Xingxing Kuang

Review on climate change on the Tibetan Plateau during the last half century

The Tibetan Plateau (TP) is undergoing significant warming since the 1950s. During the past two decades, extensive research has been conducted to investigate the climate change on the plateau. This review presents an overview of recent progress on climate change on the TP with the aim of providing a comprehensive understanding of changes in climate variables. Long-term observation data from meteorological stations presented by the published literature were used to show the trends in various climate variables. The TP is overall getting warmer and wetter during the past decades. Temperature is significantly increased, especially since the 1980s. The overall warming rate ranges from 0.16 to 0.67°C decade−1 since the 1950s during different periods. The TP shows a uniform warming trend with the most significant warming in the northern part. Precipitation is slightly increased, and the spatial pattern of changes in precipitation is variable. The annual precipitation is increasing in most areas of the TP. Some subregions are becoming wetter, while some subregions are becoming drier. Pan evaporation, reference evapotranspiration, and potential evapotranspiration have been found to decrease since the 1960s. Actual evapotranspiration is significantly increased since the 1960s. Wind speed and sunshine duration increased up to the 1970s and then decreased significantly afterwards. Relative humidity fluctuated up and down to the end of the 1990s and appeared to decrease afterwards. Vapor pressure deficit shows an overall increasing trend since the 1970s. Causes of changes in the climate variables are presented, and future research directions are recommended.

An integrated permeability‐depth model for Earth's crust

Permeability, which generally decreases with depth, is the most important parameter that controls fluid flow in Earths crust. There are two categories of models that describe the permeability-depth relationship: one category forces permeability to approach infinity at the surface, and the other category leads to too much decrease in permeability with depth. Here we present a new model that integrates and reconciles existing models thus allowing for complete description of crustal permeability from the surface and through the entire crust. Our model provides improved description of observed data and is applicable to both continental crust and oceanic crust. It can be used to obtain a better understanding of the role of fluids in crustal processes.

Accumulation and transport of ammonium in aquitards in the Pearl River Delta (China) in the last 10,000 years: conceptual and numerical models

