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Applied Sciences
  • Feature Paper
  • Article
  • Open Access

29 January 2021

Calculation of Agro-Climatic Factors from Global Climatic Data

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1
Department of Geomatics, Faculty of Applied Sciences, University of West Bohemia in Pilsen, Univerzitní 8, 306 14 Pilsen, Czech Republic
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WIRELESSINFO, Cholinská 19, 784 01 Litovel, Czech Republic
3
Plan4All z.s., K Rybníčku 557, 330 12 Horní Bříza, Czech Republic
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Author to whom correspondence should be addressed.
This article belongs to the Special Issue Visualisation of Big Data in Agriculture

Abstract

Abstract

This manuscript aims to create large-scale calculations of agro-climatic factors from global climatic data with high granularity-climatic ERA5-Land dataset from the Copernicus Climate Change Service in particular. First, we analyze existing approaches used for agro-climatic factor calculation and formulate a frame for our calculations. Then we describe the design of our methods for calculation and visualization of certain agro-climatic factors. We then run two case studies. Firstly, the case study of Kojčice validates the uncertainty of input data by in-situ sensors. Then, the case study of the Pilsen region presents certain agro-climatic factors calculated for a representative point of the area and visualizes their time-variability in graphs. Maps represent a spatial distribution of the chosen factors for the Pilsen region. The calculated agro-climatic factors are frost dates, frost-free periods, growing degree units, heat stress units, number of growing days, number of optimal growing days, dates of fall nitrogen application, precipitation, evapotranspiration, and runoff sums together as water balance and solar radiation. The algorithms are usable anywhere in the world, especially in temperate and subtropical zones.

1. Introduction

There is a growing need in agriculture to analyze data and, following this, synthesize as much relevant information as possible to support decision making. Such information is essential in current situations, where climate change is discussed. Calculations on hard data provide objective outputs and help agriculture experts understand what changes they are facing in their region.
Therefore, agriculturally oriented IT experts work on the utilization of Earth Observation data (both multi and hyperspectral), climatic data, in-situ sensor data (connected to IoT), crowdsourced and linked data together with traditional geographic data. They search for innovative methods of data processing and analysis to enable evidence-based decision making in agriculture.
This manuscript analyses global climate data (open big data by its nature) and its value for agriculture, particularly for the calculation of so-called agro-climatic factors (climatic factors influencing crop growth). Based on the knowledge of agro-climatic factors and their variability in time, a farmer can select appropriate crops, proper cultivation methods, and also optimize field works.

3. Materials and Methods

3.1. Materials

As particular agro-climatic factors were described in the previous section, demand for relevant information about soil and air temperatures, precipitation, evapotranspiration, and sunlight was settled. Fortunately, such information can be found in a worldwide coverage dataset with hourly-series of data providing an enormous amount of relevant data-ERA5-Land dataset (of Copernicus Climate Change Service []). Such data can be related to another dataset containing information about the uncertainty of data used-Ensemble of Data Assimilations model (of Copernicus Climate Change Service). Finally, for the evaluation of the input data from the global data, we also obtained information from in-situ sensors to compare the values for calculated agro-climatic factors. The description of the mentioned sets of data is in the following sections.

3.1.1. ERA5-Land Hourly Data from 1981 to Present

ERA5-Land is a replay of the land component of the ERA5 climate reanalysis [], but with a series of improvements making it more accurate for all types of land applications. ERA5-Land is a reanalysis dataset providing a consistent view of the evolution of land climatic variables over several decades. Horizontal coverage is global with resolution 0.1° × 0.1° (arc-deg). Vertical coverage is from 2 m above the surface level to a soil depth of 289 cm. Temporal coverage is now from January 1981 to present with hourly resolution. The data format is GRIB or NetCDF [].
ERA5-Land is still under development and should be completed during 2020 and incorporates data from 1950 to 2–3 months before the present []. During the calculation of agro-climatic factors presented in this manuscript, the data were available first for the period 1990–2019, later for 1981–2019 (the year 1981 was incomplete). Therefore, the calculations of individual agro-climatic factors are based on these periods. Occasionally, faulty units appeared for some variables. For example, a runoff was supposed to be in meters, but it was in units of m * 0.0001, the appropriate constants corrected such errors in the algorithm.
The climatic model used in the production of ERA5-Land is the tiled ECMWF Scheme for Surface Exchanges over Land incorporating land surface hydrology (HTESSEL). More information about the used climatic model CY45R1 can be found in its documentation (how individual variables are calculated, spatial interpolations, and so on) [].
Note that before the numerical experiment, we checked the normality of the ERA5-Land hourly data. We performed two statistical tests (namely Chi-squared goodness-of-fit test and the Kolmogorov-Smirnov test), and the results were a rejection of the null hypothesis of both tests at the 1% and 5% significance level, i.e., data did not come from a standard normal distribution.

