Spatiotemporal characteristics of the ancient water wells for the past 3,000a in Zhejiang Province, China: a perspective of geography

ABSTRACT Water wells are very important in the history of human development. The identification of spatiotemporal patterns of ancient water wells is a key to understanding the relationship between ancients and water, the evolution of ancient settlement patterns, and the history of population migration. However, at present, there are few reports to quantitatively explore the spatiotemporal evolution of ancient water wells from the perspective of geography. There is still a knowledge gap. Therefore, we show that a spatiotemporal kernel density estimation (STKDE) model and the centre-of-gravity method are useful for studying the spatiotemporal evolution of ancient water wells over the past 3,000 years in Zhejiang Province of southern China. The results show that in the past 3,000 years, the ancient water wells there have experienced an evolution from ‘single-core’ to ‘multicore’ aggregation, and the scope has gradually shifted from northern Zhejiang to southern Zhejiang. In addition, Hangzhou, Shangyu and ChunAn have always been aggregation centres. Socioeconomic factors, political and social stability, natural environmental conditions, population density and technological progress are the most important variables associated with water well ‘hot spots’ in time and space. This article provides a new perspective for the study of ancient water wells and fills the knowledge gap in understanding the spatiotemporal evolution characteristics of ancient water wells and other point or line features in the archaeological record.


