RU2770821C1 - Method for forecasting crop yield by determining complex of meteorological parameters in daily resolution - Google Patents

Abstract

FIELD: agriculture.

SUBSTANCE: invention relates to agrometeorology and can be used to predict crop yield. Essence: series of meteorological data is formed for the past period of not less than 30 years. Meteorological data used are daily average values of temperature, number of hours of sunshine, number of hours of air humidity deficiency and daily precipitation for the period from April to September of each year of the selected observation period, recorded by meteorological stations. Method includes processing meteorological data by mathematical transformations, obtaining simulated daily values of meteorological data. Generated simulated daily series of meteorological data are loaded into the Climate-Harvest-Soil system as input data and the economic yield is calculated for a specific agricultural crop, and also determining heat and moisture availability during the vegetation period of a specific year.

EFFECT: higher yield prediction accuracy.

1 cl, 5 dwg

Description

The field of technology to which the claimed invention belongs

The claimed invention relates to the field of meteorology and agrometeorology and can be used to assess changes in agro-climatic resources and crop productivity in Russia under global warming conditions based on meteorological data of a certain resolution.

Agrometeorological support of agriculture implies the provision of operational, medium-term and long-term information to the consumer and includes the analysis and forecast of the prevailing and expected agrometeorological conditions and the forecast of crop productivity on this basis. It is based on the wide use of observational data from the state network of hydrometeorological stations and posts, visual and instrumental surveys, and other types of observations.

Due to the extreme vulnerability of agricultural production in Russia and, as a result, the volatility of the grain market, regular agro-climatic monitoring of the state of crops in the agricultural zone of Russia and the forecast of crop yields are carried out. In this regard, the task of improving the methods for predicting yields for a large number of crops remains relevant.

State of the art

The list of created meteorological data databases is determined on the basis of the requirements of the Global Climate Observing System, and includes the main measured climatic parameters, such as air temperature, precipitation, free atmosphere parameters, and others. At the network of observation stations of Roshydromet, a complex of surface meteorological observations is carried out, ensuring the reliability and uniformity of the series [Instruction for meteorological stations and posts. 1985. Release. 3. Part 1. L., Gidrometeoizdat]. Urgent meteorological data (air temperature, precipitation and other parameters) are received by regional centers, where they are entered into the Persona MIS regime system, where, after analysis and control, they are summarized and generated in the form of daily, ten-day, average monthly data and other characteristics. Only a small part of this data is publicly available (http://www.meteo.ru/data). More accessible is the regime information of meteorological monthly, which presents the generated average monthly data on the observed meteorological parameters, such as air temperature and precipitation. On the other hand, predictive estimates of climate change obtained using global atmospheric and ocean circulation models (AGCMs) contain data only in monthly resolution, mainly on air temperature and monthly precipitation in the form of absolute or relative deviations from the climatic norm at the nodes of a regular grid [ Sirotenko O.D., Pavlova V.N., 1986. Stochastic modeling of daily climate data for calculations using dynamic weather-harvest models, Proceedings of the All-Russian Research Institute of Agriculture, Mathematical modeling in agrometeorology, vol. 21, p. 75-83.2].

Currently, dynamic modeling of the production process is a generally accepted methodological approach in solving many applied problems in agrometeorology and related sciences (ecology, biology, geoecology, etc.). Most modern dynamic models require input meteorological information with daily resolution.

From the prior art, various methods are known for obtaining daily meteorological data for various purposes. Thus, Bruhn J.A., Fry E.W., Fick G.W., 1980. Simulation of Daily Weather Data Using Theoretical Probability Distribution, J. Appl, Meteor, vol. 19, no. 9, pp. 1029-1036.] to determine the possible yield losses associated with late blight of potatoes, a Monte Carlo method was developed that provides the ability to determine precipitation, maximum and minimum temperature, relative humidity and solar radiation. In this case, the sequence of precipitation dates was modeled by a simple Markov chain, and their magnitude was modeled by the parameters of the gamma distribution.

The disadvantage of this method is the lack of connection between the date of precipitation and their value with the values of other meteorological parameters on this date, which is observed in real conditions, which leads to a high percentage of errors in the forecast of yield losses.

A method for modeling the time series of meteorological elements in the daily interval by stationary Gaussian sequences is proposed in the source [Kagan R.L., Sibir E.E. On one algorithm for statistical modeling of series of meteorological observations. 1970. Proceedings of the GGO, no. 268, p. 146-172]. The simulated series quite realistically reproduce the main statistical features of the statistical structure of air temperature within a day for the winter season.

