsense that we try to model the future climate but we do not know the present climate.

Calculation of the new climatological standard normals for the period 1991–2020 was a motivation to carry out the homogenization of the required climatic variables in the Spanish Meteorological Agency (AEMET).
The national observation network has undergone changes along its history that often introduce non-climatic interferences to the series. On the other hand, for the calculation of various parameters and climatic indices, it is essential to have complete daily series. With this in mind, homogenization of daily series of precipitation, maximum and minimum temperatures, sunshine hours, relative humidity, station level pressure, mean wind speed, and maximum wind gust was carried out.
This paper shows how the homogenization process was performed, covering the period 1975–2020 with carefully selected daily data sets from the national climatological database. The homogenization software Climatol v.4.0 was used for this process, and derived variables such as average temperature, sea level pressure, and vapor pressure were calculated from their related homogenized series.
The peculiarities and issues of each variable are explored and, finally, the homogenization results were used to readily calculate the 1991–2020 climatological standard normals with the dedicated software CLINO_tool v.1.5.

In Hungary, the regular precipitation measurements began in the 1850s under the direction of the then Austrian Meteorological Institute based in Vienna, and from 1870 onwards continued under the Budapest-based "Meteorológiai és Földdelejességi Magyar Királyi Központi Intézet", now HungaroMet Hungarian Meteorological Service. Over the decades, the measurements have undergone many changes, including changes in instrumentation and relocation of stations, which cause inhomogeneities in the data series. In addition, the number of stations and the density of the station network have also changed significantly. As a result, the data series need to be homogenized and interpolated to a uniform grid in order to study the climate and its changes over the long term. In this paper, we present the methods used, discuss the station systems used for precipitation homogenization and interpolation in different periods, analyze the main verification statistics of homogenization and also the results of interpolation, and examine the annual, seasonal, and monthly precipitation data series and their extremes for the period 1854–2022.

Precipitation gauges used for observations in the 19th century are reconstructed and pairs of gauges are installed at two, climatologically different, regular weather observation sites (Norrköping and Katterjåkk). Norrköping is a quite well sheltered site with a low degree of frozen precipitation, while Katterjåkk is an open site with a high degree of frozen precipitation. One of the gauges at each site is equipped with a wind shield. Parallel observations are conducted from November 2016 through May 2021. Regular observations are also conducted manually with modern gauges and with automatic gauges at the sites.
The wind shield effects (larger observed precipitation sums due to the inclusion of a wind shield) for the sheltered (Norrköping) and the open (Katterjåkk) sites are 7% and 16% for snow and 2% and 1% for rain, respectively.
The modern gauges generally collect more precipitation than the historical shielded gauges, the difference is 0–8% for rain and almost up to 50% for snow. However, these differences can, in part, be ascribed to micrometeorologal conditions at the sites.
The differences between observation methods are larger for snow and sleet than for rain. There are also larger differences in the open site than in the sheltered site.
The most closely placed modern gauge relative to the historical gauges (automatic gauge in Norrköping, manual gauge in Katterjåkk) gives the most similar precipitation sums, suggesting that micrometeorology is more important than the observation method.
The undercatch due to lacking wind shields in historical observations can probably not explain more than 20% of the increased observed precipitation in the late 19th and early 20th century.
The question of potential influence on climatological precipitation series due to the transition from historical to modern observation methods remains unconcluded.

The earlier versions of our method MASH (Multiple Analysis of Series for Homogenization; Szentimrey) were developed for homogenization of the daily and monthly data series in the mean, i.e., the first order moment. The software MASH was developed as an interactive automatic, artificial intelligence (AI) system that simulates the human intelligence and mimics the human analysis on the basis of advanced mathematics. This year we finished the new version MASHv4.01 that is able to homogenize also the standard deviation, i.e., the second order moment. The problem of standard deviation is related to the monthly and daily data series homogenization.

Spatial kriging interpolation has been a widely popular geostatistical method for decades, and it is commonly used to predict both gridded and missing climatic variables. Climate data is typically monitored across a variety of timescales, from daily measurements to thirty-year periods, known as long-term averages (LTAs). LTAs can be constructed from daily, monthly, or annual measurements so long as any missing values in the data are infilled first. Although spatial kriging is an available method for the prediction of missing data, it is limited to a single moment in time for each imputation. Not only can missing values only be predicted with observations measured at the same instance in time, but the entire imputation process must be repeated up to the number of timesteps in which missing data is present. This study investigates the imputation performance of spatiotemporal regression kriging, an extension of spatial regression kriging which simultaneously accounts for data across both space and time. Hence, missing data is predicted using observations from other points in time, and only a single imputation process is required for the entire data set.
Spatiotemporal regression kriging has been evaluated against a variety of geostatistical methods, including spatial kriging, for the imputation of monthly rainfall totals for the Republic of Ireland. Across all tests, the spatiotemporal methods presented have outperformed any purely spatial methods considered. Furthermore, three different regression methods were considered when de-trending the data before interpolation. Of those tested, generalized least squares (GLS) was shown to provide the best results, followed by elastic-net regularization when GLS proved computationally unavailable. Finally, the data set has been infilled using the best performing imputation method, and precipitation LTAs are presented for the Republic of Ireland from 1981–2010.

Commonly studying climate is gaining more and more space thanks to the expansion of the tools of statistical climatology and the development of the informatical background. Trend analyses of annual and seasonal mean temperature values clearly show that the Hungarian values are mostly in line with the global trend, and in some cases exceed it. Since a sufficient number of measurements are only available from the 1970s, we used hourly temperature values (03 UTC, 09 UTC, 15 UTC, 21 UTC) of the period 1971–2020 for station data series in Hungary for the trend analysis. In order to make the examined datasets sufficiently representative, we homogenized the station data series, filled in data gaps, and performed quality control using the MASH software. To ensure spatial representativeness, we interpolated the homogenized station data onto a dense, regular grid network with the MISH system. In addition, we used the ANOVA method to examine the expected values, standard deviations assigned to the hourly values, and we analyzed on maps how the values within the day changed in each region over 50 years.

This study concerns the interpolation of daily and hourly precipitation data in regions where small but intense thunderstorms, such as supercells, have occurred, and which, due to their size, often evade conventional meteorological stations. Consequently, relying solely on these measurements for interpolation can introduce errors and yield incomplete representations. To mitigate these issues, this research incorporates radar background information. The study selects days marked by significant precipitation during summer season and employs the Meteorological Interpolation based on Surface Homogenized Data (MISH) method for interpolation, both with and without radar-derived background data. Furthermore, our research also investigates the adaptability of the MISH method in handling radar anomalies, which encompass errors, missing data, and spurious measurements resulting from unintended radar reflections. Additionally, it examines whether the precipitation measured by radar can be used for climatic purposes on its own (without traditional measurements). Statistical techniques are employed to assess the improvement in interpolation quality with the inclusion of radar data and to quantify the relationship between interpolations with and without supplementary radar information. The study underscores the critical role of combining measurement data and radar products in the interpolation framework. This approach has implications for societal and agricultural sectors and offers potential benefits for hazard forecasting accuracy.