3.1.2. ERA5 Ensemble of Data Assimilations (ERA5 EDA)

To know how precise the data from the ERA5-Land dataset are, we need to reach for such information elsewhere, because, for the time being, ERA5-Land in Copernicus Climate Change Service does not allow the download of information about uncertainties of an associated EDA (Ensemble of Data Assimilations) model for specific ERA5-Land places. In case of an attempt to download the associated uncertainties based on the EDA, it is necessary to go through the download of EDA information connected with the ERA5 dataset.
ERA5 climate data contain some uncertainty provided by the EDA system. Uncertainty estimation helps to understand the relative accuracy of the ERA5 (or ERA5-Land) system to identify areas/periods where the products are thought to be less or more reliable. However, the uncertainty values provided by the EDA system should not be taken at face value. The EDA system addresses uncertainties related to the observing system, sea surface temperature, and the model (through its physical parametrizations) [].
The uncertainty of ERA5-Land does not represent a classical measure of error. Uncertainties of Ensemble Data Assimilations (EDA) model related to ERA5-Land takes into account mostly random errors in observations (such as a sea surface temperature, physical parametrizations of the model, uncertainties related to the observing system, etcetera). If we assume that these uncertainties are described properly, and there are no additional sources of uncertainties in the model’s input values, then EDA represents uncertainties in ERA5-Land correctly. Moreover, systematic model errors are not taken into account by the EDA, and the uncertainties, as defined by the EDA, are uncorrelated. On the other hand, the EDA model related to ERA5-Land in Copernicus Climate Change Service is available neither in the same spatial resolution nor in the same time interval. ERA5-Land is provided in a regular equiangular grid with the spatial resolution of 0.1° × 0.1° (arc-deg) (10 km × 10 km), while the spatial resolution of its uncertainty is five-time larger, i.e., 0.5° × 0.5° (arc-deg) (50 km × 50 km). Further, the time interval of data available in ERA5-Land is one hour, while EDA provides the uncertainty in the interval with the regular time step of three hours. For more details about EDA, please see [].

3.1.3. Case Study Area in Kojčice

Observations used for the evaluation of global ERA5 data to compare physical variables were produced during the air and soil monitoring campaign in the year 2018 in the location of Kojčice village (15.22 E, 49.46 N) near Pelhřimov in the Czech Republic (see Figure 1). There was a set of sensor nodes deployed in the pilot locality in the fields. Most of the deployed nodes were equipped with sensors for soil monitoring, and one node was equipped with soil and air monitoring sensors. The air temperature in 2-m height above the ground was selected as the phenomena for comparing with the global ERA5-Land data set. The air temperature was measured by the combined multisensor VP-3 from the Decagon(R) Devices company. This sensor was measuring air temperature, humidity, and vapor pressure every 2 h from 21 March 2018 to 29 December 2018. Specifications of the used VP-3 multisensor for air temperature phenomenon are resolution 0.1 °C, range from −40 °C to +80 °C, and accuracy is defined by the continuous function where the maximum error is the function of the temperature. The maximum error for the measured range in the pilot locality is ±0.75 °C, but for most observations is ±0.5 °C and less. The distance between the sensor node position and the ERA5-Land reference point is approximately 350 m.
Figure 1. Location of the sensor node, and reference point for ERA5-Land model, location of the locality in the Czech Republic (overview map).

