Quantifying the Cloud Water Resource: Basic Concepts and Characteristics

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  • Corresponding author: Yuquan ZHOU, zhouyq@cma.gov.cn
  • Funds:

    Supported by the National Key Research and Development Program of China (2016YFA0601701) and National High Technology Research and Development Program of China (2012AA120902)

  • doi: 10.1007/s13351-020-9125-7
  • Note: This paper will appear in the forthcoming issue. It is not the finalized version yet. Please use with caution.

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  • The water in the air is composed of water vapor and hydrometeors, which are inseparable in the global atmosphere. Precipitation basically comes from hydrometeors instead of directly from water vapor, but hydrometeors are rarely focused on in previous studies. When assessing the maximum potential precipitation, it is necessary to quantify the total amount of hydrometeors present in the air within an area for a certain period of time. Those hydrometeors that have not participated in precipitation formation in the surface, suspending in the atmosphere to be exploited, are defined as the cloud water resource (CWR). Based on the water budget equations, we defined 16 terms (including 12 independent ones) respectively related to the hydrometeors, water vapor, and total water substance in the atmosphere, and 12 characteristic variables related to precipitation and CWR such as precipitation efficiency (PE) and renewal time (RT). Correspondingly, the CWR contributors are grouped into state terms, advection terms, and source/sink terms. Two methods are developed to quantify the CWR (details of which are presented in Part 2 of this study) by use of satellite observations, atmospheric reanalysis data, precipitation products, and cloud resolving models. The CWR and its contributing terms over North China in April and August 2017 are thus derived. The results show that CWR has the same order of magnitude as surface precipitation (Ps). The hydrometers converted from water vapor (Cvh) during the condensation process is the primary source of precipitation. It is highly correlated with Ps, and contributes the most to the CWR. The state variables and advection terms of hydrometeors are two orders of magnitude lower than the corresponding terms of water vapor. The atmospheric hydrometeors can lead to higher PE than water vapor (several tens of percent versus a few percent), with a shorter RT (only a few hours versus several days). For daily CWR, the state terms are important, but for monthly and longer-time mean CWR, the source/sink terms (i.e., cloud microphysical processes) contribute the largest; meanwhile, the advection terms contribute less for larger study areas.
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  • Fig. 1.  Daily variations of numerical quantification results of the CWR contributing terms (unit: 1012 kg, i.e., billion ton) in North China in April 2017. (a) Mh1, Cvh, and Qhi, and (b) Mh2, Chv, Ps, and Qho.

    Fig. 2.  Spatial distributions of (a) MMh, (b) Qhi, (c) Cvh, (d) Ps, (e) GMh, and (f) CWR in North China for April 2017 (unit: mm). The thick black curves denote the provincial boundaries and the red curve denotes the Yellow River.

    Fig. 3.  Scatter plots and fitting curves of observed daily Ps versus Cvh (unit: mm) at each grid in North China for (a) April and (b) August 2017.

    Fig. 4.  Daily variations of CWR, Ps, and GMh (unit: 1012 kg, i.e., billion ton), as well as PEh (unit: %) in North China in April 2017.

    Table 1.  The CWR and related variables (unit: 1011 kg; equivalent to 0.77 mm for the study region) quantified by the CWR-NQ and CWR-DQ methods over North China (with an area size of 1.34 × 1012 km2) in April and August 2017

    VariablesApril 2017 August 2017
    CWR-NQCWR-DQCWR-NQCWR-DQ
    MMh2.194.333.107.41
    MMv82.61150.46430.19478.34
    Qhi151.79220.44216.92253.83
    Qho126.16180.44231.46263.69
    Qvi3545.304403.109393.0910037.83
    Qvo3512.934362.069266.059933.74
    Cvh380.71362.112513.622164.60
    Chv178.1499.21703.4358.71
    Ps228.73301.301814.932094.30
    Es237.00335.541595.301760.78
    CWR304.83282.06944.66331.37
    GMh533.56583.362733.782425.67
    GMv4079.974907.0012107.4112425.41
    Download: Download as CSV

    Table 2.  Results of numerically quantified CWR and its contributors (Unit: 1012 kg, i.e., billion ton) in different calculation periods