Generation, accumulation and migration of ammonium in the coastal aquifer-aquitard system of the Pearl River Delta, China, are a result of complex and long-term processes including sea-level changes, shoreline migration, sedimentation, decomposition of organic matter, solute-transport processes, and chemical reaction during the Holocene. Simulation of long-term ammonium distribution is not well addressed in the literature due to the difficulties in quantifying the complex geochemical processes. Salinity and ammonium profiles in the aquitards at two typical sites were obtained from geochemical analyses of soil and water samples. One-dimensional numerical models were used to integrate present knowledge of stratigraphy, historical evolution of the geological system during the Holocene, and the processes related to the generation and migration of ammonium. The ammonium generation and accumulation were approximated by an exponential function, and a moving boundary condition was used to reflect the sea-level changes during the Holocene. The observed salinity profiles were used to estimate flow and dispersion parameters, then the observed ammonium profiles were used to estimate the reactive parameters related to ammonium generation. The reasonably good match between the simulated and observed results demonstrates that the models can capture the dominant processes that control the generation and movement of ammonium.RésuméLa genèse, l’accumulation et la migration d’ammonium dans le système d’aquitards côtier du delta de la Rivière des Perles, Chine, sont le résultat de processus complexes à long terme incluant des changements de niveau marin, des migrations de la ligne côtière, la décomposition des matières organiques, des processus de transport de solutés, et des réactions chimiques durant l’Holocène. La simulation d’une distribution de l’ammonium à long terme n’est pas bien abordée dans la littérature en raison de la difficulté de quantifier les processus géochimiques complexes. Des profils de salinité ammonium dans les aquitards de deux sites typiques ont été obtenus à partir d’analyses géochimiques de sol et d’échantillons d’eau. Des modèles unidimensionnels ont été utilisés pour intégrer la connaissance actuelle de la stratigraphie, de l’évolution historique du système géologique durant l’Holocène, et les processus liés à la génération et à la migration de l’ammonium. La génération de l’ammonium et son accumulation ont fait l’objet d’approximation par une fonction exponentielle avec conditions aux limites variables pour prendre en compte les variations du niveau marin durant l’Holocène. Les profils de salinité observés sont été utilisés pour estimer débit et paramètres de dilution, puis les profils ammonium ont été utilisés pour estimer les paramètres contribuant à la génération de l’ammonium. La correspondance relativement bonne entre les résultats simulés et l’observation montre que le modèle peut représenter le processus dominant qui contrôle la genèse et le déplacement de l’ammonium.ResumenLa generación, migración y acumulación de amonio en el sistema acuífero – acuitardo del Delta del Río Pearl, China, son el resultado de procesos complejos y de largo plazo, incluyendo cambios del nivel del mar, migración de la línea de costa, sedimentación, descomposición de materia orgánica, procesos de transporte de soluto, y reacciones químicas durante el Holoceno. La simulación de la distribución a largo plazo del amonio no está bien abordada en la literatura debido a las dificultades en la cuantificación de los complejos procesos geoquímicos. Se obtuvieron perfiles de salinidad y de amonio en el acuitardo a partir de análisis geoquímicos y muestreos de agua en dos sitios típicos. Se usaron modelos numéricos unidimensionales para integrar el conocimiento actual de la estratigrafía, evolución histórica del sistema geológico durante el Holoceno, y los procesos relacionados a la generación y migración de amonio. La generación y la acumulación de amonio fueron aproximados por una función exponencial, y se usó una condición de borde en movimiento por reflejar el cambio del nivel de mar durante el Holoceno. Se usaron los perfiles de salinidad observados para estimar los parámetros de flujo y dispersión, luego se usaron los perfiles de amonio observados para estimar los parámetros reactivos relacionados con la generación de amonio. El razonablemente buen acuerdo logrado entre los resultados simulados y los observados demuestra que los modelos pueden capturar los procesos dominantes que controlan la generación y movimiento del amonio.摘要中国珠江三角洲滨海含水层-弱透水层系统中铵的形成、积累和运移,是全新世以来一系列复杂过程长期作用的结果,包括海平面升降、海岸线进退、沉积、有机质降解、溶质运移和化学反应等。由于定量刻画这些复杂地球化学过程存在困难,目前还很少有模拟铵的长期分布演化的文献。通过对两个典型场地土水样的水文地球化学分析,获得了弱透水层中盐分和铵的剖面分布特征。综合现有关于地层、全新世以来地质系统演变历史以及铵化反应方面的认识,本文提出了铵的累积运移过程的一维模型。铵的生成和累积用一个指数经验公式近似描述。采用移动上边界来表现全新世时期海平面的变化。首先利用观测的盐分剖面识别水流和水动力弥散参数,在此基础上利用观测的铵分布剖面来反演铵的生成反应参数。模拟结果与实测结果之间具有良好的一致性,这说明所提出的模型刻画了铵在弱透水层中积累和运移的主要过程。ResumoA geração, acumulação e migração de amónio no sistema costeiro aquífero-aquitardo do Delta do Rio Pearl, na China, são o resultado de processos complexos e de longo prazo, incluindo mudanças no nível do mar, migração da linha de costa, sedimentação, decomposição de matéria orgânica, processos de transporte de solutos e reações químicas durante o Holocénico. A simulação a longo prazo da distribuição de amónio não é bem abordada na literatura, devido às dificuldades em quantificar os complexos processos geoquímicos. Foram obtidos perfis de salinidade e de amónio nos aquitardos, em dois locais típicos, a partir de análises geoquímicas de amostras de solo e água. Foram usados modelos numéricos unidimensionais para integrar o conhecimento atual da estratigrafia, a evolução histórica do sistema geológico durante o Holocénico e os processos relacionados com a geração e migração de amónio. A geração e acumulação de amónio foram estimados por uma função exponencial, e foi usada uma condição fronteira móvel para refletir as mudanças do nível do mar durante o Holocénico. Os perfis de salinidade observados foram utilizados para estimar os parâmetros de fluxo e de dispersão, e, em seguida, os perfis observados de amónio foram utilizados para estimar os parâmetros reativos relacionados com a produção de amónio. A correspondência razoavelmente boa entre os resultados simulados e observados demonstra que os modelos podem capturar os processos dominantes que controlam a geração e a circulação de amónio.