3.1.4. Case Study Area in the Pilsen Region

The Pilsen region (location of such a region is shown in Figure 2) was chosen as a case study for calculation of all agro-climatic factors mentioned in Section 3.2 because this area of interest is being investigated in various research projects supporting this contribution (see part Funding stated after Section 6. Conclusions).
Figure 2. Regions of the Czech Republic with the highlighted Pilsen region in yellow.
It is worth stressing, even though the area of interest was chosen, the calculation of agro-climatic factors using hourly ERA5-Land data can be done for almost any particular place or area on the Earth, where the coverage of such a dataset is provided. Furthermore, thanks to the interactivity of scripts created, they have an area or place of interest as an input parameter. Methods, which are implemented for the area of interest, while respective outputs are provided here for each of such factors in basically two forms. In the form of graphs representing time-dependent manners of the particular factor for a specific place in the area of interest (geographical center of the Pilsen region) and the form of maps of such a region enable to see a spatial (or spatial-temporal) distribution of the calculated factor in the area. Examples of such maps are placed in Appendix A, whereby all the maps and graphs created for this area are available in []. The web page on GitHub was created to keep all of the Supplementary Materials in one place.

3.2. Methods

This section describes methods designed and developed for the calculation of certain agro-climatic factors. As a description of each method used is quite extensive, there is the first method described in full detail, and the rest of the method is outlined, stressing the critical parts of the process described by a flowchart of a particular method. In contrast, the comprehensive description of all the methods, together with the developed source code, is available as Supplementary Materials at https://github.com/JiriVales/agroclimatic-factors/wiki []. It is also worth mentioning that the algorithms are deployed at the https://test.euxdat.eu/ (The platform is being migrated to https://platform.euxdat.eu/) []—a cloud platform allowing the calculation of the particular agro-climatic factors on demand (for registered users only).

3.2.1. Frost-Free Periods

The agricultural season is primarily determined by the period of suitable temperatures for growing crops. Frost has a devastating effect on crops. In light frost (between 0 °C and −1/−2 °C), the tender plants are killed. Moderate freeze (between −2 °C and −4 °C) is widely destructive to most vegetation, and lower frost is already causing severe damage to most plants [,]. It is just a general simplification; the effects also vary for different growth stages (see [] for details) and different crops. Therefore, farmers need to know the frost-free period in their agricultural areas. Significantly, the last spring frost date for starting agricultural work and the first fall frost date for the cessation of agricultural activities. The likelihood of frost and frost trends over the years helps effective fieldwork planning.
The last spring date is usually called the last day during spring (more correctly from winter to summer) when the minimum daytime temperature is less than 0 °C. The first fall date is the first day in the second half of the year (during autumn) when the minimum temperature is below zero. Usually, this date is given with a 50% or 10% probability (statistically from several years) that it will freeze later (spring date) or sooner (fall date). For farmers, knowledge of days with a low probability of frost is necessary for farming planning and decision-making to avoid destructive effects, hence dates with a last/first frost with a low probability (e.g., 10%) are desirable. The frost-free period is then a period from the last spring frost to the first fall frost. It includes a period suitable for growing crops.
The minimum daily temperature is a necessary variable for determining frost dates. The daily minimum is determined as the lowest value of the hourly temperatures each day. We search for the days where the minimum is below 0 °C for at least one hour, see [] for detailed justification. Subsequently, the algorithm calculates the last freezing day of each year for the spring period and the first freezing day for the autumn period. For the sake of simplicity, the coldest month is designated as January for the northern hemisphere and July for the southern hemisphere, which is the central month of the meteorologist winter season [,]. The hemisphere is determined from latitude. The resulting last spring frost date and first autumn frost date are calculated from the annual frost dates with a corresponding probability. The frost-free period is calculated as the period between the last and the first frost date. Similarly, it is possible to calculate the dates for another temperature threshold (e.g., for moderate freeze −2 °C).
By altering the input parameters, it is possible to calculate more days of frost in a row as the last/first frost date. The last/first frost date with defined probability is calculated from all selected years using the normal distribution, while the standard deviation and mean for the normal distribution is calculated from the frost dates of each year. Frost-free period with defined probability is calculated as the difference between these last and first frost dates. The flowchart of the designed algorithm is shown in Figure 3.
Figure 3. Scheme of the algorithm for calculation frost dates and frost-free period (adapted from []).

