Probabilistic analysis of the controls on groundwater depth using Copula Functions

The response mechanism of groundwater to climate change and human activities in cities within arid and semi-arid regions, such as the Urban Planning Area of Baotou City (UPABC), northern China, is a complicated problem to understand. We analyzed the climate change relationships, including precipitation and temperature, and analyzed changes in human activities, such as groundwater consumption, and then statistically analyzed the main factors affecting groundwater depth. Furthermore, cross-wavelet and wavelet coherence methods were used to analyze the response relationship and hysteresis of groundwater depth to precipitation to better understand the groundwater depth response law. The results showed that the annual precipitation in the UPABC reduction rate was 3.3 mm/10 yr, and the annual average temperature increase rate was 0.43 °C/10 yr, from 1981 to 2017. The unconfined water decrease rate was 0.50 m/yr, and the confined water decrease rate was 0.7 m/yr. The unconfined and confined water depths were affected by precipitation and groundwater exploitation, respectively, with correlation coefficients of 0.58 and 0.57, respectively. The hysteresis of groundwater depth to precipitation was about 9–14 months. However, changes in groundwater depth, especially confined water depth, were greatly affected by groundwater exploitation. This reflected the imbalance in consumption and recharges in the UPABC, highlighting the long-term risk in areas relying on access to this resource. Therefore, arid inland zones of northern China, such as the UPABC, should pay more attention to the rational development of groundwater and strengthen the management and protection of groundwater resources.

Water resources in arid and semi-arid areas are limiting factors for ecosystem health and economic development. Therefore, an accurate and reasonable assessment of ecological water demand is crucial for efficient water resource utilization. In this study, we used vegetation coverage and groundwater depth to assess the state of vegetation growth in the Zhenglanqi, located at the southeastern edge of Otindag Sandy Land. Our results indicate the existence of a statistical power index function between vegetation coverage and groundwater depth scatter plots, where even minor changes in groundwater depth can have a significant impact on vegetation growth. In order to quantitatively assess the impact of subsidence on vegetation ecology, we propose a maximum allowable subsidence level under conditions that maintain normal ecological conditions, based on the initial subsidence depth and ecological guarantee rate. Our findings suggest that regions with shallower initial groundwater depths are more sensitive to changes in their environment than regions with deeper groundwater depths. The total groundwater consumption in the study area was 83 million cubic meters while maintaining an ecological guarantee rate of 80%; thus, while ensuring normal environmental conditions, human exploitation of shallow groundwater accounts for only 16 percent.

Copulas have become an important analytic tool for characterizing multivariate distributions and dependence. One is often interested in simulating data from copula estimates. The process can be analytically and computationally complex and usually involves steps that are unique to a given parametric copula. We describe an alternative approach that uses \probability{proportional{to{size" (PPS) random sampling with weights formed from the copula likelihood function. The method is flexible and can be applied to parametric and nonparametric marginal density estimates. The precision of the simulation can be calibrated by adjusting the density of the multidimensional grid used in the simulation process. The approach is fully transparent to any copula function with continuous random variables. An example evaluates a number of goodness-of-fit criteria and provides strong support for the validity and practicality of the method.

Groundwater, as the limiting resource in arid ecosystems, can have profound effects on the functional structure and distribution of plant communities. However, studies are too few to unveil the impacts of groundwater depth on plant functional traits in such communities. We collected data on vegetation, topography and soil properties from 180 quadrats (60 trees/shrubs and 120 herbaceous) in the desert‐wetland ecosystem of Shule River Basin in Northwest China. We measured 10 key community‐level functional traits, together with the resource topography (i.e., groundwater depth) and seven soil properties. We found that the increase of groundwater depth significantly reduced community‐level specific leaf area and maximum leaf photosynthesis rate, while boosted leaf dry mass content and leaf thickness. However, the leaf phosphorus content remained relatively stable. By contrast, with the increase of groundwater depth, soil carbon, soil nitrogen, soil phosphorus and total dissolved salts first increased but then declined, while soil pH and soil bulk density exhibited the opposite trend. The soil moisture content decreased drastically with the decline of groundwater. The change in groundwater depth, thus, was found the main driver of species distribution in the arid zone, contributing 21.16%, followed by soil K+ (9.94%) and soil total nitrogen content (4.9%), as well as a strong interaction of the three (41.7%). Changes in groundwater depth can thus alter the structure and nutrient enrichment of the soil, which in turn affects the distribution of vegetation through water–soil–plant interactions.

