HadUK-Grid is a historical gridded meteorological dataset derived from station observations interpolated to a 1 km grid , using multiple regression combined with inverse-distance-weighted interpolation to account for local geographic and topographic factors . It has been published as a companion to the UKCP18 climate projections. Variables are available at a monthly time step, and selected variables are also available daily. The start date of each variable is dependent on the availability of station data. The earliest available data are monthly rainfall values from 1862, and coverage of variables increases with time, so all of the variables are available from 1969 onwards. This study used the data at 1 km resolution, with v1.0.3.0 for 1969–2020 inclusive and v1.1.0.0 for 2021. There are no differences between the two versions for 1969–2020 for the variables used. It is also available at 5, 12, 25 and 60 km resolutions. HadUK-Grid is representative of the meteorology at the centre of each grid box at the grid box centre elevation rather than providing grid box mean meteorology.

The HadUK-Grid daily climate variables used were the following.

Maximum air temperature measured between 09:00 UTC on day D and 09:00 UTC on day D+1 (tasmax, Tmax, ∘C)

The UKCP18 Regional Projections on a 12 km grid over the UK for 1980–2080, v20190731 , are a perturbed parameter ensemble of regional climate model (RCM) output for the years 1980–2080 provided at various time resolutions from daily to decadal. The RCM was run on a rotated pole grid, but the outputs are also available regridded onto a 12 km resolution grid aligned with the British National Grid (OSGB36); the latter data are used here. The domain covers the UK and surrounding waters and includes a small part of northern France. The first ensemble member (EM) 01 uses the default parameterisation of the Hadley Centre climate model GC3.05 (HadGEM3-GC3.05) for the GCM and a regional version of this for the nested RCM . The HadGEM3-GC3.05 configuration is very similar to HadGEM3-GC3.1 , which was used for Met Office contributions to the sixth phase of the Intergovernmental Panel on Climate Change (IPCC) Coupled Model Intercomparison Project (CMIP6; ), except for some differences in the atmosphere model and the sea ice model . The other ensemble members have had perturbations applied to several of the parameters within reasonable ranges informed by the fifth phase of the IPCC's Coupled Model Intercomparison Project (CMIP5; ). The HadGEM3-GC3.1 model has a relatively high climate sensitivity , so the UKCP18 ensemble range of climate sensitivity is high compared to CMIP5 but is consistent with the move to higher climate sensitivities in CMIP6 . All UKCP18 ensemble members used the same emissions scenario, Representative Concentration Pathway 8.5 (RCP8.5), which is a high-emissions scenario with no target for climate change mitigation . However, in order to provide a wider range of possible scenarios, each of the ensemble members was run with a different CO2 concentration trajectory. Each of these is consistent with RCP8.5 but represents uncertainty in the emissions scenarios . Details of the trajectories are given in Sect. .

The calculations were carried out on daily mean variables only for grid boxes that were modelled as land in the RCM. The variables used for both PET and PETI were the following.

Daily mean specific humidity at 1.5 m (huss, qa, kg kg-1)

Future climate projections also include the global atmospheric CO2 concentration. Although derived from the same emissions scenario, the atmospheric CO2 concentration pathways used by the Met Office as input to the UKCP18 RCM runs were different for each ensemble member to reflect global carbon cycle uncertainties . Ensemble member 01 used the concentrations prescribed in RCP8.5 for concentration-driven runs. The other ensemble members used CO2 concentrations that were calculated by selected CMIP5 emissions-driven ensemble members. These had different future trajectories, resulting in CO2 concentrations in 2080 ranging from 708 to 920 ppm across the ensemble . These trajectories are shown in Fig. . The values of CO2 were provided as annual values .

The surface elevation data used in the calculation of HadUK-Grid were from EU-DEM v1.1 , aggregated from 25 m spatial resolution to 100 m and then linearly interpolated to the centre point of each 1 km grid box following the method used in the generation of the HadUK-Grid 1 km dataset .