3.2.2. Crop Growth-Related Temperatures

There are four temperature thresholds, the cardinal temperatures, that define the relationship between temperature and crop growth. These thresholds are the absolute minimum, the optimum minimum, the optimum maximum, and the absolute maximum []. Based on such thresholds, the following three factors are defined and briefly described.
Heat stress units (HSU) are used to detect high temperatures unsuitable for crop growth. When the maximum daily temperature is higher than the absolute maximum temperature for crop growth, HSU is accumulated []. For example, if the threshold is exceeded by three degrees, three units are added.
Growing degree units (GDU) are used to relate temperature to crop development. GDU is accumulated when the average daily temperature exceeds the absolute minimum temperature threshold for the growth of a given crop. The difference between the daily temperature average and the temperature threshold of the plant is the accumulated GDU value for a given day []. For example, when the temperature is two degrees higher than the minimum for plant growth, two growing degree units are added.
The number of (optimal) growing days includes all growth days, days when the average temperature is in the interval from the absolute minimum to the absolute maximum of the selected crop. The number of days with optimal temperatures for growth is the sum of days when the average daily temperature is at the best temperatures for crop growth, between the optimal minimum and optimal maximum of the selected crop [].
A flowchart of the designed algorithm for all three mentioned factors above is shown in Figure 4.
Figure 4. Scheme of the algorithm for calculation of growing degree units (GDU), heat stress units (HSU), and the number of growing days (adapted from []).

3.2.3. Uncertainty of Input Variables

Let us introduce how uncertainties of input variables for selected temperature-related agro-climatic factors (frost-free periods, growing degree units, heat stress units, number of (optimal) growing days, etc.) have been estimated. The data used for this section are described in the previous text, particularly in Section 3.1.1. ERA5-Land hourly data from 1981 to present and Section 3.1.2. ERA5 Ensemble of Data Assimilations.
To unify EDA and ERA5-Land data in the spatial domain, we decided to interpolate uncertainties for the test point in Kojčice, Czech Republic (see Section 3.1.3. Case study area in Kojčice for further information) from EDA by inverse distance method (defined by [], with power parameter equal to 2). The computation of selected agro-climatic factors is mostly based on the daily averages of temperatures. Thus, the uncertainty of the daily temperature average has been calculated from interpolated values related to EDA. An exact formula was obtained by applying the error-propagation law to the average and has the following form:
σ ^ D =   σ T 1 2 + σ T 2 2 + + σ T 8 2 n
where D stands for the estimated uncertainty for a day D calculated from the interpolated values of temperature uncertainties σ T i 2 ,   i = 1 , 2 8 ,   for the test point for each time i and n is equal to 8. The uncertainty of year temperature Y has been computed similarly to the uncertainty of day temperature. The exact formula is in the form:
σ ^ Y = σ D 1 2 + σ D 2 2 + + σ D 365 ( 366 ) 2 n ,  
where n = 365 (366 for the leap year). The last two uncertainties dedicated to the temperature are uncertainties of daily maximum and minimum temperature denoted as σ ^ D m a x and σ ^ D m i n , respectively. These have been computed by the following procedure. If the daily maximum and/or minimum temperature have been achieved at the same time as being in EDA, we took corresponding uncertainty from EDA. We remind readers that uncertainties in EDA are provided with the regular time step of three hours (please see 3.1.2). Otherwise, σ ^ D m a x and σ ^ D m i n have been interpolated by the linear interpolation from two uncertainties with neighboring hours in EDA.