Abstract. In spite of the relative importance of groundwater in costal dune systems, studies concerning the responses of vegetation to ground water (GW) availability variations, particularly in Mediterranean regions, are scarce. Thus, the main purpose of this study is to compare the responses of co-occurring species possessing different functional traits, to changes in GW levels (i.e. the lowering of GW levels) in a sand dune ecosystem. For that, five sites were established within a 1 km2 area in a meso-mediterranean sand dune ecosystem dominated by a Pinus pinaster forest. Due to natural topographic variability and anthropogenic GW exploitation, substantial variability in depth to GW between sites was found. Under these conditions it was possible to identify the degree of usage and dependence on GW of different plant species (two deep-rooted trees, a drought adapted shrub, a phreatophyte and a non-native woody invader) and how GW dependence varied seasonally and between the heterogeneous sites. Results indicated that the plant species had differential responses to changes in GW depth according to specific functional traits (i.e. rooting depth, leaf morphology, and water use strategy). Species comparison revealed that variability in pre-dawn water potential (Ψpre) and bulk leaf δ13C was related to site differences in GW use in the deep-rooted (Pinus pinaster, Myrica faya) and phreatophyte (Salix repens) species. However, such variation was more evident during spring than during summer drought. The exotic invader, Acacia longifolia, which does not possess a very deep root system, presented the largest seasonal variability in Ψpre and bulk leaf δ13C. In contrast, the response of Corema album, an endemic understory drought-adapted shrub, seemed to be independent of water availability across seasons and sites. Thus, the susceptibility to lowering of GW due to anthropogenic exploitation, in plant species from sand dunes, is variable, being particularly relevant for deep rooted species and phreatophytes, which seem to depend heavily on access to GW.

Influenced by the hydrogeological structure and other factors, the change in groundwater depth shows seasonal fluctuation characteristics. Human activities have disrupted the long-term stable pattern of groundwater change, which makes the short-term prediction of groundwater depth important. To cope with the emergence of short-term groundwater prediction scenarios, for the first time, a discrete grey seasonal model with fractional order accumulation is proposed in this paper (FDGSM(1,1)). First, the DGM(1,1) model, which has a relative advantage over fluctuating data, was chosen as the basis for the transformation of the proposed model. Then, the fractional order accumulation operator is used to reduce the seasonal fluctuations in the data series. Finally, grey seasonal variables are introduced to construct the time response function. The proposed model has the basic properties of the traditional grey forecasting model, which is proven to be stable and seasonal. Additionally, the prediction performance of the proposed model is verified in a real scenario of Handan groundwater. This paper expands the seasonal prediction field of the grey prediction model, enriches the research system of the grey system theory and fractional order, and has a positive influence on the short-term prediction of groundwater depth.

QuestionsDoes the plant hydrotype composition of phreatophytic vegetation alter with drawdown of the water table? Can alternative states of phreatophytic vegetation be identified, and do they persist despite a multi‐decadal drying of a mediterranean‐type landscape?LocationField study, coastal sandy plain, Gnangara Groundwater System, south‐western Australia.MethodsWe used a data set spanning 35 yr to determine alternative states of phreatophytic vegetation and how they relate to spatial variation and temporal change in hydrological habitat. Multivariate regression trees (MRT) were used to identify the range in depth to groundwater associated with vegetation states (characteristic hydrotype compositions). Logistic regression analyses were conducted to predict the proportional representation of each hydrotype. Hydrotype compositions of recent observations were correlated against modelled values derived from historic observations to test whether the relationship between vegetation states and supporting hydrological habitats remains valid after significant decline in the water table.ResultsThe MRT analyses for the historic and recent observations produced a main split criterion at 2.0 and 2.9 m groundwater depth, respectively, essentially dividing records into those dominated by hydrophytes or xerophytes. No hydrophytes were present at groundwater depths >10.5 m (>8.5 m for recent observations), where xerophytes and generalists were dominant. Only extreme groundwater depths were dominated by a single hydrotype class (hydrophytes or xerophytes), while intermediate clusters represented a transition across the hydrotype classes. The logistic regressions of the proportion of hydrotypes as a function of groundwater depth resulted in good fits for hydrophytes and xerophytes only.ConclusionsVegetation states were consistent over 35 yr of progressive increase in depth to water table. Distribution of alternative states along a gradient in groundwater depths was exponential and was reflected in the distribution of hydrophytes and mesophytes. The ranges of groundwater depths at which individual states occur suggest that as groundwater depth increases, the degree of habitat specificity decreases. The narrow range of groundwater depths within which hydrophytes and mesophytes are dominant suggests that small changes in depth could lead to transitions between states. With ongoing drying of the landscape, persistence of these vegetation states can be expected to diminish.

