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History of modifications

List of datasets covered by this document

Related documents

Acronyms

General definitions

Scope of the document

This document describes NGCD input data sources and the algorithms used to generate the products.

Executive summary

NGCD is a high‐resolution observational gridded dataset for daily temperature and precipitation covering Fennoscandia (Finland, Sweden and Norway). It covers the period 1971‐present, and it has a grid spacing of 1 km in both the Northing and Easting directions.

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The climate dataset consists of two independent datasets, NGCD-1 and NGCD-2, derived using different spatial interpolation algorithms applied to the same input observation dataset. The gridded dataset is based on observations of daily precipitation and daily mean, minimum and maximum temperatures. A historical archive of NGCD is made available in subsequent versions, released twice a year, in March and September. A provisional archive of NGCD is updated daily and it provides fresh data for those applications that require data availability closer to real time than two releases per year.

For more information on NGCD, such as how to access the data and product information updated to the latest version, we refer to the C3S Product User Guide and Specification for NGCD (Nordic Gridded Climate Dataset: Algorithm Theoretical Basis Document (ATBD))D1).

The input data sources are described in the next section. Then, the spatial interpolation methods are described in the Nordic Gridded Climate Dataset: Algorithm Theoretical Basis Document (ATBD) Algorithms section.

In a nutshell, NGCD-1 mean, minimum and maximum temperature are based on residual kriging with five explanatory variables, the weights of which, in the trend expression, are estimated from long term climatology on a monthly scale. Precipitation is estimated by triangulation with a terrain adjustment. NGCD-2 is based on Bayesian spatial interpolation methods. For temperature, a two‐step scale separation OI is applied. Precipitation is based on a multi‐scale optimal interpolation over a cascade of (decreasing) spatial scales. The programs used for production are available at https://github.com/metno/NGCD.

Input Data Sources

The in-situ observations used have been measured by networks of traditional weather stations managed by public institutions. The list of data providers is shown in Table 1.

Note that for the production of the NGCD historical archive, the station data over Finland and Sweden are obtained via ECA&D (Klein Tank et al., 2002), while for the provisional archive the data over the two countries are retrieved from the FMI and SMHI open data application programming interfaces.

NGCD input data are non-homogenized time series. For the historical archive, the time series used are the non-blended ECA&D dataset. Therefore, NGCD uses a larger set of observations than we could have using only homogenized stations, particularly for more recent years. In this way, the estimates of precipitation and temperatures should include phenomena on a more local scale, as we use a denser observational network. This characteristic is important for hydrological applications, for instance. However, the drawback is that long-term temporal trends extracted from NGCD can be affected by possible local inhomogeneities in the input data (Masson and Frei, 2016). For this type of application, a suggestion could be to spatially aggregate the NGCD grid points at spatial scales coarser than 1 km, in order to filter out some of the variations due to changes in the observational network over time.

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The automatic quality checks applied  have been implemented in the TITAN software (Båserud et al. 2020), which in turn make use of the functions made available through the titanlib library. Those software are designed to test, simultaneously, all the observations referring to the same observation time using spatial quality control methods, such as buddy-check or spatial consistency tests. Currently, the statistics of the individual station time series are not considered.

List of in-situ data providers

Algorithms

Interpolation of temperature, type 1

The spatial interpolation of temperature for NGCD-1 is based on a residual kriging model developed by Tveito et al. (2000) to derive monthly, long term climatologies for Fennoscandia. Residual kriging is a conventional and frequently used concept to produce gridded temperature data. Kriging (and in principle any 2D spatial interpolation method) assumes second order spatial stationarity. There are several reasons why this assumption is difficult to fulfill when considering meteorological observations directly. Meteorological station networks are normally biased, especially towards lower elevations (populated areas, Figure 1). They will therefore not represent the whole spatial domain they are meant to cover. Fields of meteorological elements are also strongly influenced by the local physiography and environment. In areas with large variations in topography and other physiographical and environmental conditions, the spatial field of meteorological elements will not exhibit second order stationarity or show an isotropic behaviour in its spatial covariance structure.