3.2.4. Uncertainty of Calculated Agro-Climatic Factors

Uncertainties defined above allow us to calculate uncertainties of temperature-related agro-climatic factors, namely: (i) Annual number of frost days, (ii) annual number of days with growing temperatures, (iii) annual number of days with optimal growing temperatures, (iv) last spring frost date, (v) first fall frost date, (vi) frost-free periods, (vii) growing degree units, and (viii) heat stress units. In what follows, we will explain step by step how the uncertainty of all above mentioned temperature-related agro-climatic factors have been estimated.
We used the minimum temperature over a day and its uncertainty for the estimation of the uncertainty of (i) annual number of frost days, (iv) last spring frost date, and (v) first fall frost date. The uncertainty of (i) has been calculated as follows. Firstly, we calculated the number of frost days over a year as a summation of days in which the temperature was below 0 °C. Then uncertainties have been applied and we determined the maximum N_(f_max) and minimum number N_(f_min) of frost days by the following relation:
N f m a x = i D i ,   where   D i = 1   if   ( D m i n i σ ^ D m i n i ) 0   ° C ,   else   D i =   0 ,
N f m i n = i D i ,   where   D i = 1   if   ( D m i n i + σ ^ D m i n i ) 0   ° C ,   else   D i =   0 .
Note that the symbol D m i n i represents the minimum temperature over an i-th day and σ ^ D m i n i is its uncertainty. Finally, we set the confidence interval for the point estimator in the form ( N f m i n , N f m a x ).
If N f m i n > N f m a x , the value N f m a x has been replaced by N f m i n   in the confidence interval. Otherwise, i.e., if N f m i n < N f m a x , we substituted N f m i n   by N f m a x . The confidence interval for (iv) last spring frost date has been gained by the following procedure:
1. We found the latest date of the last spring frost date L f m a x from the condition
( D m i n i σ ^ D m i n i ) 0   ° C .
2. Then we identified the earliest date of the last spring frost date L f m i n from the condition
( D m i n i + σ ^ D m i n i ) 0   ° C .
3. We put the values L f m i n and L f m a x into the confidence interval ( L f m i n , L f m a x ).
The uncertainty of (v) first fall frost date has been estimated by applying the same procedure as for (iv). The only change is that we have been searching for the latest F f m a x and earliest date F f m i n of the first fall frost date and the confidence interval was then ( F f m i n , F f m a x ). The agro-climatic factor, (vi) frost-free periods, is based on the frost days. Its uncertainty was estimated from the values of the earliest L f m i n and latest L f m a x date of the last spring frost date and the earliest F f m i n and latest F f m a x date of the first fall frost date. Uncertainties of frost-free period F p m i n and F p m a x have been calculated from:
F p m i n = F f m i n L f m a x   , F p m a x = F f m a x L f m i n .
The average temperature over an i-th day D a v e i and its uncertainty σ ^ D a v e i have been used for the determination of confidence intervals for (ii) annual number of days with growing temperatures, (iii) annual number of days with optimal growing temperatures, and (vii) growing degree units. The uncertainty of (ii) was obtained as:
Firstly, we calculated the minimal N g m i n and the maximal N g m a x number of growing days over a year as a summation of days as follows:
N g m a x = i D i ,   where   D i = { T a b s m i n D a v e i + σ ^ D a v e i T a b s m a x D a v e i σ ^ D a v e i ,
N g m i n = i D i ,   where   D i = { T a b s m i n D a v e i σ ^ D a v e i T a b s m a x D a v e i + σ ^ D a v e i .
Note that symbols T a b s m i n and T a b s m a x represent the minimum and maximum temperature for crop growing.
Secondly, we have values of N g m a x and N g m i n in our pocket so we can define the confidence interval ( N g m i n , N g m a x ) for the annual number of days with growing temperatures.
The confidence interval of the annual number of days with optimal growing temperatures N o g has been calculated by the above-mentioned approach. The only difference is the replacement of the minimum and maximum temperature for crop growing by the minimum and maximum temperature for optimal crop growing. The uncertainty of (vii) growing degree units was obtained by application of the following algorithm:
1. Calculation of minimal D g d u m i n and maximal D g d u m i n daily growing degree units as follows
D g d u m a x = { D a v e i + σ ^ D a v e i T a b s m i n   if   T a b s m i n <   D a v e i + σ ^ D a v e i   D a v e i + σ ^ D a v e i T a b s m i n   if   T a b s m a x   D a v e i σ ^ D a v e i   0   ( otherwise ) ,
D g d u m i n = { D a v e i σ ^ D a v e i T a b s m i n   if   T a b s m i n <   D a v e i σ ^ D a v e i   D a v e i + σ ^ D a v e i T a b s m i n   if   T a b s m a x   D a v e i + σ ^ D a v e i   0   ( otherwise ) .
2. To get confidence intervals for growing degree units over a year we calculated minimal A g d u m i n and maximal A g d u m i n daily growing degree units by summation of D g d u m a x and D g d u m i n .
The maximum temperature D m a x i and its uncertainty σ ^ D m a x i has been applied for calculation of confidence interval for (viii) heat stress units. In the first step, we calculated maximal D h s u m a x and minimal D h s u m i n values of heat stress units from the following condition:
D h s u m a x = { D m a x i + σ ^ D m a x i T a b s m a x   if   T a b s m i n <   D m a x i + σ ^ D m a x i 0   ( otherwise ) ,
D h s u m i n = { D m a x i σ ^ D m a x i T a b s m a x   if   T a b s m i n <   D m a x i σ ^ D m a x i 0   ( otherwise ) .
The maximal A h s u m a x and minimal A h s u m i n values of heat stress units over a year has been obtained as follows:
A h s u m a x = i D h s u m a x i   ,   A h s u m i n = i D h s u m i n i .
Finally, we got the confidence interval ( A h s u m i n , A h s u m a x ).