    Quantification periodMh1Mh2QhiQhoCvhChvPsCWR
    April1–100.110.065.945.0212.118.674.3813.75
    11–200.060.055.934.9518.776.2113.5611.20
    21–300.050.013.322.657.192.934.945.59
    1–300.110.0115.1812.6238.0717.8122.8730.44
    August1–100.320.674.636.7583.9422.6659.4830.08
    11–200.671.324.474.1172.0521.3550.3226.78
    21–311.330.9812.5912.2995.3826.3371.6939.60
    1–310.320.9821.6923.15251.3670.34181.4994.47
    Download: Download as CSV

    Table 3.  Correlation coefficients (R) of daily Ps with the CWR contributors in April and August 2017 for numerical (NQ) and diagnostic (DQ) quantification results

    MMhQhiCvhCvh ChvMMvQviQvi Qvo
    AprilRNQ0.620.550.950.970.320.140.14
    RDQ0.370.460.990.990.460.540.13
    AugustRNQ0.710.440.900.900.330.590.54
    RDQ0.630.530.990.990.300.750.69
    Download: Download as CSV

    Table 4.  Correlation coefficients (R) of diagnosed CWR contributors over each 1° grid with Ps in April and August 2017

    PeriodMMhQhiCvhMMvQvi
    April1-day0.280.390.980.360.35
    5-day0.300.530.980.460.57
    10-day0.220.580.980.520.69
    1-month0.220.580.980.520.69
    August1-day0.490.510.990.280.41
    5-day0.460.490.990.300.48
    10-day0.510.520.990.390.54
    1-month0.530.640.990.540.62
    Download: Download as CSV
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Quantifying the Cloud Water Resource: Basic Concepts and Characteristics

    Corresponding author: Yuquan ZHOU, zhouyq@cma.gov.cn
  • 1. CMA Key Laboratory for Cloud Physics, Chinese Academy of Meteorological Sciences, China Meteorological Administration (CMA), Beijing 100081
  • 2. State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, CMA, Beijing 100081
  • 3. School of Physics, Peking University, Beijing 100871
Funds: Supported by the National Key Research and Development Program of China (2016YFA0601701) and National High Technology Research and Development Program of China (2012AA120902)

Abstract: The water in the air is composed of water vapor and hydrometeors, which are inseparable in the global atmosphere. Precipitation basically comes from hydrometeors instead of directly from water vapor, but hydrometeors are rarely focused on in previous studies. When assessing the maximum potential precipitation, it is necessary to quantify the total amount of hydrometeors present in the air within an area for a certain period of time. Those hydrometeors that have not participated in precipitation formation in the surface, suspending in the atmosphere to be exploited, are defined as the cloud water resource (CWR). Based on the water budget equations, we defined 16 terms (including 12 independent ones) respectively related to the hydrometeors, water vapor, and total water substance in the atmosphere, and 12 characteristic variables related to precipitation and CWR such as precipitation efficiency (PE) and renewal time (RT). Correspondingly, the CWR contributors are grouped into state terms, advection terms, and source/sink terms. Two methods are developed to quantify the CWR (details of which are presented in Part 2 of this study) by use of satellite observations, atmospheric reanalysis data, precipitation products, and cloud resolving models. The CWR and its contributing terms over North China in April and August 2017 are thus derived. The results show that CWR has the same order of magnitude as surface precipitation (Ps). The hydrometers converted from water vapor (Cvh) during the condensation process is the primary source of precipitation. It is highly correlated with Ps, and contributes the most to the CWR. The state variables and advection terms of hydrometeors are two orders of magnitude lower than the corresponding terms of water vapor. The atmospheric hydrometeors can lead to higher PE than water vapor (several tens of percent versus a few percent), with a shorter RT (only a few hours versus several days). For daily CWR, the state terms are important, but for monthly and longer-time mean CWR, the source/sink terms (i.e., cloud microphysical processes) contribute the largest; meanwhile, the advection terms contribute less for larger study areas.