Introduction
Water wells have been an important source of potable water for human beings since prehistoric times (Kuhn 2004;Yu et al. 2018).Groundwater removal (or withdrawal) and the construction of water wells have gradually freed human beings from the restriction that they had to live near rivers or lakes, which greatly expanded the scope of human activities and led to the formation of ancestor settlements or the foundation of towns (Chang 2012).As one of the important carriers of human history and culture (Tegel et al. 2012), ancient water wells have had a profound effect on the formation of China's special and unusual social structure and 'street culture' in the development of Chinese civilization.Water wells are at least 9,000 years old in China (Net 0000) though the earliest wells dated in Zhejiang province thus are approximately 5,500 to 6,000 years old (Jiao 2007).Chinese people built wells with a variety of materialsincluding wood, earthenware, and brick -in many architectural styles throughout the Dynastic Period (2070 BC −1912 AD) (Voudouris et al. 2019;Jiao 2014).Archaeologists have excavated 3-D models of wells crafted from ceramic and bronze from Han Dynasty tombs (Voudouris et al. 2019;Jiao 2014), an archaeological context that demonstrates the cultural, political, and socioeconomic importance of wells.The cultural significance of water wells is clearly evident in historical analyses of Chinese language (井), architecture (-'jing'), and water well rituals through time (Xie 2019;Zheng 2014).
However, from the currently published literatures, most of the studies on ancient water wells are scattered in those articles that mainly focused on the historical and cultural investigation of a single ancient water well, the study of architectural types and the exploration of religious humanities (Lin 2018).There are few reports on using quantitative approaches to study the spatiotemporal evolution characteristics of ancient water wells from the perspective of geography, and there is still a knowledge gap.In fact, the study of ancient water wells, especially their spatiotemporal evolution characteristics, will make it possible for us to understand the changes of the aquifer system in ancient time, and ancient human production and lifestyles in some ways, reveal the relationship between ancients and water, and explore the driving forces of ancient settlement changes and population migration.Prehistorians often analyse differences in settlement patterns and material culture through time and across space to explain culture change.However, these analyses are often separate endeavours.A single, unified analysis of archaeological change in a conjoined spacetime are rare (Grove 2011).
It is well known to us that the use of water wells tends to be a type of humanity activity that concentrates in certain areas.Various approaches have been applied to discover or investigate spatiotemporal patterns of geographical incidents of human activities.The first type is called quantitative spatial statistics, whose basic idea is to aggregate incidents based on geographic locations, and then employ multivariate regression analysis to study the relationship between them.For example, Bernasco, Johnson, and Ruiter (2015) proposed to study the space-time patterns of repeat and near repeat burglary victimization in West Midlands, UK by analysing the relationship between the offender's address and the geographic grid.Lord and Mannering (2010) used the application of count-data regression methods to identify the spatial and temporal elements associated with vehicle crashes.This type of method exhibits advantages in terms of high accuracy, simple calculation, and performing really well when the samples are large.However, limitations to this approach are also obvious, for example, it is inherently restricted by the available data, and an extraordinary amount of effort need to be spent to develop models with good statistical fitting.
Another line of approach for identifying the spatiotemporal patterns of geographical incidents is spatiotemporal kernel density estimation (STKDE), which is an extension of kernel density estimation (KDE) commonly used for space-time cluster detection.It can accommodate different levels of measurement for the temporal dimension ranging from a compilation of numerical ages to a simple ordering of periods, and it has been shown to be effective across diverse spatiotemporal datasets including those related the study of crime (Brunsdon, Corcoran, and Higgs 2007;Nakaya and Yano 2010), ancient sites (Sun et al. 2017;Zhu et al. 2021) and disease (Kulldorff et al. 2005;Davies, Marshall, and Hazelton 2017;Hu et al. 2018) as well traffic safety and congestion (Cheng et al. 2013;Ouni and Belloumi 2018).Kernel density estimation, which was first proposed by Rosenblatt (1956) and Emanuel Parzen (1962), is a nonparametric way to estimate the probability density of a random variable in statistics.The core idea is that there is a smooth surface above each sample point, and the highest surface value is at the position where the sample point is located and decreases gradually with increasing distance from the sample point.When the distance from the sample point is equal to the bandwidth, the surface value is 0. The free parameters of kernel density estimation are the kernel function (or kernel type), which specifies the shape of the distribution placed at each data point, and the kernel bandwidth, which controls the size of the kernel at each data point.Examples of kernel type include Gaussian, Uniform, Triangle, Epanechnikov, and so on.Kernel bandwidth is analogous to the bin size of a histogram.The quality of a kernel estimate depends more on the value of its bandwidth than its shape.A bandwidth value that is too small creates a probability density estimate that is rough and jagged (under smoothing) while a bandwidth that is too large essentially creates an unimodal distribution (over smoothing).Recently, the KDE model has been a popular hotspot mapping approach (Li et al. 2020), and it is usually applied to discover the distribution characteristics of data from the data samples themselves.However, the standard KDE model also has some shortcomings, which can be frustrating in some cases.For example, it uses the Euclidean distance of data to calculate the bandwidth, which tends to overestimate the results of the analysis (Borruso 2008;Li et al. 2011), and the 'boundary effects' will occur when estimating the boundary region, which leads to biases in the KDE model (Shi and Pun-Cheng 2019).Therefore, various KDE extensions, such as conditional KDE (Hyndman and Yao 2002), time-dependent KDE (Gray and Moore 2003), multivariate KDE (Duong and Hazelton 2005), spatiotemporal KDE (STKDE) (Brunsdon, Corcoran, and Higgs 2007) and networkconstrained KDE (Xie and Yan 2008), were proposed to overcome these drawbacks by introducing different kernel functions to the model and using different weighted distances instead of Euclidean distance in computing bandwidth.
In this article, we take Zhejiang Province, China as the study area, which can reflect the situation of ancient water wells in southern China to a certain extent, especially in the Yangtze River Delta, and is of great significance to explore the changes and evolution of human activity footprints and settlements in this area.We used a spatiotemporal kernel density estimation model with weighted distances as the kernel bandwidth is applied to analyse the spatial and temporal patterns of ancient water wells, and then a centre-of-gravity method is employed to discover the shift characteristics of the centre of gravity of ancient water wells in different historical periods.The main contributions of this study are listed as follows: (1) To the best of our knowledge, this article possibly is the first attempt of extending spatiotemporal kernel density estimation approach to the study of ancient water wells, which provides a new perspective for exploring the relationship between ancients and water, revealing the changes in ancient settlements and population migration, protecting historical and cultural relics, and so on.It fills the knowledge gap in understanding of the spatiotemporal evolution characteristics of ancient water wells in Zhejiang Province, China.This method can also be applied to the study of ancient water wells or ancient sites in other areas and other point or line features in the archaeological record.
(2) We employ the plug-in bandwidth selector for the selection of bandwidth within spatiotemporal kernel estimator and demonstrated to be more effective in discovering the spatiotemporal patterns of geographical incidents of human activities.
The rest of this paper is organized as follows.Section 2 introduces the study area, data sources and the methods employed in this article.Section 3 presents the details of the spatiotemporal evolution characteristics of ancient water wells in Zhejiang Province.In section 4, the results are discussed.In addition, the conclusions are presented in section 5.