4. Results

Firstly, the input climatic data uncertainty and accuracy needed to be evaluated. This evaluation was proceeded in the pilot locality near Kojčice village (see Section 3.1.3. Case study area in Kojčice for further information). The village lies in a similar climatic environment as the main area of interest (Pilsen region), and we were able to gain access to at least a year-long time series of climatic measurements—which turned to be a complicated task to gain the sensor data directly from the Pilsen region.
After the evaluation process, we calculated the agro-climatic factors mentioned in Section 3.2. Methods, using data described in Section 3.1.1. ERA5-Land hourly data from 1981 to present for the case study areas (see Section 3.1.3 and Section 3.1.4 for information about such areas).

4.1. Uncertainty of Input Temperatures

Firstly, the annual temperature uncertainties were calculated according to the first two formulas mentioned in Section 3.2.4, for the period 1982–2019 of the Kojčice area (depicted in Figure 5).
Figure 5. Graph of average annual temperature with Ensemble Data Assimilations (EDA) uncertainties during the years 1982–2019 in the Kojčice area.
As can be seen from the graph in Figure 5, the annual temperature uncertainties provided by the EDA dataset are less than 0.5 °C, namely: min = 0.33 °C, max = 0.44 °C, a standard deviation of uncertainties is 0.3 °C. A table of particular values in the graph of Figure 5 is available in []. Similar tests can be run for other input data, using the same methodology.

4.2. Accuracy of the Global Climatic Data Evaluated Using In-Situ Sensors

Next, the local in-situ sensor dataset was used for global model data accuracy evaluation. Comparison of values calculated from the model and values measured by the sensor directly in the field is useful for defining the reliability. Model data were provided hourly, while the sensor node was measuring every 2 h. Thus, the daily average temperature was selected as a value to be compared. A comparison of daily average temperatures calculated from ERA5-Land data and in-situ observations is depicted in Figure 6 below.
Figure 6. Graph of daily average temperatures calculated from ERA5-Land data (blue line), in-situ observations (red line). The Pearson correlation coefficient is equal to 0.99.
The difference chart depicted in Figure 7 clearly shows the differences between average daily temperatures calculated from ERA5-Land data and in-situ sensors during the period of observations. The differences are characterized by a standard deviation of 1.06 °C and min = −3.06 °C and max = 3.8 °C. Tables of particular values illustrated in Figure 5 and Figure 7 are available in [].
Figure 7. Graph showing the differences between ERA5-Land data and in-situ observations.
The comparison of the temperatures gathered from global climatic data to in-situ sensor data, was possible to calculate from the limited period, but even that gives us a view of the reliability of the EDA dataset, describing the global data uncertainties. Results can be read in a way that the global data has (at least for our control measurements) approximately 3.5 times worse accuracy than the uncertainty described by the EDA (compare the 0.3 °C standard deviation of uncertainty to 1.06 °C standard deviation of the accuracy). Even with this disadvantage, the global data keep their value for the long time series provided. The relation of uncertainty and accuracy can (and will be) studied further, see discussion for details.
Also, it can be read from the above text and graphs, that the global temperature data oscillate around the temperatures measured by the in-situ sensor, which is here taken as a ground-truth for its inner accuracy of 0.1 °C. The oscillation is very problematic for frost-free period calculation, however the cumulative aspect of crop growth-related factors calculation (see Section 3.2.2) allows the use of global climatic data for the calculation of these factors (see also more in the discussion section).