The disadvantage of this method is that this method is designed to restore urgent daily observations (8 periods of observations during the day) for the winter period and is used to assess the conditions of overwintering crops.

A stochastic weather generator LARS-WG is known [Racsko P., Szeidl L., Semenov M.A., 1991. A serial approach to local stochastic weather models, Ecol. Model, vol. 57, pp. 27-41; Semenov M.A., Barrow E.M., 1997. Use of a stochastic weather generator in the development of climate change scenarios, Climatic Change, vol. 35, pp. 397-414]. To generate stochastic time series of daily data in the LARS-WG, when calculating according to the SRES climate scenarios, meteorological data for the period 1961-1990 were used [Sommer R., Glazirina V., Yuldashev T., Otarov A., Ibraeva V., Martynova L. , Bekeno M., Kholo B., Ibragimov N., Kobilov R., Karaev S., Sultanov M., Khasanjva F., Esanbekov M., Mavlyanov D., Isaev S., Abdyrahimov S., Ikramov R., Shezdykova L., de Pfuw E. (2013). Impact of climate change on wheat productivity in Central Asia // Agriculture, Ecosystems and Environment. Vol. 178. P 78-99].

The disadvantages of this method include the absence of a multiple correlation between the parameters of the meteorological complex. The absence of a statistical relationship between meteorological parameters can lead to unreliable estimates in climatic and agro-climatic calculations based on the generated daily data series according to such a calculation scheme.

In the practice of operational agrometeorological support, statistical forecasting methods based on the identification of quantitative statistical relationships between yield (predictant) and selected values of agrometeorological parameters (predictors) are widely used. Correlation and regression analysis is used to search for and identify these dependencies. The most common indicators of the thermal regime in the existing regression models are the air temperature for interfacial periods, for a decade, for a month, data on the minimum and maximum temperatures. Precipitation data in statistical models are also presented as averages for interphase periods, decades, months, and critical phases of development. Relatively often used data on the deficit of air humidity and relative humidity.

As examples of statistical methods for forecasting yields, one can cite the method for predicting the yield of winter wheat [Ulanova E.S. 1975. Agrometeorological conditions and productivity of winter wheat. L. Gidrometeoizdat, 302 pp.], methods for predicting the yield of spring wheat and spring barley and other methods [Guide to agrometeorological forecasts. 1984. Gidrometeoizdat. 309 p.].

The main disadvantages of the statistical approach include the uncertainty associated with the choice of the main predictors that affect the predicted value (yield), i.e. limited choice, which exhausts all a priori information included in the forecast scheme. Another drawback is determined by the fact that static circuits work well in the range of the parameter values on which they were built. In the event of extreme weather events (drought, long periods without rain, high temperatures), forecast estimates based on statistical schemes have large errors.

Currently, dynamic modeling of the production process is a generally accepted methodological approach in solving many applied problems in agrometeorology. With the help of well-known dynamic models [Menzhulin G.V., Savateev S.P., 1981. Influence of modern climate change on crop yields, In: Problems of carbon dioxide, L., Gidrometeoizdat, p. 186-197; Poluektov R.A., Smolyar E.I., Terleev V.V., Topaj A.G., 2006. Models of the production process of agricultural crops, SPb., Izd. St. Petersburg University, 392 p.] can be solved many applied agrometeorological problems associated with the assessment of agroclimatic resources. But predictive estimates of expected yields are not the targets of these models.

In the practice of forecasting, a dynamic-statistical method is used to predict the yield and gross harvest of agricultural crops, described in [Polevoi A.N. 1988 Applied modeling and forecasting of crop productivity. L., Gidrometeoizdat. 308 p.]. The method of dynamic-statistical forecasting includes two stages: 1) forecasting by the yield time series and 2) assessing the conditions for crop formation using the basic productivity model.

The input agrometeorological information includes the average annual dates of germination and the dates of the onset of wax ripeness, the average ten-day air temperature and the number of hours of sunshine, the reserves of productive moisture by soil layers (actually observed) by the calculated decades. According to this method, the yield time series is considered as the sum of two terms - a non-random time function (trend) and random deviations from it. The yield trend is calculated using statistical methods, and the assessment of the degree of difference between the conditions of a given year and the average long-term values is based on the base model.