For the UKCP18 RCM ensemble, the climate model was run using elevation derived from EU-DEM v1.1 , smoothed appropriately for use as the lower boundary condition of the atmospheric model. After the model was run, the elevation was then regridded to the 12 km grid aligned with OSGB for distribution with the regridded climate variables – this is the elevation used in this study.

For these datasets, we first calculated Penman–Monteith PET. We then calculated PETI by applying an interception correction on rain days. We used the methodology of MORECS v2.0, again with the parameters of a short grass to estimate the amount of rainfall which is intercepted by the canopy . This was done by calculating the potential interception (PEI, mm d-1), which is the rate of evaporation from water intercepted by the canopy. This is subject to the same aerodynamic resistance as PET but is not limited by stomatal resistance, and so it was calculated by setting the canopy resistance rs to zero in the Penman–Monteith equation. The PETI was calculated as a combination of PET and PEI, dependent on how much water was intercepted by the canopy each day. The interception was dependent on the amount of precipitation and the LAI. A monthly enhancement factor was applied to account for the different characteristics of rainfall in different months (see Table ). Details of the calculations are in Appendix .

The HadUK-Grid dataset does not provide exactly the variables required as input for the Penman–Monteith equation, so these were derived from the existing variables. First, all variables that were only available monthly – the sunshine hours, wind speed, vapour pressure and sea level air pressure – were interpolated to a daily time step. These were then used in combination with the existing daily variables to calculate the appropriate input variables. Details are in Appendix , and an overview of the interpolation procedure is shown in Fig. .

Note that, since we do not have an exact estimate of net radiation from HadUK-Grid, we use a modified form of the Penman–Monteith equation that includes a correction for the radiative transfer between the surface and the screen height (Eq. ).

The Penman–Monteith calculations were carried out using the daily mean values of the output from the climate model (see Appendix ). In this case, UKCP18 provides net short-wave and long-wave radiation, so the unmodified Penman–Monteith equation was used (Eq. ). In order to account for rising levels of atmospheric CO2, a fertilisation effect was applied to the stomatal resistance following the method of (see Appendix  for details).

Since the UKCP18 output is provided for all land and sea points in the domain but PET and PETI are only valid over land, we only carried out the calculations for land points. The land points were selected using the land–sea mask provided by the Met Office , which defines grid boxes as either 100 % sea or 100 % land. There are some grid boxes which, although they are classified as sea in the RCM, do actually contain a small fraction of land. This is particularly important for hydrological models which run by disaggregating the meteorological inputs to a higher spatial resolution for calculating river flows. In order to allow the PET and PETI to be used as input to such hydrological models, these grid boxes were filled with valid data. To do this, a mapping was created between each grid box which needed to be filled and the nearest comparable land grid box. Then the PET and PETI were copied from the existing land grid boxes to the target grid boxes. This was done rather than calculating the PET and PETI with the existing meteorology in the RCM output, because the meteorology over the sea would be unrepresentative of land.

As the Hydro-PE method has been designed to calculate PETI to be comparable with MORECS PE for short grass, we have compared Hydro-PE HadUK-Grid and Hydro-PE UKCP18 RCM with MORECS. We have also compared it with the existing CHESS-PE PET and PETI datasets. We have calculated mean monthly climatologies for the common period 1981–2017 and for Great Britain (GB) only, as this is the land area that is common to all four datasets. These can all be seen in Fig. . Both Hydro-PE HadUK-Grid PET and the ensemble mean of Hydro-PE UKCP18 RCM PET are lower than MORECS PE, which is as expected (because of the inclusion of the interception correction in MORECS), but Hydro-PE UKCP18 RCM PETI is higher than MORECS PE in the summer and Hydro-PE HadUK-Grid PETI is higher than MORECS throughout the year. CHESS-PE PET and PETI are both lower than MORECS due to differences in the PE calculations and parameterisations. (The related FAO reference crop evaporation is a PET calculation that does not consider interception, so it will give a low estimate of PE when used for hydrology compared to PETI.) The 90th percentiles calculated over 1980–2000 for GB are in Fig. . The Hydro-PE UKCP18 RCM values are consistent with CHESS-PE throughout the year, while the Hydro-PE HadUK-Grid 90th percentiles are higher than CHESS-PE, particularly between October and April. This is due to the temporal interpolation from monthly to daily combined with the assumptions used to calculate the required inputs from the available HadUK-Grid variables (Appendix ). This is further discussed in Sect. .