4.3. Uncertainty of Calculated Agro-Climatic Factors

As the accuracy estimation needs the comparison to sensor data, it is not available, for the whole time series. Therefore, only the uncertainties of the input values were included in the calculation of the agro-climatic factors. As a result, we have the factors calculated together with information on the uncertainty of the calculation. All the factors were calculated for the whole available time series (years 1982–2019) and all the output graphs below portray the yearly values together with the uncertainty of the value.
The first group of graphs relates to frost temperatures. Graphs of last spring and first fall frost dates are depicted in Figure 8 and Figure 9. The graph in Figure 10 shows the length of frost-free periods. Note that only if the uncertainty is large enough for the scale of the following graphs, it is visible.
Figure 8. Graph of last spring frost dates with uncertainties between the years 1982 and 2019.
Figure 9. Graph of first fall frost dates with uncertainties between the years 1982 and 2019.
Figure 10. Graph of frost-free periods with uncertainties between the years 1982 and 2019.
The next group of graphs is related to a particular crop type. The graphs portray the heat stress unit factor (Figure 11), growing degree unit factor (Figure 12), and the number of days with growing temperatures (Figure 13). These factors were calculated for C3 plants (such as wheat, soybean, and alfalfa) []. Crop temperature thresholds were therefore set as the average of a given group threshold range. The absolute minimum was set to 3.5 °C, the optimum minimum as 17.5 °C, the optimum maximum as 28 °C, and the absolute maximum to 32.5 °C. Please note that the heat stress occurs only exceptionally in the area of interest.
Figure 11. Graph of annual HSU for C3 crops between the years 1982 and 2019.
Figure 12. Graph of the number of days with growing temperatures for C3 crops with uncertainties between the years 1982 and 2019.
Figure 13. Graph of annual GDU for C3 crops between the years 1982 and 2019.
In order to demonstrate the spatial variability of the agro-climatic factors, two maps are attached as examples in Appendix A. The first map shows the average Growing Degree Units for C3 Crops 2010–2019 in the Pilsen Region (Figure A1). The second map shows the average Number of Growing Days for C3 Crops 2010–2019 in the Pilsen Region (Figure A2). A complete set of maps of agro-climatic factors created by the team are available in [].

5. Findings and Discussion

The first significant output of this contribution lies in the evaluation of uncertainty and accuracy of the input climatic data. The example of temperature, as the climatic quantity, influencing the majority of agro-climatic factors, shows that even if the uncertainty in the data are pretty small (less than 0.5 °C for the whole period, with the standard deviation of 0.3 °C), the comparison to real in-situ measured data shows more significant differences (standard deviation of 1.06 °C and min = −3.06 °C and max = 3.8 °C). Such a difference urges caution in relying just on climatic data for calculation agro-climatic factors describing extremes (such as heat stress or frost dates). Still, the risks calculated from global data can be indicative, and a farmer naturally complements such information with a weather forecast.
The random character of the difference between climatic and sensor data ~ absence of a systematic shift (see graph in Figure 7) allows a farmer to rely on the temperature from climatic data for cumulative agro-climatic factors, such as the Number of growing (optimal) degree days or Number of (optimal) degree units.
Therefore, such results allow us to rely on the climatic data for calculation of at least temperature-dependent agro-climatic factors in the areas climatically similar to Kojčice (which is the area of the Pilsen region as well).
The algorithms were applied to the area of interest of the Pilsen region in the manuscript. However, they were also successfully deployed and tested in other areas during three hackathons: Climatic services for Africa (https://www.plan4all.eu/2019/04/team-2-progress-report-i/), leveraging of the algorithms by different teams in the San Juan hackathon (https://www.plan4all.eu/2019/10/san-juan-inspire-hackathon-2019/), and searching for Climate Change trends for Africa (https://www.plan4all.eu/2020/03/challenge-6-climate-change-trends-for-africa/).
Usage of the whole time series of the input data for calculation of the factors can document a local impact of climate change in a place of interest. For example, enlargement of the frost-free period in the Pilsen region can be interpreted from the time-dependent manners of last freezing and first freezing days graphs available in [].
All the algorithms of agro-climatic factors calculation—designed, developed, and deployed in a cloud environment—can be widely re-used and evaluated by the scientific community, as they are available as open-source. It is also worth mentioning that the algorithms use the ERA5-Land dataset for now, but they can be easily applied to any other climatic data available.
There are limitations of visualization of big and multidimensional data—such as the agro-climatic factors calculated from the climatic data. Graphs perfectly describe the changes in a factor of time, but they are locked at one location. On the contrary, maps can describe the spatial distribution of a factor, but at one time, or its change during one period of time. As future work, the Space-Time Cube [] principle can be leveraged for visualization of spatio-temporal aspects of a factor at once. Another limitation is related to the input data uncertainty and accuracy. As demonstrated in the manuscript, the input data uncertainty influences each agro-climatic factor differently. Therefore, we feel that it is crucial to work not only with the data values, but also the uncertainties in order to keep a final user of the algorithms informed.
We see several options to develop the work on this topic further. First, the rest of the agro-climatic factors (related to soil temperature, solar radiation, and water cycle) can also be calculated, including both input and output uncertainties. Moreover, we plan to compare the climatic data to more in-situ sensors in the future, once we gain access to such a data source, cooperation with the ISIDOR (http://www.emsbrno.cz/p.axd/en/Srážky.a.teploty.ISIDOR.html) network just started. It is also worth to mention, that Copernicus Climate Change Service continues in the reduction of the climatic data uncertainty, at least for Europe, see details in Copernicus regional reanalysis for Europe (CERRA) (https://climate.copernicus.eu/copernicus-regional-reanalysis-europe-cerra). Furthermore, last but not least, Copernicus Climate Change Service just announced that the ERA5 dataset has been reanalyzed and provides now time series going back to 1950.