Although public and financial support for stream restoration projects is increasing, long‐term monitoring and reporting of project successes and failures are limited. We present the initial results of a long‐term monitoring program for the Lower Red River Meadow Restoration Project in north‐central Idaho, U.S.A. We evaluate a natural channel design’s effectiveness in shifting a degraded stream ecosystem onto a path of ecological recovery. Field monitoring and hydrodynamic modeling are used to quantify post‐restoration changes in 17 physical and biological performance indicators. Statistical and ecological significance are evaluated within a framework of clear objectives, expected responses (ecological hypotheses), and performance criteria (reference conditions) to assess post‐restoration changes away from pre‐restoration conditions. Compared to pre‐restoration conditions, we observed ecosystem improvements in channel sinuosity, slope, depth, and water surface elevation; quantity, quality, and diversity of in‐stream habitat and spawning substrate; and bird population numbers and diversity. Modeling documented the potential for enhanced river–floodplain connectivity. Failure to detect either statistically or ecologically significant change in groundwater depth, stream temperature, native riparian cover, and salmonid density is due to a combination of small sample sizes, high interannual variability, external influences, and the early stages of recovery. Unexpected decreases in native riparian cover led to implementation of adaptive management strategies. Challenges included those common to most project‐level monitoring—isolating restoration effects in complex ecosystems, securing long‐term funding, and implementing scientifically rigorous experimental designs. Continued monitoring and adaptive management that support the establishment of mature and dense riparian shrub communities are crucial to overall success of the project.

This study investigates the sensitivity and uncertainty of hydrological droughts frequencies and severity in the Weihe Basin, China during 1960–2012, by using six commonly used univariate probability distributions and three Archimedean copulas to fit the marginal and joint distributions of drought characteristics. The Anderson-Darling method is used for testing the goodness-of-fit of the univariate model, and the Akaike information criterion (AIC) is applied to select the best distribution and copula functions. The results demonstrate that there is a very strong correlation between drought duration and drought severity in three stations. The drought return period varies depending on the selected marginal distributions and copula functions and, with an increase of the return period, the differences become larger. In addition, the estimated return periods (both co-occurrence and joint) from the best-fitted copulas are the closet to those from empirical distribution. Therefore, it is critical to select the appropriate marginal distribution and copula function to model the hydrological drought frequency and severity. The results of this study can not only help drought investigation to select a suitable probability distribution and copulas function, but are also useful for regional water resource management. However, a few limitations remain in this study, such as the assumption of stationary of runoff series.

Prosopis tamarugo Phil. is a strict phreatophyte tree species endemic to the “Pampa del Tamarugal”, Atacama Desert. The extraction of water for various uses has increased the depth of the water table in the Pampa aquifers threatening its conservation. This study aimed to determine the effect of the groundwater table depth on the water relations of P. tamarugo and to present thresholds of groundwater depth (GWD) that can be used in the groundwater management of the P. tamarugo ecosystem. Three levels of GWD, 11.2 ± 0.3 m, 10.3 ± 0.3 m, and 7.1 ± 0.1 m, (the last GWD being our reference) were selected and groups of four individuals per GWD were studied in the months of January and July of the years 2011 through 2014. When the water table depth exceeded 10 m, P. tamarugo had lower pre-dawn and mid-day water potential but no differences were observed in minimum leaf stomatal resistance when compared to the condition of 7.1 m GWD; the leaf tissue increased its δ13C and δ18O composition. Furthermore, a smaller green canopy fraction of the trees and increased foliage loss in winter with increasing water table depth was observed. The differences observed in the physiological behavior of P. tamarugo trees, attributable to the ground water depth; show that increasing the depth of the water table from 7 to 11 m significantly affects the water status of P. tamarugo. The results indicate that P. tamarugo has an anisohydric stomatal behavior and that given a reduction in water supply it regulates the water demand via foliage loss. The growth and leaf physiological activities are highly sensitive to GWD. The foliage loss appears to prevent the trees from reaching water potentials leading to complete loss of hydraulic functionality by cavitation. The balance achieved between water supply and demand was reflected in the low variation of the water potential and of the variables related to gas exchange over time for a given GWD. This acclimation capacity of P. tamarugo after experiencing increases in GWD has great value for the implementation of conservation strategies. The thresholds presented in this paper should prove useful for conservation purposes of this unique species.