The disadvantages of the method are as follows. Meteorological data averaged over a decade are used as input information, which can significantly affect the accuracy of calculations under extreme weather conditions. The model does not have a submodel for calculating soil moisture, so the observed values for soil moisture are used, which are determined only on the 8th, 18th and 28th of each month, which also affects the accuracy of the calculations and narrows the potential number of calculation points. The model does not allow calculating the yield in absolute units, c/ha. The proposed method for calculating the yield in the form of the sum of terms - the yield trend calculated for previous years, and deviations from it, can lead to a large calculation error in extreme years in terms of agro-climatic conditions.

The closest in technical essence to the claimed method is the solution previously used in the Climate-Soil-Harvest (CPU) system (Sirotenko O.D., 1981. Mathematical modeling of the water-thermal regime and productivity of agroecosystems, L .: Gidrometeoizdat, 167 p. )

The formation of daily meteorological data was carried out by approximating the initial average monthly data by trigonometric polynomials [Boiko A.P., N.S. Slavov, V. Vylkov, 1984. Reconstruction of the average daily values of meteorological elements in accordance with the average monthly values. Hydrology and meteorology. XXXIII, No. 4. S. 26-33]. These series are the input parameters for the dynamic weather-crop model.

The disadvantages of this method:

1) does not take into account the statistical dependencies between the monthly course of the values of a particular parameter, as well as the relationship between various parameters and individual physical features of synoptic events, which negatively affects the accuracy of estimating the expected yield level;

2) not applicable for precipitation, due to the discrete nature of the daily values of this meteorological parameter;

3) disadvantage in relation to the dispersion of daily values of meteorological parameters. With trigonometric interpolation, smooth curves of the vegetation course of meteorological parameters are obtained, which naturally does not reflect the real process, which is characterized by significant daily variability. Due to the significant nonlinearity of the KPU model, with an increase in the dispersion of average daily values of meteorological elements, there is a tendency to reduce the level of calculated yield (productivity of agricultural crops), since the average values obviously lie in a region close to optimal. Therefore, when calculating the yield, using the prototype method, a systematic error occurs, leading to an overestimation of the level of yield.

It is possible to ensure the accuracy and statistical reliability of estimates in monitoring agro-climatic conditions and assessing the productivity of agricultural crops based on the KPU simulation system, both under the current climate and its expected changes until the end of the 21st century, only if a large array of daily meteorological data is available.

Thus, the technical problem solved by the claimed invention lies in the need to ensure the restoration of the average daily values of individual meteorological parameters from monthly averages, which makes it possible to predict the expected level of yield with a high degree of accuracy. The claimed invention is aimed at improving the accuracy and reliability of the calculated indices in the KPU simulation system by switching from the average monthly values of the measured meteorological parameters, such as air temperature, the amount of precipitation, to daily resolution data (temperature and air humidity deficit, the number of hours of sunshine and the amount of precipitation), taking into account correlation and cross-correlation relationships between the parameters of the complex.

Brief summary of the invention

The technical result achieved by using the claimed invention is to improve the accuracy of forecasting crop yields, as well as agro-climatic indicators of thermal and humidity conditions and estimates of the impact of extreme weather conditions on the formation of crop yields through the use of average daily values of individual meteorological parameters restored from monthly averages.

The advantages of the claimed invention also lie in providing an increase in the value (significance) of global estimates of climate change obtained from models of the general circulation of the atmosphere and ocean, by temporally scaling the values of meteorological parameters to a daily resolution. The method allows to generate a realistic local climatic dynamics of meteorological parameters according to the following indicators: average daily temperature and air humidity deficit, number of hours of sunshine and amount of precipitation per day based on changes in the average monthly temperature and amount of precipitation at a given point on a given time slice. In particular, to confirm the possibility of implementing the method, experimental predictive calculations were carried out for the periods of 2030-2040, 2050-2060, 2080-2090.

The claimed technical result is achieved by the fact that the method for predicting crop yields by determining a set of meteorological parameters in daily resolution is a sequential implementation of the following steps:

, число часов солнечного сияния

, число часов дефицита влажности воздуха

и суточные суммы осадков

за период с апреля по сентябрь каждого года выбранного периода наблюдений, зарегистрированные метеорологическими станциями (МС); определяют среднеквадратические отклонения этих параметров σ

, σ

, σ

;1) form series of meteorological observation data for the past period of at least 30 years, while the observed average daily temperature values are used as such data

, the number of hours of sunshine

, the number of hours of air humidity deficiency

and daily precipitation

for the period from April to September of each year of the selected observation period, recorded by meteorological stations (MS); determine the root-mean-square deviations of these parameters σ

, σ

, σ

;