6. Conclusions

The calculation of air temperature-related agro-climatic factors and their uncertainties from the open ERA5-Land dataset has been investigated within this manuscript. We designed algorithms for calculation of the most significant agro-climatic factors (frost-free period, heat stress units, growing degree units, number of growing days, dates of nitrogen application, water balance, and solar radiation), however only air temperature-related factors and their uncertainties (frost-free period, heat stress units, growing degree units, and number of growing days) have been elaborated further in the manuscript.
The developed algorithms were employed in numerical experiments. The first numerical experiment was validation of temperatures from the global ERA5-Land dataset on the in-situ sensor located in the area of Kojčice in Czechia. The direct comparison of temperature time series with the length of nine months showed an excellent fit between these two counterparts with a standard deviation better than 1.1 °C and with a correlation of 99%. This finding allowed us to estimate the frost-free period, heat stress units, growing degree units, and the number of growing days and their uncertainties in the Pilsen region from the ERA5-Land dataset over the period 1981–2019.
The conducted experiments showed that even global and relatively roughly distributed climate data are suitable for the calculation of agro-climatic factors on a regional scale with good accuracy. In addition, one could eventually use them if in-situ time series are not available or mix data from global models with terrestrial observations if time series are not long enough for agro-climatic factors calculation and analysis.

Supplementary Materials

Main supplementary material is available at https://github.com/JiriVales/agroclimatic-factors/wiki [], containing a detailed description of agro-climatic factors for Section 3.2. Methods, data for Section 4.1. Uncertainty of input temperatures and Section 4.2. Accuracy of the global climatic data evaluated using in-situ sensors, together with maps for Section 3.1.4. Case study area in the Pilsen region.

Author Contributions

K.J. and J.V. designed the study. J.V. and M.K. devolved software. J.V., M.K., and M.P. performed numerical experiments. K.J. and P.H. drafted the manuscript. All authors have read and agreed to the published version of the manuscript.

Funding

The following projects supported the authors: Research and development of intelligent components of advanced technologies for the Pilsen metropolitan area (InteCom), by the Czech Ministry of Education, Youth and Sports CZ.02.1.01/0.0/0.0/17_048/0007267. European e-Infrastructure for Extreme Data Analytics in Sustainable Development (EUXDAT). H2020: EINFRA-21-2017, no.: 777549. www.euxdat.eu. Aggregate Farming in the Cloud (AFarCloud). H2020 ECSEL JU, no.: 783221. www.ecsel.eu/projects/afarcloud. European Union’s Horizon 2020 Research and Innovation Programme, under Grant Agreement No. 818187, project STARGATE.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

Figure A1. Average GDU for C3 Crops 2010–2019 in Pilsen Region.
Figure A2. Average Number of Growing Days for C3 Crops 2010–2019 in Pilsen Region.

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