1.   Introduction
  • Water cycle is one of the important cycles of the substances in the world. It also acts as a cycle of the phase and energy in the earth system (Baumgartner and Reichel, 1975). As the only source of clean water indispensable for human survival, the water in the atmosphere has always been highly valued by atmospheric and hydrological scientists. Atmospheric water includes water vapor and hydrometeors (also termed as cloud water in both liquid and solid phases). The formation and distribution of hydrometeors are jointly affected by dynamic and thermodynamic processes in the atmosphere, playing an important role in the global water cycle (Ramanathan et al., 1989).

    Atmospheric water continuously changes in the air, in the form of quantity and phase. As a phase cycle, the requirement for phase closure must be met in this process. The water cycle originates from ground evaporation. Surface water (in solid and liquid phases) undergoes the first phase change through evaporation, forming water vapor and entering the atmosphere. The water vapor in the atmosphere is horizontally transported and vertically lifted due to various dynamic processes of the atmosphere. After reaching saturation, a second phase change occurs when the water vapor condenses to form high concentrations (107–108 m−3) of hydrometeors (cloud droplets or ice crystals, about 1–100 μm in diameter) (Scorer, 1972); these cloud droplets grow through complicated cloud microphysical processes to form large-size particles (approximately 102–103 μm in diameter) with low concentrations (102–103 m−3) such as rain, snow, and graupel. The particles finally fall out of the clouds and form ground precipitation (Mason, 1971; Pruppacher and Klett, 1978), completing the water cycle with a closed phase cycle. This process is always accompanied by the absorption and release of latent heat during the phase changes. The evaporation of surface water absorbs latent heat, which is equivalent in magnitude to the surface sensible heat. In the condensation process when water vapor turns into cloud water, latent heat is released and subsequently affects the atmospheric circulation (Bengtsson, 2010).

    To estimate the maximum potential precipitation over a specific region and period, it is not enough to only examine the water vapor and its convergence in the atmosphere. This is because water vapor cannot directly become precipitation, and only the water substance that has experienced the second phase change and turned into liquid/solid phase may form rainfall. Thus, it is the hydrometeors that can be further examined and exploited. Although the global cloud water content is no more than 1% of that of water vapor, the time needed from cloud formation to precipitation occurrence takes less than 2 h (Zhang, 2002), indicating a very fast moisture cycle in clouds. Therefore, the study of hydrometeors should be strengthened for better understanding of the water substance change in the atmosphere. Those hydrometeors that have not participated in precipitation formation in the surface, suspending in the atmosphere to be exploited to maximize possible precipitation in the atmosphere, are defined as the cloud water resource (CWR).

    The shortage in fresh water resources is a global problem, which is particularly serious in China, where the per capita share is less than a quarter of the world average. In the vast arid and semi-arid areas of West and North China, the lack of fresh water resources has seriously hindered the local socioeconomic development. Precipitation, produced by the atmospheric water cycle, is the main source of river runoff and shallow underground freshwater that can be directly used by humans. The idea to obtain more water resources from the atmosphere has a long history. Since the 1940s, countries around the world have continued to conduct rainfall enhancement experiments and various projects have been implemented, which, to a certain degree, have alleviated drought conditions on the local to regional scale. The World Meteorological Organization (WMO) proposed that weather modification should be part of an integrated water resources management strategy (Zheng and Guo, 2012). The effect of weather modification is to change the cloud microphysical processes, improve the conversion efficiency of cloud to precipitation, and eventually increase local rainfall. The research on atmospheric hydrometeors (cloud water) is essential for precipitation forecast, climate change research, and weather modification.