The differences between the four datasets are due to either (a) differences in the input meteorology or (b) differences in the methodology. Since CHESS-met is derived from MORECS meteorology, we expect the differences between MORECS PE and CHESS-PE PETI to be due to methodological differences. However, since we have developed the Hydro-PE methodology to be as similar to MORECS as possible, the differences between Hydro-PE and MORECS PE should be due to differences between the meteorology in MORECS, HadUK-Grid and UKCP18 RCM, including differences in the calculation of the input variables from the available data.

Since HadUK-Grid and MORECS meteorology are derived from the same network of station observations (although not exactly the same stations) and CHESS-met is derived directly from MORECS, we might expect the meteorology averaged over a region to be very similar in all three datasets. Indeed, there is good agreement in GB mean air temperature and precipitation between HadUK-Grid, MORECS and CHESS-met (Fig. ), although MORECS air temperature is a little lower in the winter and MORECS precipitation is a little higher in the summer – this is likely due to the slightly different spatial coverage of the different resolutions. However, the different methods of downscaling of some variables from stations or MORECS to the 1 km grid can introduce differences between datasets. Most notably, the GB mean HadUK-Grid wind speeds are much higher than all of the other datasets. This is due to very high wind speeds at high elevations in HadUK-Grid, particularly in Scotland, due to the elevation adjustment used in the HadUK-Grid calculations . Figure  shows that, in Scotland, the HadUK-Grid wind speeds are much higher than the other observational datasets, while in England they are all comparable. Since MORECS is representative of a hypothetical site at mean grid box elevation (rather than mean grid box meteorology) and has a lower resolution, it does not represent these high wind speeds. The CHESS wind speed corrections were applied to the MORECS wind speed assuming that it does represent mean grid box wind speed, so the CHESS corrections are also not able to reproduce high wind speeds. The HadUK-Grid wind speeds were adjusted based on topographic relationships without assuming a preservation of the mean . The high values of Hydro-PE HadUK-Grid are likely more representative of high elevations.

Other variables that are used in the calculation of PE are not directly observed but have been derived from the variables provided by the station observations. There are differences in the methodology between HadUK-Grid, MORECS and CHESS that lead to some differences in inputs to the PE calculations (Fig. ). The specific humidity of HadUK-Grid is lower than MORECS in the summer, which leads to a higher humidity deficit (as the air temperature is nearly the same). The net short-wave radiation is very similar between HadUK-Grid and MORECS, as they are both calculated using the same methodology. CHESS-met uses the same method to calculate downward short-wave radiation but adjusts for slope and aspect, and it uses a different albedo parameterisation, so the CHESS-met net short wave is slightly higher. The approximate total available energy (calculated with Rne, Eq. ) calculated from HadUK-Grid is very similar to that calculated from MORECS meteorology. In CHESS-met the approximate available energy is higher because the net radiation is calculated differently and because CHESS does not include a ground heat flux. Overall, it is the combination of the higher wind speed and lower specific humidity in HadUK-Grid that leads to the higher PETI in Hydro-PE HadUK-Grid than in MORECS.

In addition to the differences in the means, the differences in methodologies have also had an impact on the extremes of the datasets. In particular, the Hydro-PE HadUK-Grid 90th percentiles are relatively high due to a combination of the radiation calculations (Sect. ) and the temporal interpolation of the monthly input variables. The CHESS-PE 90th percentiles are also relatively high compared to the mean values in winter, which is likely to also be due to the use of the same short-wave radiation calculation, but the effect is not as large as for Hydro-PE HadUK-Grid, as the CHESS input variables are all daily. It was not possible to investigate the MORECS percentiles, as MORECS was only available as monthly means.