,

,

, полученных на шаге 1), формируют матрицу (К1) коэффициентов авто- и кросскорреляции по отдельным месяцам с апреля по сентябрь размерностью 90х90,2) using data series of real measurements of meteorological parameters

,

,

obtained in step 1), form a matrix (K1) of auto- and cross-correlation coefficients for individual months from April to September with a dimension of 90x90,

3) from the matrix K1 form the averaged correlation matrix K with a dimension of 15x15 as a result of determining the average values of the diagonal elements of the matrix K1 for equal time values,

4) daily deviations of meteorological parameters are determined by forming a set of normally distributed vectors on a standardized scale, determined by the correlation matrix K, as a result of statistical transformations of the indicated matrix K and incoherent normally distributed vectors with unit variance and zero mean;

,

,

от климатической нормы,5) combine the vectors obtained at the previous step into sets corresponding to the monthly values of deviations of meteorological parameters

,

,

from the climatic norm,

6) determine the daily values of climatic norms of meteorological parameters by approximating their annual variation of meteorological parameters with a trigonometric polynomial;

,

,

в абсолютных единицах в виде суммы значений суточных климатических норм, полученных на шаге 6), и нормированных суточных отклонений метеопараметров, полученных на шаге 4), умноженных на среднеквадратические отклонения σ

, σ

, σ

(шаг 1), соответственно;7) receive simulated daily values of meteorological parameters

,

,

in absolute units as the sum of daily climatic norms obtained at step 6) and normalized daily deviations of meteorological parameters obtained at step 4) multiplied by standard deviations σ

, σ

, σ

(step 1), respectively;

,

,

, полученным на шаге 7),8) determine the likelihood index (λ) from the simulated daily values of meteorological parameters

,

,

obtained in step 7),

) с помощью параметров гамма-распределения, которые определяют на основе сформированных рядов наблюдаемых суточных сумм осадков (шаг 1), а дни их выпадения определяют по показателю правдоподобия (λ) (шаг 8);9) determine the daily amount of precipitation (

) using the gamma distribution parameters g , which are determined on the basis of the generated series of observed daily precipitation amounts (step 1), and the days of their fall are determined by the likelihood index (λ) (step 8);

,

,

,

в качестве входных параметров и выполняют расчет хозяйственной урожайности по конкретной сельскохозяйственной культуре, а также определяют показатели тепло- и влагообеспеченности в течение периода вегетации конкретного года.10) load into the KPU system the generated simulated daily series of meteorological data

,

,

,

as input parameters and calculate the economic yield for a particular crop, and also determine the indicators of heat and moisture supply during the growing season of a particular year.

The claimed method is based on the use of the Monte Carlo method and discriminant analysis to generate a complex of average daily meteorological parameters according to generalized data (average monthly temperature and air humidity deficit, number of hours of sunshine and monthly precipitation from January to December). The method is based on the assumption that for temperature, vapor pressure deficit and sunshine duration, deviations from the corresponding seasonal course are due to a normal distribution. Due to the persistence of weather conditions for several days within the framework of synoptic patterns and mutual physical relationships between weather elements, the joint correlation matrix is determined by including auto- and cross-correlation coefficients for time lags up to five days. Correlation and cross-correlation relationships between meteorological parameters are reproduced, including temperature and air humidity deficit, number of hours of sunshine and daily precipitation.

Brief description of the drawings

The claimed invention is illustrated by the following graphics, where

in fig. Figures 1 (a-d) and 2 (a-d) present examples of a possible implementation of the determination of average daily meteorological data: air temperature (a), number of hours of sunshine (b), air humidity deficit (c) and precipitation (d) for the period from May to August (calendar dates on the abscissa) for MS Voronezh. The initial data are: for Fig. 1 - predicted average monthly values of air temperature and precipitation from January to December, obtained according to the ensemble scenario of climate change (ANS_31) for 2050-2059; for fig. 2 - data of average monthly observations of temperature and precipitation in 2015;

in fig. 3 shows the results of calculating the yield, namely

in fig. Figures 3a and 3b show yield graphs for spring (a) and winter (b) wheat for the Republic of Bashkortostan for the period 2007-2016, while the average yield (c/ha) is for (a) - according to Rosstat - 15.1; KPU - 14.6 KPU-TA (trigonometric approximation according to the prototype) - 17.1, for (b) - according to Rosstat - 20.9; KPU - 21.1 KPU-TA (trigonometric approximation of the prototype) - 23.2;