    Note that cloud formation and distribution are spatially and temporally discontinuous, which is different to that of other variables (such as temperature, humidity, wind, and so on). This feature makes it hard to observe clouds and obtain relevant cloud properties. Although various observational technologies have been developed, it is still difficult to obtain complete and continuous cloud observations due to the complicated structure of clouds. Satellite remote sensing is the major approach to obtaining amount and macro-structure of large-scale clouds. At present, several popular satellite products have been widely used globally, including products of the International Satellite Cloud Climatology Project (ISCCP; Rossow and Schiffer, 1991), the NASA Clouds and the Earth’s Radiant Energy System Experiment (CERES; Young et al., 1997; Zhang et al., 2012), and the Moderate Resolution Imaging Spectroradiometer (MODIS; Ackerman et al., 2008; Wang et al., 2011). Cloud products include two-dimensional cloud amount, cloud liquid water path, and so on. CloudSat can detect clouds, provide retrievals of cloud type and cloud water content along the orbit (Stephens et al., 2008; Zhou and Zhao, 2008). Vertical distributions of cloud structure and cloud water content can also be obtained. However, CloudSat has a narrow scanning trajectory with adjacent orbits spaced about 2.5° apart. It crosses the equator at exactly the same geographic longitude once every 16 days. The observation by aircraft through clouds is the most straightforward method, but can only obtain macro and micro information of clouds along the flight track during the observed period (Hobbs et al., 1980; Wang et al., 2015). Some ground-based remote sensing instruments including cloud radar, laser ceilometer, and microwave radiometer can be used to retrieve continuous observations of cloud structure, cloud base height, and cloud liquid water path at specific locations (Clothiaux et al., 2000; Xi et al., 2010; Zhao et al., 2012). As a whole, to obtain three-dimensional, high-spatiotemporal-resolution distributions of clouds is extremely difficult based on these observations.

    Although many studies in China have discussed the cloud water resource (CWR), most of them termed satellite retrievals of cloud water path (CWP) as local CWR. Spatiotemporal distributions of clouds and their seasonal to interannual variations, as well as the relationship between clouds and precipitation at various places of China are statistically analyzed based on the CWP products (Chen et al., 2005; Zhou et al., 2005; Zhang et al., 2006; Li et al., 2008; Peng et al., 2010; Li et al., 2015). However, CWP is a state variable that can be observed only at specific time. It is not sufficient for CWR study without considering the evolution, renewal, and supplement of hydrometeors.

    In summary, studies on the characteristics of hydrometeors in the atmosphere are not sufficient due to difficulties in three-dimensional observations and inaccurate simulations of cloud microphysical processes. From the perspective of artificial precipitation enhancement, methods to characterize and quantify the CWR for better use of water in a certain area are far less than enough. In many regions in the world threatened by water shortages, how to make full use of the CWR to increase local precipitation is an urgent social demand. Therefore, it is crucial to provide the definition and quantification method of the CWR.

    This paper focuses on atmospheric hydrometeors and the CWR. Based on the atmospheric water budget and balance, the definitions and calculation algorithms for various components and characteristic variables of the CWR in any given area for a given time period are proposed. Two sets of the CWR quantification methods are developed and applied to a CWR analysis in April and August 2017 over North China. Based on the quantification results, relevant characteristics of the CWR are revealed.

2.   Concept, definition, and algorithms for CWR
  • In the atmosphere, hydrometeors and water vapor are intimately related. Hydrometeors refer to any water or ice particles that form in the atmosphere as a result of condensation or desublimation of water vapor. Some well-known hydrometeors are clouds (cloud liquid water and cloud ice), fog, rain, snow, hail, graupel, dew, rime, glaze, blowing snow, and blowing spray. In this paper, hydrometeors mainly refer to the cloud water (liquid and solid); other types of hydrometeors are not considered. Water vapor turns into hydrometeors when its phase is changed from gaseous to liquid or solid, during which the mass of water is conserved. Based on the atmospheric water substance budget and water mass conservation (Trenberth and Guilemot, 1995), we hereby propose the concepts, definitions, and calculation formulas for the CWR and its components/contributors as well as associated characteristic variables.

    For any region over any period, the budget equation of atmospheric hydrometeors is expressed as:

    $${M_{\rm{h2}}} - {M_{\rm{h1}}} = {Q_{\rm{hi}}} - {Q_{\rm{ho}}} + {C_{\rm{vh}}} - {C_{\rm{hv}}} - {P_{\rm s}}.$$ (1)

    Here, Mh1 and Mh2 are mass of atmospheric hydrometeors at time moments t1 and t2. They are instantaneous/state quantities that can be observed at a specific moment, with the same physical meaning as CWP (comparable after unit being transformed into column water depth). The advection items, Qhi and Qho, are influx and outflux of atmospheric hydrometeors along the boundaries of the study area. For a specific region and period, advection along an individual boundary at various time moments and vertical levels can be positive or negative, representing influx and outflux of hydrometeors, respectively. The sum of the positive and negative advection are the accumulative Qhi and Qho during the study period. Cvh are the mass of hydrometeors converted from water vapor through condensation or desublimation, while Chv are the mass content of water vapor converted from hydrometeors through evaporation or sublimation. Ps is the surface precipitation. Cvh, Chv, and Ps are the source/sink terms; they accumulate with extension of the study time and expansion of the study area.