Study area
For this study, Zhejiang Province of China was selected as the study area (Figure 1  The Hemudu Cultural site (ca 5500 BC to 3300 BC), the Majiabang Cultural site (ca 5000 BC to 4000 BC), and the Liangzhu Cultural site (ca 3300 BC to 2300 BC), are all well known for their roles in the development of an agricultural economy and the rise of sociopolitical complexity.The construction of ancient water wells in Zhejiang Province also has a long history, and most of them are well preserved.According to archaeological evidence and ancient Chinese literature, as early as ca 6000 to 7000 BC, the prehistoric people living here had the ability and skills to dig deep wells for drinking water.In addition, Zhejiang is also one of the provinces with many ancient wells.According to the registration data of the third National Survey of Cultural Relics in 2011, 3641 ancient wells were registered in Zhejiang Province.With the advancement of urbanization and the revival of human and historical consciousness in Zhejiang Province, ancient water wells, as an important carrier of local human history, have attracted increasing attention in recent years.

Data sources
The ancient water well data used in this article are mainly derived from the results of the "Ancient Water Wells' Water Source Investigation Project over Zhejiang Province" jointly carried out by the Department of Water Resources of Zhejiang Province and the Cultural Heritage Bureau of Zhejiang Province from March 2020 to October 2020, as well as the registration data of 'the third national survey of cultural relics' in 2011.There are 5,958 records in total and stored in an Excel sheet.These data are mainly formed through field investigation and measurement, combining, comparing and verifying against the historical literature.The main contents include the location of the ancient wells, the construction year, the protection situation, the main function, the state of use, the structure, the water quality, etc., and more details of them are given in Figure 2 below.