in fig. 3c and 3d show yield graphs for spring (c) and winter (g) wheat for the Republic of Tatarstan for the period 2007-2016, while the average yield (c/ha) is for (c) - according to Rosstat - 20.5; KPU - 19.7 KPU-TA (trigonometric approximation according to the prototype) - 22.0, for (d) - according to Rosstat - 25.1; KPU - 27.1 KPU-TA (trigonometric approximation of the prototype) - 28.4;

in fig. Figures 3e and 3f show yield graphs for spring (e) and winter (f) wheat for the Orenburg region for the period 2007-2016, while the average yield (c/ha) is for (e) - according to Rosstat - 7.3; KPU - 6.7, KPU-TA (trigonometric approximation according to the prototype) - 9.0, for (e) - according to Rosstat - 15.0; KPU - 16.1 KPU-TA (trigonometric approximation of the prototype) - 17.0.

where the gray line reflects the actual data of Rosstat, the dotted line reflects the data obtained from the prototype, and the solid black line reflects the data obtained by applying the proposed method;

in fig. Figures 4a and 4b present estimates of the winter wheat yield in 2019, expressed as a percentage of the average level for 2009-2018. for two prognostic dates May 20 (a) and June 20 (b) on the territory of the main grain-producing regions of the Central, Southern and Volga Federal Districts.

in fig. Figure 5 shows a block diagram of predicted changes in the average yield of spring wheat for: (a) 2030-2039, (b) 2050-2059 in the Central Federal District, Volga Federal District and Southern Federal District and throughout the territory as a whole. The range of fluctuations shows the variations in spring wheat yields in the federal district. Extreme values (outliers) are indicated by dots. The top, middle, and bottom of each block are the 25th, 50th, and 75th percentiles of the sample;

Implementation of the invention

The claimed invention is carried out as follows.

The input parameters for the implementation of the proposed method are the data of real measurements of meteorological parameters for a certain period of time, the processing and conversion of which using the methods of statistical analysis will form an approach that provides the possibility of converting meteorological parameters of monthly resolution into meteorological parameters of daily resolution.

At the first stage of the implementation of the method, series of meteorological observation data are formed for a period of at least 30 years, while average daily values of temperature and air humidity deficit, the number of hours of sunshine and daily precipitation for the warm period of the year from April to September are used as such data. To obtain statistically significant results, observation points (meteorological stations, MS) were chosen located in different climatic zones. In particular, during the experimental implementation of the method, the following MS were selected: Ershov (Volga Federal District, Saratov Region, steppe zone), Voronezh (Central Chernozem Region, Central Chernozem Region, forest-steppe and steppe zone), Tver (Central Federal District), forest zone.

Then, based on the generated data series, auto- and cross-correlation matrices are calculated using known mathematical formulas [Anderson T., 1963. Introduction to multivariate statistical analysis, M., 500 p.] in the STATISTICA statistical package (https://ru.wikipedia.org /wiki/Statistica).Preliminary calculations show that in terms of climate, the correlations between meteorological parameters during the warm period of the year for individual months remain approximately the same (determined by global circulation processes).This serves as the basis for using only the averaged matrix.As a result, matrices of auto - and cross-correlations for individual months of April to September, which are then averaged over the entire period (6 months).The dimension of the averaged matrix is 90×90 (3 meteorological parameters, 30 days in a month).

), дефицита влажности воздуха (

), числа часов солнечного сияния (

) построена по данным наблюдательных пунктов степной и лесостепной зоны, расположенных рядом с территорией станций Географической сети опытов с удобрениями в бассейне рек Волги и Дона. Для метеостанций, расположенных в разных агроклиматических зонах, получены близкие по значениям элементы кросскорреляционной матрицы, что может служить основанием для предположения о пространственной стационарности моделируемого процесса (всего 27 метеостанций).Determine the average values of the diagonal elements of the resulting matrix for equal values of t (time lag) and leave for further consideration only the elements for t=1, t=2, t=3, t=4, t=5. As a result, an averaged auto- and cross-correlation matrix (K) with dimensions (15x15) is obtained, the elements of which (auto- and cross-correlation coefficients) characterize the statistical relationship between temperature, sunshine and air humidity deficit. Thus, matrix A was constructed, which determines the 3-dimensional normal distribution between the actually observed meteorological parameters x ₁ , x ₂ , x ₃ (see Table 1). Matrix of correlation coefficients of 15-dimensional random vector (3x5) for three elements: air temperature (

), air humidity deficit (

), number of sunshine hours (

) was built according to the data from the observation points of the steppe and forest-steppe zones, located near the territory of the stations of the Geographical Network of Experiments with Fertilizers in the Volga and Don River Basins. For weather stations located in different agro-climatic zones, elements of the cross-correlation matrix with similar values were obtained, which can serve as a basis for assuming the spatial stationarity of the simulated process (27 weather stations in total).