The UKCP18 variables have been obtained from a free-running climate model that has not had any bias-correction applied. This means that although the climate model has been calibrated and parameterised against historical meteorological data, it is not expected to match the observed climate exactly. This may be down to deficiencies in the model structure and/or calibration but is also due to large-scale climate variability. The UKCP18 RCM reproduces the historical air temperature well, although the ensemble is slightly cooler than the observations in the spring (Fig. ). However, it significantly overestimates precipitation through most of the year compared to MORECS and slightly underestimates precipitation from August to October. This is likely due to the global circulation in the coarser-resolution GCM within which the RCM is nested bringing more moisture to western Europe . This results in a larger interception correction than is seen in the historical Hydro-PE HadUK-Grid for much of the year.

Again, the UKCP18 RCM has a lower specific humidity than MORECS (Fig. ), which in the spring and summer leads to a higher humidity deficit. The wind speed is very similar between the climate model and the observations, but the net short-wave radiation is much higher in the summer and autumn in the climate model. This is likely to be due to a lower amount of cloud in the model and partly due to different albedo values. In particular, the climate model is run with a realistic land cover, while the net short-wave radiation is calculated for all the other PE datasets assuming short grass everywhere. Overall, the available energy (calculated with the actual net radiation Rn, Eq. ) calculated with UKCEP18 RCM is higher than that calculated with either HadUK-Grid or CHESS-met. It cannot be compared to MORECS because we do not have actual net radiation for MORECS, but since we can see that MORECS and HadUK-Grid have very similar approximate available energies, Rne, we can infer that the UKCP18 RCM actual available energy is also higher than MORECS. Therefore, the high values of Hydro-PE UKCP18 RCM PETI in the summer are likely to be due to a combination of lower humidity and much higher available energy than in MORECS. The fact that the high May values of PETI seen in Hydro-PE HadUK-Grid and MORECS are not seen in Hydro-PE UKCP18 RCM is due to the seasonal cycle of temperature, humidity and available energy being shifted later in the year in the climate model than in the observations.

So, although there are differences between the Hydro-PE products and MORECS in the historical period, these are due to understood differences in the input meteorology.

The Hydro-PE HadUK-Grid PETI data were further compared to daily MORECS PE data for 16 sites across GB available for the period 1 January 1985–31 December 1992. The MORECS PE data are derived from observed station data at each site. These are compared with the HadUK-Grid PETI from the 1 km grid box that contains each site (see Table ). We expect some differences between the MORECS PE and the Hydro-PE HadUK-Grid PETI due to the difference in location, and therefore meteorology, between the MORECS sites and the HadUK-Grid 1 km grid box centres.

Three metrics were calculated to evaluate daily Hydro-PE HadUK-Grid PE relative to daily MORECS PE: (a) bias calculated as the difference in mean daily PE values annually and seasonally, (b) difference in the standard deviation in daily PE and (c) Pearson correlation coefficient of daily PE values and of deseasonalised daily PE values. The results are presented in Fig. , with boxplots summarising results over the 16 sites (Fig. a–c) and maps showing results at the site locations (Fig. d–f).

The HadUK-Grid PETI is higher throughout the year than MORECS PE, as shown by the positive biases across all the sites and seasons (Fig. a and d). This echoes the results from the GB-wide comparison in Fig. . HadUK-Grid PETI also tends to have slightly higher variation than MORECS PE, as shown by a higher standard deviation in PE time series for 9 out of the 16 sites. Correlation between HadUK-Grid PETI and MORECS PE is generally good across all the sites, with Pearson correlation coefficients in the range 0.72–0.81. The high Pearson correlation coefficients are partly due to the fact that we represent the seasonal cycle well. With deseasonalised data, the Pearson correlation coefficients are in the range 0.30–0.47, which still shows a reasonable correlation with the MORECS PE. Even though the need for temporal interpolation of some HadUK-Grid variables from monthly to daily is likely to suppress the daily variability to some extent, the daily variability of the calculated PETI is still comparable to observations.

While PET and PETI are not directly observable quantities, they are an estimate of unconstrained evapotranspiration. In GB in the winter, spring and autumn evaporation rates are low and precipitation is high, so it can be assumed that most evaporation will occur at the potential rate. Thus we can compare eddy covariance (EC) flux measurements of actual evaporation (AE, mm d-1) with PETI calculated from the meteorological measurements at each EC site using the Hydro-PE methodology (EC site PETI). We also compare this with the Hydro-PE HadUK-Grid PETI from the 1 km grid box containing each site with the EC site PETI.

