Indicators improvement of territories spatial development

Land use planning of territorial communities is an important component of creating rational sustainable land use. The key task of planning is to find a balance between the economic and ecological components of land use. The most effective agricultural land on the territory of communities is arable land. Advanced modern software and the remote zoning data amount of land make it possible to conduct a complete analysis of land resources condition. To evaluate project decisions, plan indicators and determine land use trends, it is necessary to use integrated indicators that comprehensively describe spatial characteristics. On the basis of complex numbers, it is offered to use an indicator that consists of the territory assessment arableness and the area of land massifs to the perimeter ratio. For the assessment, a “reference” project is used, which was created taking into account the developed recommendations. The integration of the indicator makes it possible to indirectly evaluate the ecological and economic component of agricultural activity. The use of complex numbers makes it possible to expand the use of analysis tools and the capabilities of computing technology.


Spatial development planning in Ukraine
The land reform began in 1990 and was a continuation of the constant search for rational use of land from the previous period.As a result of these searches, the use of land resources is currently planned at the level of territorial communities.The main technical planning document is the Comprehensive Spatial Development Plan.Also, the calculation of the normative monetary valuation of land, which affects the amount of rent and the calculation of land tax, will be carried out in the future on the territory of territorial communities.There are projects that will use the territorial community as a unit for conducting land management works (inventory of land and natural resources) during the planning of territorial communities' spatial development.Indicators of land resources use should be objective and include as many indexers as possible related to the spatial characteristics of the territory [1].Unfortunately, modern indicators are mainly focused on the land ratio.The indicators need some improvement based on the characteristics of the territory organization.When planning the use of land resources, there are 1254 (2023) 012095 IOP Publishing doi:10.1088/1755-1315/1254/1/012095 2 many project options, and which option to apply depends on the calculated indicators, which should comprehensively characterize economic activity.
The use of land resources, as the main spatial basis and means of production, depends on the planning and design efficiency.Planning is based on evaluations of project decisions, which in turn depend on criteria [2].Currently, such indicators of land resources use as arable land, agricultural development, the coefficient of anthropogenic load, the coefficient of territory ecological stability are very popular.But the use of these indicators has both positive and negative impacts.The positives include the fact that these indicators are intuitive and can be easily compared.The negatives include the fact that all indicators do not take into account the spatial placement of objects, but only fix their ratio [3].It should be noted that indicators (indices) that characterize the spatial relationship of land exist and include: the index of the standard deviation of the counter size, the shape index, the index of the average distance between contours, the fragmentation index, etc.But all these indices are more related to the study of landscapes and to a lesser extent to agricultural activities.They also have their positive and negative sides of application.The positives include the fact that they are very closely correlated with each other.The negatives include the fact that these indicators separately are not very informative.
Indices of spatial development are evolved for many programs in different countries of the world: Poland, Spain, Taiwan, Norway, etc. Sowińska-Świerkosz and Soszyński [4] conducted a review of the relevant literature (102 articles), which allowed to choose the most similar indices of the rural areas study: an index that covers rural areas with a high risk of urbanization, an indicator of the rural areas viability, and an index of the land strategic location.Metrics used to analyze the spatial aspects of rural urbanization and those related to sustainability proved to be the most effective.The study [5] developed the Index of Prognosis Rural Landscape Preferences (IPRLP), which consists of nine variables relating to the presence or percentage of various landscape attributes.Nogués et al [6] investigated the possibility of using stability indicators to determine and measure the quantitative and qualitative spatial stability of territories.The essence of the study was to combine social, economic, environmental and spatial indicators into a single local index using robust principal component analysis and a multi-criteria decision-making method.Chang et al [7] applied the two-dimensional local indicator of spatial autocorrelation (BiLISA) to determine the spatial distribution of synergies and trade-offs between different cobenefits.The research paper [8] defines planning tools for the protection of arable land.Factors and prerequisites of spatial planning indicators are analyzed.Barneveld et al [9] evaluated the use of the connectivity index to evaluate anti-erosion measures.