Table 1

), числа часов солнечного сияния (

), дефицита влажности воздуха (

). Расчеты выполнены по суточным данным наблюдений МС Воронеж за период с апреля по октябрь.The matrix of correlation coefficients of average daily air temperature (

), number of sunshine hours (

), air humidity deficit (

). The calculations are based on daily observational data from the Voronezh MS for the period from April to October.

t x _one x ₂ x ₃ one 2 3 4 5 one 2 3 4 5 one 2 3 4 5 x _one one 1.00 0.84 0.60 0.40 0.28 0.27 0.25 0.21 0.15 0.11 0.84 0.71 0.53 0.38 0.28 2 1.00 0.84 0.60 0.42 0.25 0.27 0.25 0.21 0.15 0.71 0.84 0.71 0.53 0.38 3 1.00 0.84 0.60 0.21 0.25 0.27 0.25 0.21 0.53 0.71 0.84 0.71 0.53 4 1.00 0.84 0.15 0.21 0.25 0.27 0.25 0.38 0.53 0.71 0.84 0.71 5 1.00 0.11 0.15 0.21 0.25 0.27 0.28 0.38 0.53 0.71 0.84 x ₂ one 1.00 0.38 0.22 0.15 0.12 0.38 0.29 0.22 0.17 0.14 2 1.00 0.38 0.22 0.15 0.29 0.38 0.29 0.22 0.17 3 1.00 0.38 0.20 0.22 0.29 0.38 0.29 0.22 4 1.00 0.36 0.17 0.22 0.29 0.38 0.29 5 1.00 0.14 0.17 0.22 0.29 0.38 x ₃ one 1.00 0.81 0.63 0.47 0.36 2 1.00 0.81 0.63 0.47 3 1.00 0.81 0.63 4 1.00 0.81 5 1.00

Designation: t- time lag (t=1, 2, 3, 4. 5)

At the next stage, by setting any random number at the input (for example, equal to 126704332), using the standard RANDOM program (http://www.random.org), normally distributed random vectors with unit variance and zero mathematical expectation are iteratively obtained at the output. Then the matrix A calculated at the previous stage after factorization (factorization is the representation of a matrix as a product of two transposed matrices m A*A=K) is multiply matrix-multiplied by the implementation of a random vector. The result is a set of normally distributed vectors on a standardized scale, determined by the correlation matrix K.

.The formation of monthly implementations (30-31 days) for individual months from April to September is carried out by combining six pentads (6x5) from the set of vectors formed at the previous stage. The selection criterion is a measure of proximity with a given accuracy of the original and calculated correlation matrix (

.

The determination of the daily values of meteorological parameters in absolute units is performed by summing up the climatic norms determined, for example, in accordance with the method selected as a prototype (step 7), and the normalized daily deviations of the meteorological parameters obtained in step 6, multiplied by the values of the standard deviations of the average monthly temperature , air humidity deficit, sunshine, respectively (step 1).

по величине соотношения правдоподобия λ [Андерсон Т., 1963. Введение в многомерный статистический анализ, М., 500 с.]. Отношение правдоподобия λ рассчитывается для каждых суток по данным сформированных на шаге 8 суточных значений метеопараметров и их средним значениям для дней и осадками и без осадков по формуле:Next, the date of precipitation is determined (

by the magnitude of the likelihood ratio λ [Anderson T., 1963. Introduction to multivariate statistical analysis, M., 500 p.]. The likelihood ratio λ is calculated for each day according to the data of the daily values of meteorological parameters formed at step 8 and their average values for days with and without precipitation according to the formula:

,

,

(

) - вектор, компонентами которого являются температура воздуха (

), дефицит влажности воздуха (

), число часов солнечного сияния (

);

и

- число дней с осадками и без осадков;

и

- векторы средних значений предикторов для дней с осадками и без осадков, соответственно;

- корреляционная матрица вектора

.where

(

) is a vector whose components are air temperature (

), air humidity deficit (

), the number of hours of sunshine (

);

and

- number of days with and without precipitation;

and

- vectors of average values of predictors for days with precipitation and without precipitation, respectively;

- vector correlation matrix

.