    Sorting the positive and negative terms in Eq. (1) separately, the equation can be rewritten as:

    $${M_{\rm{h1}}} + {Q_{\rm{hi}}} + {C_{\rm{vh}}} = {M_{\rm{h2}}} + {Q_{\rm{ho}}} + {C_{\rm{hv}}} + {P_{\rm s}} = {\rm G{M_h}}.$$ (2)

    Here, we define GMh as the gross mass of atmosphe-ric hydrometeors, representing the total amount of hydrometeors over the time period t2t1 within the study region. From Eq. (2), it is inferred that GMh also equals half of the sum of the 7 terms on the left- and right-hand sides of the equation,

    As for water vapor, a similar equation is derived as follows:

    $${M_{\rm{v1}}} + {Q_{\rm{vi}}} + {C_{\rm{hv}}} + {E_{\rm s}} = {M_{\rm{v2}}} + {Q_{\rm{vo}}} + {C_{\rm {vh}}} = {\rm G{M_v}},$$ (3)

    where Es, the source item, is the surface evaporation, and GMv is the gross mass of atmospheric water vapor.

    The surface precipitation Ps is absent in Eq. (3), suggesting that water vapor is not directly associated with precipitation. The terms Cvh and Chv in Eq. (3) represent the phase changes between water vapor and hydrometeors. It is the hydrometeors produced by water vapor through condensation that are directly linked to precipitation, and the relationship is quantified in Eq. (1).

    By adding Eqs. (2) and (3), the terms of mass conversion between water vapor and hydrometeors offset each other, and the balance equation for the atmospheric water substance, which is the summation of water vapor and hydrometeors, is obtained as follows:

    $${M_{\rm{w1}}} + {Q_{\rm{wi}}} + {E_{\rm s}} = {M_{\rm{w2}}} + {Q_{\rm{wo}}} + {P_{\rm s}} = {\rm G{M_w}},$$ (4)

    where GMw is the gross mass of water substance in the atmosphere.

    Equations (2)–(4) are collectively called the atmospheric water balance equations, in which the values of the 12 independent items are positive with a unified unit of kg. Their values are determined by the size of the study area and by the length of the study period. These items/terms can also be converted into column water per unit area (kg m–2, is equivalent to mm of water depth) for comparative analysis.

  • For a specific region during a certain period of time, among all the atmospheric hydrometeors, those that have participated in the water cycle, yet have not formed precipitation, and remain in the air, are targeted for investigation in this paper, with the mass concentration of these hydrometeors defined as the quantified CWR. According to Eq. (2), the CWR is written as:

    $$\begin{split} {\rm CWR} =& \,\,\,{\rm G{M_h}} - {P_{\rm s}} \\ =& \,\,\,{M_{\rm {h1}}} + {Q_{\rm {hi}}} + {C_{\rm {vh}}} - {P_{\rm s}} \\ =& \,\,\,{{M_\rm {h2}}} + {Q_{\rm {ho}}} + {C_{\rm {hv}}}. \\ \end{split} $$ (5)

    In Eq. (5), Mh1 and Mh2 are important instantaneous/state terms for cloud water resources. For other non-renewable resources on the earth, such as minerals, these terms become the only source of origin, meaning that the more used, the less remains; in this case, the change of the state terms (Mh2 Mh1) is always negative (Mh2 <Mh1). However, the atmospheric hydrometeors are constantly replenished and renewed, so the changes of the state terms can also be positive (Mh2 > Mh1).

    Different from other contributors of CWR, the state terms do not accumulate over time; it becomes less important for long-term (e.g., monthly, yearly, etc.) CWR estimation. Previous studies largely focused on the state quantity/term of cloud water (Chen et al., 2005; Li et al., 2008; Peng et al., 2010). Although termed as CWR, it is actually only a small part of the CWR, because the two important terms—influx (Qhi) and condensation (Cvh), are ignored. In fact, the influx of hydrometeors and local condensation of cloud water contribute significantly to the CWR.