Increased Water Storage in the Qaidam Basin, the North Tibet Plateau from GRACE Gravity Data

Groundwater plays a key role in maintaining the ecology and environment in the hyperarid Qaidam Basin (QB). Indirect evidence and data from sparse observation wells suggest that groundwater in the QB is increasing but there has been no regional assessment of the groundwater conditions in the entire basin because of its remoteness and the severity of the arid environment. Here we report changes in the spatial and temporal distribution of terrestrial water storage (TWS) in the northern Tibetan Plateau (NTP) using Gravity Recovery and Climate Experiment (GRACE) data. Our study confirms long-term (2003–2012) TWS increases in the NTP. Between 2003 and 2012 the TWS increased by 88.4 and 20.6 km3 in the NTP and the QB, respectively, which is 225% and 52% of the capacity of the Three Gorges Reservoir, respectively. Soil and water changes from the Global Land Data Assimilation System (GLDAS) were also used to identify groundwater storage in the TWS and to demonstrate a long-term increase in groundwater storage in the QB. We demonstrate that increases in groundwater, not lake water, are dominant in the QB, as observed by groundwater levels. Our study suggests that the TWS increase was likely caused by a regional increase in precipitation and a decrease in evaporation. Degradation of the permafrost increases the thickness of the active layers providing increased storage for infiltrated precipitation and snow and ice melt water, which may also contribute to the increased TWS. The huge increase of water storage in the NTP will have profound effects, not only on local ecology and environment, but also on global water storage and sea level changes.

Numerical study of variable-density flow and transport in unsaturated-saturated porous media.

Dense contaminant or solute transport in the unsaturated-saturated aquifer commonly exists in the natural environment. However, the influence of hydraulic properties of the unsaturated soil on penetration process of variable density flow in an unsaturated-saturated aquifer system is rarely investigated. In this study, a variable density, variably saturated flow and transport model based on FEFLOW is used to systematically investigate the penetration process of the solute through the unsaturated-saturated aquifer system, with a focus on the influence of the hydraulic parameters of the unsaturated soil on the penetration process. Vertical center of mass, and its speed and acceleration, are used to identify different stages of the penetration process through the unsaturated-saturated aquifer. The hydraulic parameters in the van Genuchten-Mualem model (VGM) affect the water content distribution in the unsaturated zone, subsequently the penetration time through the unsaturated zone. Through influencing the thickness of the transition zone (0.1-0.9 maximum concentration of the plume) when the plume reaches the water table, the hydraulic parameters affect the accumulation time of the solute at the boundary layer in the saturated zone. Thus, the process in not only the unsaturated but also the saturated zones is influenced by the change of the hydraulic properties of the unsaturated zone. Furthermore, the results show that the instabilities start to occur at the zone with high water content (90% of maximum saturation) in the capillary fringe. Freshwater intrudes into the zone with high water content when fingers are completely developed at the entire system. The length of freshwater intrusion above the water table has a negative correlation with the fitting parameter alpha in the VGM model. The influence of the density difference of the solute on the penetration processes is insignificant in the unsaturated zone but significant in the saturated zone. Sensitive analysis for the hydraulic properties of the unsaturated soil on the penetration process shows that pore size distribution index is the main factor influencing the penetration time through the unsaturated zone, the penetration time through the entire aquifer, the accumulation time at the boundary layer, and the development time of the fingers. Two other parameters, fitting parameter alpha and residual saturation, have minor effects.

Chloride as tracer of solute transport in the aquifer–aquitard system in the Pearl River Delta, China