The greater the value of λ, the greater the probability of precipitation on a given day.

The daily amount of precipitation is calculated using the gamma distribution parameters found by the least squares method for the generated precipitation series in step 1) and containing their monthly values and the number of days with precipitation. The total amount of precipitation in the formed sequence of days in which precipitation fell is normalized by the amount of precipitation in the month.

The set of daily meteorological data obtained by this method is the input data stream for the KPU system, the calculations in which are performed with a daily time step. An agricultural crop is selected from a set of crops - spring wheat, spring barley, winter wheat, sown perennial grasses (the parameters of these crops are determined at the stage of identification and verification of the model) and predictive calculation is carried out in the specified system based on a previously obtained set of daily meteorological data. Calculations are performed at individual points, and then averaged on the scale of the district, region, federal district.

As a result of one calculation (running the model), the predicted economic yield in c/ha is obtained at the output (at 14% moisture - for comparison with Rosstat yield data), as well as in dynamics (by day), while the following yield parameters are used :

- mass for individual plant organs (leaves, stems, roots, ears, ear shell and grain), c / ha

- weight of roots, c/ha,

- leaf area, cm ² / cm ²

- total water consumption for transpiration, mm,

- water reserves in the soil in layers 0-20, 20-50 and 50-100 cm mm,

- phenological dates and other parameters.

The main output parameters of heat and moisture supply for monitoring the conditions of crop formation, which are calculated in the KPU system, are given in Table. 2.

Table 2 - List of indicators for monitoring agrometeorological conditions of crop formation in the KPU simulation system

Indicator, dimension Designation Average air temperature by calendar seasons of the year, °C T _winter , T _spring , T _summer , T _autumn Average air temperature for the period with temperatures above 5°C, °C _T5 Average air temperature during the growing season of spring wheat, °C T _yar.psh. The sum of air temperatures for the period with temperatures above 5, 10°C, °C ΣT ₅ , ΣT ₁₀ Dates of transition through 5, 10°C in spring, DD.MM _d5 , _d10 Duration of the period with temperature above 5.10°C, days N ₅ , N ₁₀ Duration of the growing season of spring wheat, days N _yar.psh. The amount of precipitation by calendar seasons of the year, mm R _winter , R _spring , R _summer , R _autumn The amount of precipitation for the period with temperatures above 5°C, mm _R5 The amount of precipitation for the growing season of spring wheat, mm _R

Soil moisture reserves in the 0-20 and 0-100 cm layer in May and June, mm _W20V , _W20VI , _W100V , _W100VI Hydrothermal coefficient of G. T. Selyaninov for May-August, units GTK Bioclimatic potential, c ha ^-1 BKP Climatically determined yield, centner ha ^-1 KOU

Thus, the series of daily meteorological parameters, formed in accordance with the claimed method and being input data for the KPU system, make it possible to obtain predictive estimates of the expected crop yields and the corresponding parameters of the agro-climatic conditions of a particular year. At the same time, the reliability of forecasting the yield of the main grain crops increases (up to 85-90%).

Specific Implementation Examples

Verification of the performance of the proposed method was carried out on an independent material.

Example 1. An array of observational data at 180 meteorological stations for the period 1976-2019, contained in the “Climate” database (Institute for Global Climate and Ecology of Roshydromet) in the form of monthly average values of air temperature and precipitation, was converted into an array of meteorological parameters in daily resolution using the algorithm above. The daily data were loaded into the KPU program. The results of agro-climatic calculations for the territory of the entire agricultural zone of the Volga Federal District, performed using the KPU system, showed that the proposed method increases the reliability of estimates of indicators of agro-climatic resources under observed climate changes and makes it possible to estimate the expected yield of agricultural crops with 85-90% accuracy. This conclusion is confirmed by the visual information presented in Fig. 3, which shows the results of the calculation based on real data, the forecast and Rosstat data on yields according to these data in the KPU system, indicating the consistency of the actual and simulated yields in the main grain regions of the Volga Federal District. Yield dynamics in these areas is reproduced satisfactorily, including extreme hydrometeorological conditions in 2010, when exceptionally dry conditions were noted, and relatively favorable agrometeorological conditions in 2007, 2008, 2011, and 2016. The relative calculation error is from 5 to 10%. When calculating the prototype, the error ranges from 10 to 25%.