Application of spatial development complex indicators
Economic activity is a complex ecological and economic process, and therefore we suppose it appropriate to consider the use of more complex indicators.The indicators, indices and coefficients listed above are displayed as real numbers.Although mathematical sciences, computer technology has taken a big step forward and researchers for spatial planning have the opportunity to use mathematical objects more complex than real numbers.For example, complex numbers that can more deeply describe various factors of planning or designing the land resources use.It can be determined that scientists divide ecological, economic and social aspects of agricultural activity, as well as their ecological-economic, socio-economic, etc. integrations.To reflect such project evaluation criteria, an indicator can be used that will simultaneously take into account environmental and economic factors.It is rather difficult to directly compare environmental and economic indicators.
As a rule, ecological indicators are converted into economic indicators by calculating the amount of funds necessary to prevent the manifestation of negative natural and anthropogenic phenomena.It should be noted that economic indicators have a limited scope, because there are such phenomena as inflation, currency devaluation, etc.This forces the use of discounting methods.Also, economic processes are affected by changes in market conditions and other factors that limit long-term forecasts and the use of economic indicators that were taken into account due to environmental ones.Therefore, we suggest using the ratio of arable land to the entire area as an ecological indicator.Arable land is intensively used, while the natural environment is deteriorating [10].Ecologically stabilizing lands have a positive effect on arable land: water bodies, natural fodder lands, forested areas.
As a technical indicator that affects economic costs, usage the ratio of the area of arable land contours to the perimeter.This indicator takes into account the spatial location of agricultural production various objects.We suggest making calculations in complex numbers, which will make it possible to combine various aspects of economic activity.The number a + bi, where a and b are any real numbers, i is an imaginary unit, is called a complex number (a is the real part, bi is the imaginary part of the complex number, and b is the coefficient of the imaginary part).The real part will take into account territory, and the coefficient for the imaginary part will calculate the spatial indicator, which is the sum of the area to the perimeter ratios.Thus, our indicators will take into account both the ecological part and spatial characteristics.
Spatial indicators of forecasting the use of land resources are in the fact that there are dependencies on the shape of fields and working areas and various economic effects [11].The economic efficiency of economic activity depends on various costs, one of which is the fuel and oil cost and agricultural machinery depreciation.This is due to those idle runs and turns of agricultural machinery.That is, the shape of the field affects the amount of expenses.In turn, costs are part of the economic component.Indicators of the intensively used land and ecologically stabilizing land ratio do not take into account economic effects.With the same land ratio, the ecological effect can be different.Different configurations of fields and working areas can create more protected areas from negative natural and anthropogenic phenomena.In figure 1, we see 3 schematic views of the arable land configuration with ecologically stabilizing lands.Yellow color shows conditionally arable land, green shows ecologically stabilizing land, purple shows positive impact on arable land.By positive influence we mean anti-erosion protection, creation of microclimatic conditions for the growth of agricultural crops, etc.All three schematic options have the same land ratio.Plowability is 50%.Regarding the ease of working areas use, option A is better, option B is somewhat worse.Option C is not suitable for the use of powerful agricultural machinery at all.Regarding the impact on arable land, option C provides the best impact due to the mosaic structure of the territory.Option A has the minimum influence area.
On the one hand, the high contour and fragmentation of the territory creates biological diversity, provides greater protection against wind and water erosion, and provides a stronger interaction between ecologically stabilizing lands and intensively used lands.On the other hand, high contouring worsens the use of agricultural machinery due to idle turns, increases the costs of fuel and oil and work time (increase in wage costs), amortization, wear and tear of agricultural machinery, etc [12].Thus, we need to find a balance between the economic and ecological components of land resources use.When designing, as a rule, several options are formed according to different rules, which in turn arise due to the fact that there are no universal ideal management conditions.There are always many factors and many options to consider.At the final stage of planning, these projects are evaluated and the best one is selected.If we use only the land ratio indicator, there is no economic evaluation of the project.If we use only economic indicators, there will be no information on environmental safety.Therefore, our offered indicator based on complex numbers will at least indirectly contain both components.This will make it possible to more objectively and qualitatively find the best option for spatial planning of land resources [13].Land use is central to addressing food security, including biodiversity conservation, climate change, sustainability issues, sustainable energy, achieving social justice, and poverty alleviation.To calculate the "reference" complex indicator, the 2013 recommendations of the Derzhkomzem (State Committee of Ukraine on Land Resources) were used regarding the ecological and economic substantiation of land management and the introduction of crop rotation.These recommendations suggest that the shape of the field be rectangular or trapezoidal, have parallel sides, an aspect ratio of 1 to 5, and be located, if possible, from north to south with long sides.The area of the field should be up to 400 hectares.Field protection forest strips should be located along the boundaries of the working plots, entrances to each land plot should be provided.Field protection forest strips should be located at an angle of 90 degrees in relation to harmful winds (with a deviation of up to 30 degrees).
With the help of the software, a "reference" project was designed and the sum of perimeter and area ratio was determined.The considered perfect conditions do not take into account the relief, variegation of the ground cover, etc.For the calculation, we used an area of 1000 hectares with a plowing rate of 50%.In scientific sources, researchers have come to a consensus that the rate of plowing is too high for Ukraine and should be reduced.But there is no agreed exact data on the size of the plowability indicator.Next, using our example, we calculate how much the complex number of the "reference" project differs from the corresponding options.We make a general conclusion, which option is the best.For option A, the comprehensive assessment was 0.5 + 0.005i, for B -0.5 + 0.007i, for C -0.5 + 0.092i, for the "reference" project -0.5 + 0.008i.Next, we find the distance between the points -the length of the corresponding vector.Consequently, we can say that the closest to the standard and recommended option is B.