A 1D numerical model is constructed to investigate the impact of sedimentation and sea level changes on transport of Cl− in the aquifer–aquitard system in the Pearl River Delta (PRD), China. The model simulates the evolution of the vertical Cl− concentration profiles during the Holocene. Sedimentation is modeled as a moving boundary problem. Chloride concentration profiles are reconstructed for nine boreholes, covering a wide area of the PRD, from northwest to southeast. Satisfactory agreement is obtained between simulated and measured Cl− concentration profiles. Diffusion solely is adequate to reproduce the vertical Cl− concentration profiles, which indicates that diffusion is the regionally dominant vertical transport mechanism across the aquitards in the PRD. The estimated effective diffusion coefficients of the aquitards range from 2.0 × 10–11 to 2.0 × 10–10 m2/s. The effective diffusion coefficients of the aquifers range from 3.0 × 10–11 to 4.0 × 10–10 m2/s. Advective transport tends to underestimate Cl− concentrations in the aquitard and overestimate Cl− concentrations in the basal aquifer. The results of this study will help understand the mechanisms of solute transport in the PRD and other deltas with similar geological and hydrogeological characteristics.RésuméUn modèle numérique unidimensionnel a été construit afin d’étudier l’impact de la sédimentation et des changements du niveau de la mer sur le transport du Cl− dans un système d’aquifères et d’aquitards du delta de la rivière Pearl (PRD) en Chine. Le modèle simule l’évolution verticale des profils de concentration en Cl− durant l’Holocène. La sédimentation a été modélisée comme un problème à limites variables. Les profils de concentrations en chlorure ont été construits pour neuf forages, couvrant une large part du PRD, du nord-est au sud-est. Une concordance satisfaisante a été obtenue entre simulations et mesures de concentrations du Cl− dans les profils. La diffusion, seule, permet une reproduction adéquate des profils de concentrations en chlorure, ce qui indique que la diffusion est le mécanisme de transport vertical dominant régionalement au travers des aquitards du PRD. Les coefficients de diffusion effective estimés pour les aquitards sont compris entre 2.0 × 10–11 et 2.0 × 10–10 m2/s. Les coefficients de diffusion effective estimés pour les aquifères sont compris entre 3.0 × 10–11 à 4.0 × 10–10 m2/s. Le transport advectif a tendance à sous-estimer les concentrations en Cl− dans les aquitards et à les surestimer dans l’aquifère de base. Les résultats de cette étude permettront de mieux comprendre les mécanismes de transport de soluté dans le PRD et autres deltas de caractéristiques géologiques et hydrogéologiques similaires.ResumenSe construyó un modelo numérico unidimensional para investigar el impacto de la sedimentación y los cambios del nivel del mar en el transporte de Cl− en un sistema acuífero–acuitardo en el delta del río Pearl (PRD), China. El modelo simula la evolución de los perfiles verticales de la concentración de Cl− durante el Holoceno. La sedimentación se modeló como un problema de límite móvil. Los perfiles de concentración de cloruro se reconstruyeron para nueve pozos de sondeo, que cubren una amplia área del PRD, desde el noroeste al sureste. Se obtuvo una concordancia satisfactoria entre los perfiles simulados y medidos de concentración de Cl−. La difusión es adecuada únicamente para reproducir los perfiles verticales de la concentración Cl−, lo que indica que la difusión es el mecanismo de transporte vertical regionalmente dominante en todos los acuitardos en el PRD. Los coeficientes de difusión efectivos estimados de los acuitardos varían entre 2.0 × 10–11 y 2.0 × 10–10 m2/s. Los coeficientes de difusión eficaces de los acuíferos van desde 3.0 × 10–11 a 4.0 × 10–10 m2/s. El transporte advectivo tiende a subestimar las concentraciones de Cl− en el acuitardo y sobreestimar las concentraciones de Cl− en el acuífero basal. Los resultados de este estudio ayudarán a entender los mecanismos de transporte de solutos en el PRD y otros deltas con características geológicas e hidrogeológicas similares.摘要建立了一维数值模型研究沉积作用和海平面变化对中国珠江三角洲含水层-弱透水层系统中Cl−运移的影响。模型模拟了全新世期间Cl−垂直浓度剖面的演化。沉积作用被模拟为移动边界问题。对九个钻孔重建了氯离子浓度剖面,这些钻孔从西北到东南覆盖了珠江三角洲广大地区。模拟的和测量的浓度剖面结果非常一致。仅使用扩散就可以重建Cl−垂直浓度剖面,表明扩散是珠江三角洲地区弱透水层的区域上主要的垂直运移机理。估计的弱透水层有效扩散系数为2.0 × 10–11 至2.0 × 10–10 m2/s。估计的含水层有效扩散系数为3.0 × 10–11 至 4.0 × 10–10 m2/s。对流运移倾向于低估弱透水层中的Cl−浓度,而高估基底含水层中的Cl−浓度。研究结果将有助于了解珠江三角洲和其它具有类似地质和水文地质特征三角洲的溶质运移机理。ResumoUm modelo numérico unidimensional foi desenvolvido pata investigar o impacto da sedimentação e mudanças no nível do mar no transporte de Cl− no sistema aquífero-aquitardo do Delta do Rio das Pérolas (DRP), China. O modelo simula a evolução de perfis verticais de concentração de Cl− durante o Holoceno. A sedimentação é modelada como um problema de condição de contorno móvel. Perfis de concentração de cloreto foram reconstruídos para nove furos de sondagem, cobrindo uma ampla área do DRP, de noroeste à sudeste. Uma concordância satisfatória foi obtida entre perfis de concentração de Cl− simulados e medidos. A difusão somente é adequada para reproduzir os perfis de concentração vertical de Cl−, o que indica que a difusão é o mecanismo de transporte regionalmente dominante através dos aquitardos do DRP. Os coeficientes de difusão efetiva estimados nos aquitardos variam de 2.0 × 10–11 a 2.0 × 10–10 m2/s. Os coeficientes de difusão efetiva dos aquíferos variam de 3.0 × 10–11 a 4.0 × 10–10 m2/s. O transporte advectivo tende a subestimar as concentrações de Cl− nos aquitardos e superestimar as concentrações de Cl− no aquífero basal. Os resultados desse estudo ajudarão a entender os mecanismos de transporte de soluto no DRP e outros deltas com características geológicas e hidrogeológicas similares.