Example 2. The implementation of the proposed method makes it possible to reproduce in daily resolution the data of the observed meteorological parameters of a particular year, represented by average monthly values of air temperature and precipitation, while maintaining the existing correlation relationships between meteorological parameters. An example is Fig. 4 (Report on the peculiarities of the climate in the territory of the Russian Federation Pavlova V.N., Karachenkova A.A., Section Agro-climatic conditions. climatechange.igce.ru›). The data of ten-day monitoring of agro-climatic conditions for the formation of grain crop yields obtained for the territory of 16 subjects (republics, territories, regions) of the Russian Federation are presented. The territory under consideration includes the main grain regions in the European part of Russia: the central black earth regions, the southern and southeastern regions of the Volga Federal District, and the grain-producing regions of the Southern Federal District. In FIG. Figure 4 shows the spatial distribution of estimates of the expected yield of winter wheat in 2019 for the main forecast dates: May 20 and June 20. The presented data allow us to conclude that, in general, for the subjects of the Russian Federation under consideration, the expected yield calculated in the KPU system is lower than the average annual values by 15-20%. The decrease in the yield of winter wheat in 2019 is associated with insufficient moisture supply for crops. In the central and eastern regions of the Volga Federal District, winter wheat yield estimates are close to the level of previous years.

Example 3. The claimed method allows using ensembles of different high-resolution systems (for example, an ensemble of future climate realizations based on a regional climate model (RCM) developed at the V.A. Voeikov Main Geophysical Observatory) to obtain probabilistic estimates of the consequences of climate change in order to refine the quantitative estimates of expected changes in crop productivity. In FIG. 5 shows a probabilistic forecast of spring wheat yield for different time slices for the 21st century, obtained using the proposed method. In the short term (2030-2039), we can expect a decrease in yield in the territory of the Central Federal District (chernozem zone) by -11.7±3.0%, the value of which by the middle of the century can reach -15.8±5.1% relative to the base period. The fall in the yield of spring wheat in the Southern Federal District may reach -9.9±2.3% already in 2030-2039. By the middle of the 21st century, warming in the ER can lead to a decrease in the productivity of grain crops by 10.3±3.2% compared to the base period. In the same period, the greatest productivity losses can be -15.8±5.1% in the Central Chernozem regions, the smallest (-6.7±3.0%) - in the Volga Federal District. By the end of the 21st century, grain yields here may be reduced by a third in the absence of adaptation measures aimed at preventing negative trends in the provision of plants with moisture and a decrease in its reserves in the soil.

Claims (11)

A method for predicting the yield of agricultural crops by determining a set of meteorological parameters in daily resolution, characterized in that it represents the sequential execution of the following steps: 1) form series of meteorological observation data for the past period of at least 30 years, while the observed average daily temperature values are used as such data

, the number of hours of sunshine

, number of hours of air humidity deficiency

and daily precipitation

for the period from April to September of each year of the selected observation period, recorded by meteorological stations; determine the root-mean-square deviations of these parameters σ

, σ

, σ

; 2) using data series of real measurements of meteorological parameters

,

,

obtained in step 1), form a matrix (K1) of auto- and cross-correlation coefficients for individual months from April to September with a dimension of 90 × 90; 3) from the matrix K1 form the averaged correlation matrix K with a dimension of 15×15 as a result of determining the average values of the diagonal elements of the matrix K1 for equal time values; 4) daily deviations of meteorological parameters are determined by generating a set of normally distributed vectors on a standardized scale, determined by the correlation matrix K, as a result of statistical transformations of the indicated matrix K and incoherent normally distributed vectors with unit variance and zero mean; 5) combine the vectors obtained at the previous step into sets corresponding to the monthly values of deviations of meteorological parameters

,

,

from the climatic norm; 6) determine the daily values of climatic norms of meteorological parameters by approximating their annual variation of meteorological parameters with a trigonometric polynomial; 7) receive simulated daily values of meteorological parameters

,

,

in absolute units as the sum of daily climatic norms obtained at step 6) and normalized daily deviations of meteorological parameters obtained at step 4) multiplied by standard deviations σ

, σ

, σ

(step 1), respectively; 8) determine the likelihood index (λ) from the simulated daily values of meteorological parameters

,

,

obtained in step 7); 9) determine the daily amount of precipitation (

) using the parameters of the gamma distribution, which are determined on the basis of the generated series of observed daily precipitation amounts (step 1), and the days of their fall are determined by the likelihood index (λ) (step 8); 10) load the generated simulated daily series of meteorological data into the “Climate-Soil-Harvest” system

,

,

,

as input parameters and calculate the economic yield for a particular crop, and also determine the indicators of heat and moisture supply during the growing season of a particular year.

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