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The first step is to obtain the spatial trend. For the gridding of daily minimum (TN), daily maximum (TX) and daily mean temperatures (TG), the trend is defined by applying five external predictors, as described by Tveito et al. (2000). The five predictors are: point or grid cell elevation, average elevation within a 20 km circle, minimum elevation within the 20 km circle, longitude and latitude. The objective is to use these five predictors, each of them available as a gridded field on the NGCD grid, to obtain monthly spatial trends (i.e. one gridded field per month). In order to obtain these monthly trends, a multiple linear regression is applied where the five predictors are the independent variables and the dependent variables are mean monthly long term (normal) temperatures. The regression parameters are optimized by fitting the best multiple linear relationship between the dependent and independent variables. In this way, fixed monthly trend expressions are established, and the same trend expressions are applied for TN, TX and TG. This will ensure consistency between the three temperatures.

The spatial trend used for NGCD-1 is a similar concept as the first-guess or pseudo-background used for NGCD-2. In the context of kriging models, the term "trend" is commonly used, while for OI, terms like first-guess or background (see Interpolation of temperature, type 2) are used with a similar meaning. In this document, we have decided to keep the terms used in the referenced articles. Note that there is a difference between NGCD-1 and NGCD-2 which is worth noting. The NGCD-1 trend is the same for every day of a month. The NGCD-2 pseudo-background varies every day.

The trend expressions show a strong annual cycle (Figure 2), indicating that the influence of the predictors varies throughout the year. The effect of the smoothed terrain is stronger in winter and the local terrain is stronger in the warmer seasons. This is, among other things, due to the small scale variability caused by temperature inversions during the winter season. The strong seasonal variation in the longitude parameters reflects continentality and the opposing coast-inland temperature gradients in winter and summer.

Figure 3 shows the trend fields based on linear regression models for January and April. They clearly show the different influence of the external parameters included in the trend field. The spatial variability of the trend field in January is characterized by variations on larger spatial scales than in April. In fact, in April the signal of the high resolution terrain model is very distinct.

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Figure 3: NGCD-1 temperature trend fields (background fields) for January (left) and April (right)

Interpolation of temperature, type 2

The statistical method applied is described in detail by Lussana et al. (2018a). The core of the method is a modified Optimal Interpolation (OI) scheme, where the pseudo-background (or first-guess) field is the blending of several spatial trends of temperature. Each trend is centered on a subregion and it is obtained by fitting non-linear analytical functions to a subset of the observations. In this sense, the method is based on a two-step scale-separation concept. First, the pseudo-background temperature at grid points is computed, based on the dozen, nearest observations. Second, the OI locally adjusts the temperature fields at grid points based on the few (i.e. much less than for the pseudo-background), nearest observations. The exact number of the observations used at a location by the OI depends both on the local station density and and the geophysical characteristics of the area. The weights of each observation in the OI is determined by the correlation function, as explained in this section, below. A spatial consistency test (Lussana et al., 2010) has been included, so that the method is robust from a statistical point of view.

The main improvement in the NGCD procedure is the inclusion of the land-area fraction (LAF, a scalar value between: 0 = point is in the water, as in the sea or a big lake; 1 = point is surrounded by land) among the geographical information used (Lussana et al, 2018a). The others are: geographical coordinates and elevation. LAF is used in the definition of the correlation function (Eq.(1), Lussana et al., 2018a) to decorrelate grid points along the coast from inland grid points. The correlation function ⍴ between the two points r_i and r_j is then:

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The exponential function on the right hand side of the equation is the same correlation function used in (Lussana et al, 2018a), where: Δd indicates the horizontal distance, Δz the elevation difference. The parameter values used are: the horizontal decorrelation length (D^h), which is set to 60 km; the vertical decorrelation length (D^z), which is set to 250 m. The OI requires the specification of the ratio between observation and background error variances, which is set to 0.5 (i.e. we assume that observations are twice as precise as the background).