We used measurements of AE and meteorology from two EC sites in England. Berkshire Organic Grassland (BD-OG)

This site is located on an organically managed grassland in the Berkshire downs at an elevation of 184 m above sea level . EC measurements are available from 1 January 2017 to 16 November 2019 .

In order to evaluate the impact of temporal interpolation and the calculations applied to the HadUK-Grid input data, we used the PLUMBER2 dataset , which consists of gap-filled and quality-controlled observational data from 170 global flux sites. We used the half-hourly meteorological variables from the 33 grassland sites in the Northern Hemisphere. We first applied the Hydro-PE calculations directly to daily means of the observed variables: precipitation, air temperature, specific humidity, wind speed, air pressure and net radiation. We then used the half-hourly variables to calculate the equivalents of the HadUK-Grid variables: daily minimum and maximum air temperatures were calculated from the half-hourly air temperature, sunshine hours were calculated from the half-hourly downward short-wave radiation using the World Meteorological Organisation threshold of 120 W m-2, and vapour pressure was calculated from specific humidity and air pressure by inverting Eq. (). The sunshine hours, vapour pressure, wind speed and surface air pressure were then averaged to monthly. We used these monthly variables plus the daily precipitation and the derived daily minimum and maximum air temperatures in the same calculations as for the HadUK-Grid meteorology and performed the same interpolation to daily (Appendix ). Finally, we applied the Hydro-PE calculations to these interpolated and derived daily variables.

We compared the PETI calculated using derived and interpolated variables with the PETI calculated using the original daily mean variables using three metrics: the bias, the error in the standard deviation of the daily values and the Pearson correlation coefficient of the raw daily values and deseasonalised daily values (Fig. ). The PETI calculated using the interpolated derived meteorology is overall higher than that calculated from the daily mean, although for some sites it is lower, with the bias being between -0.12 and 1.01 mm d-1 across the sites. The largest difference is in the summer, which has a bias between -0.26 and 1.65 mm d-1. The errors in the standard deviation are roughly evenly distributed, with 19 sites having a higher standard deviation and 14 sites a lower one. The Pearson correlation coefficient is between 0.75 and 0.94, calculated with the raw data. With the deseasonalised data it has a larger range, being between 0.14 and 0.70; it is greater than 0.5 for 19 sites. Results were very similar for PET.

We also compared the monthly median and the 10th and 90th percentiles of the PETI for each site calculated (a) using the daily mean meteorology, (b) using the meteorology derived and interpolated following the methods applied to HadUK-Grid, and (c) using the monthly mean meteorology (Fig. ). The median is well represented, as are the summer 90th percentiles and the winter 10th percentiles. However, the PETI calculated using derived and interpolated input variables tends to overestimate the 90th percentile in the autumn and winter and overestimate the 10th percentile in the spring and summer compared to using the original daily means. However, despite this, it does perform better than simply using monthly mean inputs, which is equivalent to the use of MORECS monthly PE and which overestimates the 10th percentile and which underestimates the 90th percentile throughout the year. Most of the variability in the PETI calculated using derived and interpolated variables is due to using the daily air temperature and precipitation compared to using the monthly means of all the variables. There is a negligible difference between using the actual daily mean air temperature and the approximation using daily minimum and maximum temperatures (Eq. ).

One source of the overall positive bias is the derived and interpolated net radiation, which has a high bias compared to the daily PLUMBER2 net radiation values, with mean bias error ranging between 3.39 and 51.9 W m-2 across the sites. This is largely due to a high bias introduced in spring and summer by the calculation of short-wave radiation from sunshine hours (Sect. ), which also causes the 10th percentiles of net radiation in the summer and the 90th percentiles of net radiation outside of the summer to be higher than those of the daily PLUMBER2 data. The temporal interpolation further enhances this impact on the extremes due to the effect of the reduced variability on the complex interplay between the different physical variables.