Spatiotemporal kernel density estimation model
The spatiotemporal kernel density estimation (STKDE) model, an extension of KDE, was first developed by Brunsdon, Corcoran, and Higgs (2007) to consider the effectiveness of a wider range of visualization techniques in permitting an understanding of spatiotemporal trends.It was defined by Li et al. (2020) to refer to a spatiotemporal analysis technique commonly applied to transform a geographically and temporally distributed set of points into a density surface in a threedimensional environment, i.e. it multiplies a bivariate kernel placed over the x-y (spatial) domain with a univariate kernel along the temporal dimension t to estimate the density of an event.The formula is given by: where f x; y; t ð Þ represents the estimated density on location x i ; y i ; t i ð Þ in the space-time domain, K x;y ; ð Þ and K t ðÞ are the kernel functions for the spatial and temporal domains, respectively h x and h y are the spatial bandwidths, h t is the temporal bandwidth, and n is the number of data samples within the spatial and temporal bandwidths.
At present, many forms of kernel functions can be used to measure the 'distance decay effect' for spatial weights, such as Gaussian, conic, quadratic, epanichnekov, and negative exponential (Gibin, Longley, and Atkinson 2007;Levine 2004).In this study, we choose to use the multivariate Gaussian kernel because it is one of the most commonly used nonparametric density models for spatiotemporal multivariate data, which can realize the dimension expansion of data sample features and does not need to assume the parametric form of density.The formula is as follows: where Eq. ( 2) and Eq.(3) conform to zero mean and equal standard deviations σ in every dimension.
The choice of bandwidth within any kernel-based estimator is extremely important to finding a suitable density estimate and is the knob that controls the biasvariance trade-off in the estimate of density: too narrow a bandwidth leads to a high-variance estimate (i.e.overfitting), where the presence or absence of a single point makes a large difference.Too wide a bandwidth leads to a high-bias estimate (i.e.under-fitting) where the structure in the data is washed out by the wide kernel.Currently, a variety of methods have been developed to aid the selection of an appropriate bandwidth, such as the rule-of-thumb (Silverman 1986), plug-in (Scott 1992;Amboage et al., 2019), cross-validation (Brunsdon 1995), and distance-based (Fotheringham, Brunsdon, and Charlton 2000) approaches.In this study, we employ the plug-in bandwidth selector, which is derived from asymptotic mean integrated squared error (AMISE), because it does not require assumptions about the underlying distribution of data, which makes this method more suitable for real-world datasets.The plugin technique consists of minimizing the dominant terms of the mean integrated squared error (MISE) of the estimator, and it can be written as: and f is its estimate based on a sample of n independent and identically distributed random variables.Here, E denotes the expected value with respect to that sample.Once the MISE is set as the error criterion to be minimized, our aim is to find: where SPD p is the set of positive definite matrices of size p.In practice, obtaining (5) is unfeasible, and the first step towards constructing a usable selector is to derive a more practical (but close to the MISE) error criterion, such as the AMISE.The AMISE is given by: In addition, the Eq. ( 5) can be written as: However, despite the closed expression of AMISE, it is not possible to obtain a general bandwidth matrix that minimizes AMISE, that is, to obtain explicitly.It is possible in the special case in which Þ and, differentiating with respect to h, it follows that Even if Eq. ( 8) has been obtained by means of an important simplification, it gives a very important insight: the larger the dimension p, the larger the optimal bandwidth needs to be.However, neither the computation of Eq. ( 7) (through numerical optimization overSPD p ) nor of Eq. ( 8) can be performed in practice, as both depend on the function of Hf � ð Þ.Therefore, to escape the dependence of AMISE on the function of Hf � ð Þ, we can replace it with the gradient and Hessian of a multivariate normal density ;� � À μ ð Þ, for which the curvature term in Eq. ( 7) can be computed.Conveniently, this replacement also allows us to explicitly solve Eq. ( 7) and, with the normal kernel, the results in where � can be replaced by the sample covariance matrix, which is given by: where i ¼ 1; 2, and σ 2 11 ¼ σ 2 21 ¼ 1, σ 2 12 ¼ σ 2 22 ¼ 2, ρ 1 ¼ 0:5, and ρ 2 ¼ À 0:5.

The Centre-of-gravity (CoG) method
The centre of gravity is a physical concept derived from the law of universal gravitation, which is used to describe the mutual attraction between two objects.It has been widely adopted to study the geographic distribution of various natural or human phenomena, such as population distribution (Duan, Wang, and Chen 2008;Jones 2014), immigration (Beine, Bertoli, and Fernández-Huertas 2016), land use (Chen and Zhou 2011), economic growth (Abidin, Shah, and Haseeb 2018), energy consumption (Zhang et al. 2012), and pollutant emissions (Song and Zhang 2019).
It is essential to obtain accurate knowledge of the centre of gravity and its movement for the spatiotemporal distribution of ancient water wells because the centre of gravity (CoG) positions can be affected by loading conditions, such as the spatiotemporal distribution of ancient settlements, the migration of populations, and political and societal stability.In this study, the gravity model is used to investigate the variation in spatiotemporal centres of gravity for ancient water wells over the past 3,000 years in Zhejiang Province, China.According to the theory given by Song and Zhang (2019), the centre of gravity for an attribute (M) in year t can be represented by where (x i ; y i ) represents the coordinates of the ith well, x i and y i are the longitude and latitude of the ith well, respectively; X t and Y t are the longitude and latitude of the centre of gravity for the attribute value in year t, respectively; and M t i represents the attribute value of the ith well in year t.