Difficulties and issues that need to be refined regarding complex indicators
Using complex numbers, as opposed to real numbers, makes comparisons difficult.We can compare only the real and imaginary parts.To avoid this problem, we suggest developing a "reference" assessment object.That is, a project that will take into account all existing recommendations from the ecological and economic side.When evaluating project options or different projects for the offered indicator, we will compare them with the evaluation of the "reference" object -how far is our indicator from this point.
The offered complex indicator proposed can be used in two directions.The first, when you need to compare different project options of the same territory.The second, when you need to compare (evaluate) different territories.After conducting a spatial and statistical analysis, it is possible to develop "benchmarks" for various natural and agricultural areas.The lands on the territory of Ukraine are located in several natural climatic zones, which are divided into natural and agricultural areas, which differ from each other in relief, natural and climatic conditions, as well as contour and fragmentation.It is precisely because of such significant differences between natural and agricultural areas that it is not desirable to use the same "standard" for comparison.In the calculation of these indicators, with which the existing farms or project options will be compared in the future, it is planned to apply the terrain characteristics.If previously it was difficult to calculate such indicators due to the lack of necessary data and the difficulty of calculation, now using modern geographic information systems and appropriate software (QGIS, ArcGIS, Digitals) it is possible to quickly calculate the above spatial indicators.
A certain obstacle to the calculation and implementation of the above indicators is the lack of information on the characteristics of the communities' territory.Territorial communities have appeared recently and there is no generalized up-to-date and verified information on spatial resources.Information on land resources in full is not yet available.In the direction of overcoming the obstacle, very significant steps are being taken, for example, the use of an information portal, which is constantly filled with information on the land resources use.It should be noted that for a full-scale assessment of the entire territory of Ukraine or even within the boundaries of the natural-agricultural region, there is still not enough information.There is a certain positive trend thanks to services (sites) that provide free satellite images of the earth's surface.With the help of GIS programs, you can find information about the physical properties of land plots.
Another obstacle to the use and calculation of complex indicators is the lack of a form of statistical reporting related to the use of land resources.According to the old form, there is data up to 2016.The new form has not been implemented and is at the stage of development, and therefore there is a certain "information vacuum regarding the use of land resources".
Therefore, a promising application of the offered indicator is the monitoring of changes related to the progress and impact of the land reform.For example, after analyzing satellite images of the Earth's surface taken in 2000 and images of 2021, we see that there are two trends.The first trend is an increase contour and fragmentation without changes in the structure of the land.This is due to the increase in the number of land users and business entities.The second trend is a change in the structure of land, by involving intensive cultivation of fodder land.Both the first and second trends can be calculated and analyzed using the offered indicator.This will make it possible to conduct at least a partial and intermediate assessment of land reform effectiveness.Land relations is a complex multifaceted system and it is difficult to characterize it with one indicator.But there is an opportunity to note trends and evaluate prospects.When spatial planning of the communities' territory, design and planning solutions of larger territorial units (districts, regions of the country) must be taken into account.
The use of complex indicators in land management should help to identify patterns that were not the focus of scientists' attention before.In the future, it is planned to improve the real part of the indicator (the ratio of arable land to the total area).Various multidimensional statistical searches, finding the correlation dependence of environmental effects and economic gains on the value of the above-mentioned indicator will help to do this.But it should be noted that economic calculations are also characterized by a lack of information.There are two levels of problems with statistical data: practical and methodical.The practical one is that costs directly related to production are a trade secret.The methodological level is that the final result of agricultural activity is influenced not only by the production component, but also by others, such as marketing.It is difficult to investigate the direct influence of land, contour, and fragmentation ratio on the economic component of economic activity.

Conclusions
The offered evaluation of design and planning solutions index will make it possible to evaluate both the ratio of lands and their spatial placement in an integrated manner.The use of complex numbers will make it possible to implement new analysis approaches in land management to find regularities in the influence of spatial placement on the economic activity results.For territorial communities in Ukraine, an important success factor is the use of arable land, as the most effective agricultural land.Finding a balance between economic benefit and ecological stability is a key task of the territory spatial planning.
The offered approach application requires a significant amount of relevant information.Unfortunately, there are certain obstacles regarding access to the characteristics of the land resources use.Modern software and land remote sensing data allow highly complex analyses.The indicators mentioned above must be tested and improved.Including relief characteristics in complex indicators will provide even more accurate spatial analysis data.
Prospective areas of use of the proposed indicator are the determination of average statistical characteristics of the spatial indicators of the most productive lands.On their basisdetermination of optimization parameters, ways of reducing economic costs, achieving ecological balance.First, it is possible to determine the most successful (effective) design and planning solutions.Secondly, there is an opportunity to analyze trends and trends in the development of land relations, to draw conclusions about problems and proposals to overcome them.Territorial

Figure 1 .
Figure 1.Options of spatial development comprehensive assessment.