Experimental study of airflow induced by pumping tests in unconfined aquifer with low-permeability cap

The airflow in unsaturated soils is an issue of great importance in various fields such as in agricultural, nuclear, environmental engineering. However, up to now, little attention was paid to the generation of the airflow induced by a pumping test in an unconfined aquifer with a low-permeability cap and its influence on the pumping test. In this paper, pumping tests were carried out experimentally in the aquifer with a low-permeability cap in order to study the influence of the airflow induced by the pumping on the drawdown of the tests. It is shown that: (1) there is an airflow with negative pressure generated by the pumping tests, (2) the Negative air Pressure (NP) is increased with the pumping rate but decreased with the radial distance, and (3) the NP also changes with the initial water table. The results provide a good basis for further theoretical study of the airflow induced by pumping.

Air and water flows in a large sand box with a two-layer aquifer system

The pumping of water from a sand box with a finer layer on the top was studied theoretically and experimentally. The sand box, saturated at its lower portion and initially in hydrostatic equilibrium, was pumped at constant rate. The results show that significant negative air pressure can be generated in the vadose zone during pumping. The negative air pressure increases quickly in the earlier stage of pumping, reaches a maximum, and then gradually becomes zero. The initial water-table depth has a significant effect on the generated negative air pressure. The shallower the initial water table, the larger the vacuum, and the longer the time to reach the maximum vacuum. A transient, three-dimensional model was constructed using TOUGH2-MP to simulate the air-water two-phase flow processes in the sand box. The reasonable match between the numerical solutions and the experimental data indicates that the numerical model can reproduce the dynamic process of air and water flows. The study has implications in pumping test analyses. If the air pressure in the two-layer system is ignored, the drawdown in the system will be underestimated, especially when the upper layer has low permeability and the initial water table is close to the interface of the two layers.RésuméLe pompage d’eau d’une boîte remplie de sable avec une fine couche au sommet a été étudié du point de vue théorique et expérimentale. Un pompage à débit constant a été effectué dans une boîte de sable, saturée dans sa partie inférieure et initialement en l’équilibre hydrostatique . Les résultats montrent qu’une pression significative négative de l’air peut être générée dans la zone vadose durant le pompage. La pression négative de l’air augmente rapidement dans les premiers instants du pompage et atteint un maximum, puis devient nulle progressivement. La profondeur initiale du niveau de la nappe a un effet significatif sur la pression négative générée de l’air. Plus le niveau initial de la nappe est superficiel, plus le vide est grand et plus grand est le temps pour atteindre le vide maximum. Un modèle tri-dimensionnel transitoire a été construit en utilisant le code TOUGH2-MP afin de simuler les processus d’écoulement diphasique air-eau dans la boîte remplie de sable. La similitude acceptable entre les solutions numériques et les données expérimentales indique que le modèle numérique peut reproduire les processus dynamiques des écoulements de l’air et de l’eau. L’étude a des conséquences sur l’analyse des essais de pompage. Si la pression de l’air dans un systèmes aquifère à deux couches est ignorée, le rabattement du niveau d’eau au sein du système sera sous estimé, spécialement lorsque la couche supérieure est de faible conductivité hydraulique et que le niveau initial de la nappe est proche de l’interface entre les deux couches.ResumenSe estudió teóricamente y experimentalmente el bombeo de agua