A statistical analysis method for significant wave height and spectral peak frequency considering the random and time-varying effects based on copula function and Bayesian inference

A combination of relative microgravity measurements at ground surface, and depth to water and water table measurements from adjacent wells were used to estimate geospatial variation of groundwater. A highly accurate portable Grav-Map gravimeter was used for gravimetric measurements at locations nearby a 42 well water table monitoring program. To efficiently correlate the two data sets, wells were clustered into five groups by geological unit and water saturation. Microgravity data was processed, interpreted, and correlated with both the depths to groundwater and the water table levels. Regression analyses revealed a strong negative correlation for microgravity and depth to groundwater in all five clusters; correlation coefficients varied between 0.70 and 0.97, and measured 0.78 over the entire study area. Microgravity values increased as groundwater depth decreased, likely because rising groundwater fills voids and fractures within soil and rocks, increasing rock density and therefore relative gravity. To validate the correlation, we superimposed a map of depths to water on the first derivative of microgravity measurements. The shallowest groundwater depths were positively related to the zero first derivatives, having intersection areas within a 75 % significance interval. Negative first derivatives covered the rest of the study area, with relative gravity decreasing with increasing groundwater depth. This technique can precisely and efficiently determine changes in subsurface geology and geospatial changes in depths to the groundwater table. Distances between microgravity stations should be small, to better detect small changes in gravity values, reflecting density contrasts underground.

Models of diameter and height distributions play an important role in forest mensuration and inventory, and many models and fitting methods are available for fitting these distributions separately. Very few models and methods appropriate for fitting the joint distribution of diameters and heights are available. The S BB and distributions obtained using Plackett's method are the only appropriate models published in the forestry literature to date. A bivariate joint distribution can be represented in terms of its underlying marginals and a copula function that models the dependency structure. A copula is a function that joins or “couples” a multivariate distribution function to its one-dimensional marginal distributions. The copula approach provides a general way of constructing bivariate distributions, including previously used bivariate models. The basics of the copula representation, the most useful copula functions, and maximum likelihood estimation (MLE) of the copula function are introduced. The emphasis of this article is on the choice of copula function(s) appropriate for modeling the joint distribution of tree diameters and heights. Using an empirical dataset of 102 Chinese fir (Cunninghamia lanceolata Lamb.) plantation plots, we fit each of the copula functions that we considered to each sample-plot joint distribution of tree diameters and heights. A two-stage MLE approach with a nonparametric (empirical) approach to the marginal distributions is adopted. In this case study the normal copula proves to be the best for modeling the joint distribution (dependence) of tree diameters and heights.

The role of groundwater in the spatio-temporal variations of vegetation water use efficiency in the Ordos Plateau, China

To clarify the physiological mechanism of different groundwater depths affecting soybean evapotranspiration, photosynthetic characteristics and yield, a field experiment with four groundwater depth levels (1 m (D1), 2 m (D2), 3 m (D3) and 4 m (D4)) was conducted through the groundwater simulation system in 2021 and 2022. In this study, a quantitative analysis was conducted on the groundwater recharge and irrigation water demand and evapotranspiration (ET) of soybean fields with different treatments, and the effects of different treatments on soybean leaf area index (LAI), chlorophyll content index (SPAD), intercepted photosynthetic active radiation (IPAR), photosynthetic gas exchange parameters, dry matter accumulation (DMA) and yield were explored. The results showed the following: (1) Groundwater depth affected soybean ET and the source of ET. With the increase in groundwater depth, groundwater recharge and its contribution to ET gradually decreased, but the amount of irrigation required gradually increased, resulting in the ET as D1 > D4 > D2 > D3. (2) Soybean LAI, SPAD and IPAR were significantly affected by the different groundwater depths, of which the D1 treatment always maintained the maximum, followed by the D4 treatment, and the D3 treatment was the minimum. The photosynthetic gas exchange parameters under different treatments changed synergistically, showing significant differences in the flowering and podding stages, notably D1 > D4 > D2 > D3. Soybean DMA and yield first decreased and then increased with the increase in groundwater depth, and the average DMA and yield under the D1 treatment increased by 27.71%, 46.80% and 22.82% and 20.29%, 29.91% and 12.83% in the two years, respectively, compared to the D2, D3 and D4 treatments. (3) The structural equation model demonstrated that the groundwater depth indirectly affected the growth of soybean leaf area by affecting groundwater recharge, which in turn regulated soybean ET and photosynthetic capacity and ultimately affected DMA and yield. The above results showed that in the case of shallow groundwater depth (D1), the largest groundwater recharge promoted the growth of soybean leaf area and chlorophyll synthesis and increased the absorption and utilization of solar radiation. And it improved the leaf stomata conditions, accelerated the gas exchange between the plant and atmosphere, enhanced the photosynthetic production capacity and ET and achieved maximum DMA and yield. Soybean leaf growth and photosynthesis diminish with the increase in groundwater depth. In the case of deep groundwater depth (D4), the maximum irrigation improved the growth and photosynthetic performance of soybean leaves, which was favorable to ET, and ultimately led to increases in DMA and yield.