The exponential function is is multiplied by a linear function of the LAF differences, Δw. w_min is set to 0.5. As a result, if two points, r_i and r_j, of the same LAF class are considered (i.e. Δw=0), then the LAF term is equal to 1 and it does not affect the correlation between r_i and r_j. On the other hand, when for r_i and r_j the LAF difference is such that Δw=1 (e.g. one point is on land and the other over the sea), then the LAF term in the square brackets is equal to w_min. This means that, with our settings, when Δw=1, the correlation is half of that which would occur with the exponential function alone.

Interpolation of precipitation, type 1

Precipitation is a more challenging element to interpolate in space due to its non-continuous, non-Gaussian characteristics. This means that the spatial interpolation of precipitation is usually a two-step procedure; first, determine the areas that have precipitation and secondly, determine the precipitation amount in those areas. It also means that the assumptions of the statistical interpolation methods are difficult to fulfill. The method used for estimating precipitation in NGCD-1, therefore, takes a different approach. It is based on Delaunay triangulation and is therefore in its basics, closely related to the nearest neighbour, Thiessen method that has been frequently used to estimate areal precipitation. The main difference is that while Thiessen polygons represent precipitation as flat surfaces (terraces), triangulation represents precipitation as a surface where the precipitation "height" at the three stations at the corners of the triangle, defines the linear slope of that triangle.

Both experience and theory shows that precipitation increases with elevation, and this is implemented in the type 1 interpolation as an altitude adjustment term. In practice, this means that two fields are interpolated: ( i ) precipitation amount and (ii) station elevation. The difference between the station elevation grid and the 1x1 km terrain model is used to adjust the precipitation grid. The height adjustment is 10% per 100 m at elevations below 1000 metres above sea level (m.a.s.l) and 5% at higher elevations. Since most of the precipitation stations are located at the lowest elevations, this adjustment is quite large in some places. The procedure is shown in Figure 4.

Figure 4: NGCD-1. Daily total precipitation (RR) field for 15 October 1987 based on triangulation.

Interpolation of precipitation, type 2

The gridded precipitation data of NGCD-2 is based on the statistical interpolation method presented by Lussana et al. (2018b). It builds upon classical methods such as OI and successive-correction schemes (Daley, 1991) adapted to the peculiar characteristics of precipitation. It is an iterative method as shown in Figure 5. In the first iteration, the estimation of precipitation over the grid points involves all the observations simultaneously, such that the field is constant and equal to the mean observed value. Then, each iteration adjusts the field locally at the grid points and this adjustment involves fewer and fewer observations each time. As a result, the effective resolution of the final fields depends on the local station density. In data-dense areas, the precipitation field includes all the available details. On the other hand, for data-sparse regions, such as in the mountains or in the north of the domain, the precipitation field in the proximity of a station is very close to its observation, while in between stations the field is actually representative of a larger-scale mean precipitation.

In the case of NGCD-2, the main differences compared to Lussana et al. (2018b) are that: (1) in the specification of the OI correlations between two points, the elevation differences are not taken into account; (2) the "identification of events" has been removed because the benefits are not evident and sometimes it creates unrealistic border effects between rain/no-rain regions.

The reason that led us to choice (1) above is that the number of RR observations decreases significantly as the elevation increases (see C3S Product User Guide and Specification for NGCD (Nordic Gridded Climate Dataset: Algorithm Theoretical Basis Document (ATBDD1))). Therefore, in mountainous areas it is necessary to use the nearby observations to estimate the precipitation, regardless of any differences in altitude. Note that as a result of choice (1), the spatial interpolation method does not rely on user-defined parameters and this strengthens the portability of the method to other areas.

Figure 5: NGCD-2. Daily total precipitation (RR) field for 2 June 1995 based on the iterative OI method. The top row shows two iterations for the larger spatial scales. The bottom row shows two iterations for the smaller-scales. The dots show the observations.

References

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