desde una caja de arena con una capa más fina en su parte superior. La caja de arena, saturada en su porción inferior e inicialmente en equilibrio hidrostático, fue bombeada a un caudal constante. Los resultados muestran que se pueden ser generar presiones negativas de aire en la zona vadosa durante el bombeo. Las presiones negativas de aire se incrementan rápidamente en las etapas más tempranas del bombeo, alcanzando un máximo, y luego gradualmente se convierten en cero. La profundidad inicial de la capa freática tiene un efecto significativo sobre la presión negativa de aire generada. Cuanto más somero esté el nivel freático inicial, mayor será el vacío, y mayor el tiempo para alcanzar el máximo de vacío. Se construyó un modelo tridimensional transitorio usando TOUGH2-MP para simular los procesos de flujo bifásicos aire – agua en la caja de arena. El ajuste razonable entre las soluciones numéricas y los datos experimentales indican que el modelo numérico puede reproducir el proceso dinámico de los flujos de aire y agua. El estudio tiene implicancias en los análisis de los ensayos de bombeo. Si la presión del aire en el sistema de doble capa se ignora, la depresión en el sistema será subestimada, especialmente cuando la capa superior tiene baja permeabilidad y el nivel freático inicial está próximo a la interfase de las dos capas.摘要本文从理论上和实验上对一个上部存在一层细粒层的砂箱中的抽水试验进行了研究。抽水前砂箱下部饱和并处于静水平衡状态,在砂箱中以定流量抽水。结果表明抽水过程中在砂箱包气带中可以产生显著的空气负压。产生的空气负压在抽水早期迅速增大,然后达到平衡,之后再缓慢下降至零。初始水位埋深对产生的空气负压有显著的影响。初始水位埋深越浅,产生的空气负压越大,达到最大空气负压所需的时间也越长。基于TOUGH2-MP建立了一个非稳定三维流模型以模拟砂箱中的水气二相流过程。模拟与试验结果较好的吻合表明所建立的数值模型能够重现砂箱中水、气的流动规律。该项研究对抽水试验的数据分析有一定的指导意义。如果忽略这个双层系统中的空气负压,抽水引起的降深将被低估,尤其是当上层渗透系数较低并且初始地下水位接近两层的分界面时,降深的低估将更为严重。ResumoO bombeamento de água numa caixa de areia com uma camada fina no topo foi estudado teórica e experimentalmente. A caixa de areia, saturada na base e inicialmente em equilíbrio hidrostático, foi bombeada a caudal constante. Os resultados mostram que pode ser gerada uma pressão negativa significativa na zona vadosa durante o bombeamento. A pressão negativa do ar aumenta rapidamente na primeira fase de bombeamento, atinge um máximo e volta gradualmente a zero. A profundidade do nível freático inicial tem um efeito significativo na geração da pressão negativa no ar. Quanto menos profundo for o nível freático inicial, maior será o vácuo, e mais longo será o tempo para atingir o máximo de vácuo. Implementou-se um modelo tridimensional transitório, utilizando o programa TOUGH2-MP, para simular a interação de processos de fluxo entre as duas fases gás-agua na caixa de areia. A coerência das simulações com os dados experimentais indica que o modelo numérico pode reproduzir a dinâmica dos fenómenos de fluxo do ar e da água. Este estudo tem implicações na análise de ensaios de bombeamento. Se a pressão de ar no sistema de duas camadas for ignorado, o rebaixamento será subestimado, especialmente quando a camada superior tiver baixa permeabilidade e o nível freático inicial estiver próximo da interface entre as duas camadas.

The influence of low-permeability cap on capillary pressure during pumping in unconfined aquifer

The pumping test in an unconfined aquifer with and without a low-permeability soil was studied experimentally to reveal the influence of the negative air pressure (NP) caused by the upper layer on the water content (w), the water pressure (Pw), as well as on the capillary pressure (Pc). The study demonstrates that the NP generated in the vadose zone during pumping in the capper aquifer has a significant influence on w, Pw and Pc. The Pc obtained from the capped aquifer is smaller than that without the upper layer. After the NP reaches a peak, the influence of the NP on Pc is gradually declined as the air inflows through the upper layer which makes the NP gradually return to zero. When the air pressure returns to the atmospheric pressure, Pc in the vadose zone is only correlated with Pw, the same as the case with no upper layer.