Spatial distribution characteristics of ancient water wells in Zhejiang Province in different historical periods
Since the chronological information collected in this study is only accurate to the dynasty, to facilitate calculation and analysis, according to the historical chronological distribution of the ancient water well data, the temporal distribution of the study object is divided into the pre-Qin dynasty period (11 th century.BC-3 rd century.BC), Qin-Han dynasties period (3 rd century.BC-AD.3 rd century), and the three Kingdoms-Wei-Jin-Southern and Northern dynasties period (AD.3 rd century-6 th century).Sui-Tang and five dynasties period (AD.6 th Century-10 th Century), Song-Yuan dynasties period (AD.10 th Century-14 th Century), Ming Dynasty period (AD.14 th Century-AD.17 th Century), Qing Dynasty period (AD.17 th Century-20 th Century) and Modern period (AD.from the 20th century to the present) and assigned values from 1 to 8 as temporal parameters in the spatiotemporal kernel density model, in which 1 represents the pre-Qin dynasty period, 2 represents the Qin-Han dynasties period, and so on; therefore, in this study, the time bandwidth is set to 1, indicating a period.In addition, because there is currently no readily available STKDE computing toolkit, we also developed a STKDE-related computing toolkit based on SciPy and GeoPandas.Based on the calculated results, the theme map is rendered in ArcGIS, and the results are shown in Figure 3.
Figure 3(a) shows the density map of the pre-Qin dynasty period.From the perspective of the development of Chinese civilization, Zhejiang Province was largely rural (or provincial) consisting mainly of comparatively small settlements.Pre-Qin dynasty peoples were broad spectrum hunters, gatherers, fishers and agriculturalists, with most fields and rice terraces located in river valleys and along lake shores.Thus, the number of ancient wells was relatively small during this period, the spatial distribution was scattered, and no aggregation core was formed.This trend continued until the Qin-Han dynasties (as shown in Figure 3(b)).
Figure 3 (c) shows the spatial density distribution of ancient water wells in the Wei, Jin, and Southern and Northern dynasties, which developed greatly both in quantity and in the scope of spatial distribution.The kernel density value of the spatial distribution of ancient water wells increased continuously and gradually formed an aggregation core with Yiwu County as the centre.During the Qin-Han dynasties, the culture of the Central Plains region began to spread to the south of the Yangtze River, and Kuaiji County was established after the Qin Dynasty unified the six Kingdoms.After that, the whole territory of Zhejiang gradually became urban, reliant on irrigation agriculture, and socioeconomically stratified.Migration and technological introductions led to the further development of Zhejiang Province during the Wei, Jin, and Southern and Northern Dynasties, when the Central Plains region extended their influence south of the Yangtze River.
The Sui-Tang dynasties and the Song-Yuan dynasties were important periods for the development of ancient water wells in Zhejiang (see Figure 3 (d, e)).The kernel density of ancient water wells increased over the course of these two periods, and the distribution expanded markedly.However, during the Sui-Tang dynasties, the high value area of the ancient water well kernel density in Yiwu County disappeared.The density value was still higher than that in the previous period, indicating that the growth rate of ancient water well expansion in Yiwu slowed down.At the same time, the kernel density value in Hangzhou increased sharply, indicating that well construction there expanded rapidly at this stage.One reason for this change is economic growth during the Sui-Tang dynasties, as the opening of the Beijing-Hangzhou Grand Canal facilitated the long distance trade of grain and other commodities between North and South China.Another factor is in-migration, as a large number of people moved southward during the An-Shi Rebellion, shifting the economic centre of gravity towards Hangzhou.The above poltical, economic, and demographic events resulted in a rapid expansion of the spatial distribution of ancient water wells in this period.During the Southern Song Dynasty, the centre of political power of China moved to Hangzhou, the economic centre of gravity of China completely moved to the south, and the economy and culture of Zhejiang began to develop and prosper.During this period, the kernel density of ancient water wells also increased significantly and gradually formed aggregation cores centred on Hangzhou, Chun'an, Wenzhou, Lanxi, Ninghai and Shangyu and fan-shaped multicore diffusion distribution from south to north with Hangzhou Bay as the centre.
The Ming-Qing dynasties were the heyday of the development of ancient water wells in Zhejiang Province (see Figure 3 (f)(g)).The kernel density value of ancient water wells' spatial distribution continues to increase, of which the high density value reached 0.8102 per square kilometre in the Ming Dynasty and 0.1587 per square kilometre in the Qing Dynasty.The geographic distribution also continues to expand, basically covering the whole province.Wells 'spring up all over the place' at this time.In fact, the number of ancient wells in the Ming Dynasty accounts for 14.28% and, number of the Qing Dynasty wells accounts for 58.56% of the total number of wells in our sample.The agglomeration pattern of ancient wells in the modern period (see Figure 3 (h)) is similar to that in the Ming-Qing dynasties, and the range of agglomeration values is relatively large during the Ming-Qing dynasties, even though water wells are basically everywhere, for example, Cixi and Jiande in Hangzhou, Shaoxing and Ningbo.The number of ancient water wells accounted for 19.76% of the total during the modern period.

Characteristics of the centre-of-gravity movement of ancient water wells in different historical periods
According to the method described in Section 2.2.2, the centre of gravity (CoG) of ancient water wells in Zhejiang Province in different historical periods was calculated.The results are shown in Table 1, which include the coordinates of the CoG, as well as the shift direction and the shift distances with respect to the preceding period.CoGs were not calculated for the pre-Qin dynasty and Qin-Han dynasty, due to the small number of ancient water wells and mostly sporadic distribution characteristics.The spatial distribution of ancient water wells gradually formed a 'single core' over the course of the Wei, Jin, Southern and Northern dynasties and Sui, Tang and five dynasties periods, but the distribution was still scattered.The CoG for wells during the Wei, Jin dynasties was located in Yiwu County.In the Sui and Tang dynasties, the aggregation centre moved 116 kilometres northwest near Hangzhou.During and after the Song and Yuan dynasties, the aggregation model of ancient wells developed into a 'multicore' pattern, which gradually took Hangzhou Bay as the centre and formed multiple centres from north to south.The Song-Yuan and Ming-Qing dynasties were the heyday of the development of water wells in Zhejiang province, during which both the geographic range and the degree of aggregation both increased, showing the characteristics of 'multicore' aggregation, especially in the Qing Dynasty.This characteristic is particularly obvious, and the aggregation pattern of Zhejiang ancient water wells in modern times is similar to that in Song, Yuan, Ming and Qing dynasties, and its aggregation range remains large.From the analysis results, we can also see that over the past 3,000 years, the spatial distribution of ancient water wells in Zhejiang Province has gradually shifted from northern to southern areas Hangzhou, Shangyu and Chun'an, however, have always been aggregation centres.

Discussion
The above results suggest that STKDE is effective in discovering and quantifying the spatiotemporal evolution of ancient water wells, while CoG method can reveal the movement of the aggregation centres.Taken together, over the past 3,000 years, the spatial distribution of the ancient water wells in Zhejiang Province has undergone an evolution from a 'single-core' aggregation pattern to a 'multicore' aggregation pattern, and the scope has gradually shifted from northern Zhejiang to southern Zhejiang.
To better understand the results, we compared them with other similar studies.Lin (2018) spatially analysed other components of the built landscape such as sites and tombs.[He or she] found that the geographic extent of agglomeration gradually shifted from northern Zhejiang to southern Zhejiang, prior to the Qin-Han dynasties, with an overall evolution from 'single-core' agglomeration centred on Hangzhou Bay to a broader 'multi-core' agglomeration.Our analysis suggests that ancient water wells were widely scattered at this time and did not form an aggregation core prior to the period of the Qin-Han dynasties.There are potentially multiple reasons why water well agglomeration temporally lags behind the agglomeration of other components of the built landscape.The overall number of pre-Qin and Han period wells in our sample is relatively small compared to the number of tombs, sites, and other cultural relic protection units analysed by Lin (2018).The paucity of wells may be the result of survey bias, as ancient wells have not received the same amount of archaeological attention as have tombs and buildings.Wells may not have been common prior to the Qin-Han dynasties, as changes in sea level, groundwater levels, groundwater salinity, and climate change may have limited their utility in selected areas of Zhejiang Province (Wu et al. 2014;Zheng et al. 2018;Zhu, Zheng, and Wu 2015;Zhu et al. 2016).Finally, well agglomeration may be a consequence, rather than a cause, of demographic nucleation.Nevertheless, the spatiotemporal distributions of ancient water wells in Zhejiang Province after the Qin-Han dynasties are very similar to the contemporaneous spatiotemporal pattern of the cultural relic protection units analysed by Lin (2018).Overall, this work presented here is of great practical significance both from the theoretical perspective in the field of historical geography and from exploring the relationship between ancients and water, revealing the changes in ancient settlements and population migration, protecting historical and cultural relics, etc.The main contribution of this article is the development of a new perspective for ancient water wells and filling the knowledge gap regarding the spatiotemporal evolution characteristics.The study reported in this article shows that the new idea is sound, and the quantitative methods used are able and effective in discovering the spatiotemporal distribution of ancient water wells.
The selection of bandwidth within any kernel-based estimator is extremely important to finding a suitable density estimate.It is the knob that controls the biasvariance trade-off in the estimate of density.We used the plug-in bandwidth selector, because it did not require assumptions about the underlying distribution of data.How to set an appropriate and adoptive bandwidth for a given kernel-based estimator is still an important research topic.It is beyond the scope of this paper to provide a detailed analysis of forces driving the spatiotemporal evolution of ancient water wells, which needs additional historical and archaeological research in the same period.We believe that our results will inspire this future research.

Conclusions
This paper reports our study on the spatiotemporal distribution of ancient water wells over the past 3,000 years in Zhejiang Province, China based upon a spatiotemporal kernel density estimation approach and the movement of their aggregation centre by using the centre-of-gravity method to discover their spatiotemporal evolution characteristics in different historical periods.The Gaussian kernel function and the plug-in bandwidth selection method are applied to calculate the spatiotemporal kernel density.Based on the above discussions and analyses, we have drawn the following conclusions: (1) In the past 3,000 years, the spatial distribution of the ancient water wells in Zhejiang Province has undergone an evolution from a 'single-core' aggregation pattern to a 'multicore' aggregation pattern, and the scope has gradually shifted from northern Zhejiang to southern Zhejiang.In addition, Hangzhou, Shangyu and Chun'An have always been water well aggregation centres.(2) Socioeconomic factors were the main forces driving the spatiotemporal evolution of ancient water wells in this area; among them, political and societal stability, natural environmental conditions, population, and technological progress were the most important.Changes in the spatiotemporal kernel density estimation map of ancient water wells through time are associated with significant socioeconomic, political, environmental, demographic, and technological changes documented in the archaeological and historic records.Clearly ancient water wells are historically significant.
), which is located on the southeast coast of China and the south wing of the Yangtze River Delta.It borders the East China Sea in the east, Fujian Province in the south, Jiangxi and Anhui Province in the west, and Shanghai and Jiangsu Province in the north.It straddles 27°02'～31° 11' north latitude and 118°01'～123°10' east longitude, as shown in Figure1.The straight-line distance between north and south is approximately 450 kilometres, and the land area is approximately 105,500 square kilometres.The terrain of Zhejiang Province slopes stepwise from the southwest to the northeast.The northeast is an alluvial plain, the east is dominated by hills and coastal plains, the middle is dominated by hills and basins, and the southwest is dominated by mountains and hills.Mountains and hills comprise nearly 75% of the land area in Zhejiang province, while plains cover about 20% of the land surface.River and lakes occupy approximately 5% of the province.The Chinese people have long called Zhejiang Province 'home'.Over 100 Neolithic sites (ca 8000 BC to 2000 BC) have been excavated here.

Figure 1 .
Figure 1.Map of the study area.

Figure 2 .
Figure 2. Distribution of Ancient Wells in various districts and cities of Zhejiang Province.

Table 1 .
Characteristics of the CoG movement of ancient water wells in different historical periods.