  • Precipitation efficiency (PE) is the ratio of surface precipitation to all available atmospheric water substance. It is a metric for measuring how much atmospheric water substance can be converted into real precipitation received at the ground surface. PE has significant implications for precipitation analysis and weather modification. Hobbs et al. (1980) (hereafter Hb80) defined PE as the ratio of total ground precipitation rate to total condensation rate in a rainbelt. Similar to Hb80, Sui et al. (2005) defined the ratio of the ground precipitation rate to the sum of water vapor condensation rate and water vapor deposition/desublimation rate as cloud microphysical precipitation efficiency (CMPE). Sui et al. (2007; hereafter Su07) further improved the definition of CMPE by treating the denominator as the sum of water vapor condensation rate, water vapor desublimation rate, and local hydrometeors loss and convergence. To ensure that CMPE is within a reasonable range of 0–100%, the hydrometeors loss and convergence terms are considered only when they are positive, otherwise they are treated as zero.

    In the present study, PEh is defined as the ratio of total ground precipitation to the gross mass of hydrometeors, expressed by:

    $${\rm{P}}{{\rm{E}}_{\rm{h}}} = {P_{\rm{s}}}/{\rm{G}}{{\rm{M}}_{\rm{h}}}.$$ (6)

    Here, PEh reflects the efficiency of cloud microphysical processes in transforming small cloud droplets into precipitable particles. It can be applied over any time period and region, and the value is between 0 and 1. Compared to the definition of Hb80, PEh calculated by Eq. (6) is more reasonable since it considers the initial state quantity/term and influx of hydrometeors, in addition to condensation and desublimation, in the denominator. Compared to Su07, additional consideration of the initial state term and the influx of hydrometeors is physically more rational than only considering the positive convergence and local change of hydrometeors. For a long-term and large-scale precipitation process, the initial value and the influx of hydrometeors become smaller than the cloud condensation term, thus the results from the three definition [Hb80, Su07, and Eq. (6) of this study] are relatively close to each other.

    Similarly, precipitation efficiency of water vapor (PEv) and that of atmospheric water substance (PEw) are calculated by:

    $$\hspace{62pt} {\rm{P}}{{\rm{E}}_{\rm{v}}} = {P_{\rm{s}}}/{\rm{G}}{{\rm{M}}_{\rm{v}}},$$ (7)
    $$\hspace{62pt} {\rm{P}}{{\rm{E}}_{\rm{w}}} = {P_{\rm{s}}}/{\rm{G}}{{\rm{M}}_{\rm{w}}}.$$ (8)

    Furthermore, when water vapor in the atmosphere undergoes phase transformation to form liquid or solid water particles through condensation or desublimation, the ratio of the condensed water particles to the total water vapor is termed as condensation efficiency of water vapor (CEv), which is calculated by:

    $${\rm{C}}{{\rm{E}}_{\rm{v}}} = {C_{{\rm{vh}}}}/{\rm{G}}{{\rm{M}}_{\rm{v}}}.$$ (9)
  • The mean mass of atmospheric hydrometeors (MMh) is the average mass content of atmospheric hydrometeors over the study period within the study region, expressed by:

    $${\rm M{M_h}} = \frac{1}{N}\sum\limits_{i = 1}^{N} {{M_{\rm h}}_i} .$$ (10)

    where Mhi is the mass of atmospheric hydrometeors at time moments ti and N is the number of observed Mh at a specific station or grid within the studied period of time.

    In the atmosphere, clouds scatter discontinuously and are constantly changing. Thus, the mass concentration of hydrometeors (Mh) may vary greatly with time and space. For long-term CWR investigations, MMh becomes a more suitable physical variable.

    The atmospheric water substance (i.e., water vapor and hydrometeors) experiences phase changes and spatiotemporal variations constantly. The time needed for the phase changes is an important metric that reflects combined effects of the environmental dynamics and physical mechanisms. We hereby define it as hydrometeor renewal time (RTh) to depict the cycle and transition features of hydrometeors over the study time and in the study area, which is calculated by:

    $${\rm{R}}{{\rm{T}}_{\rm{h}}} = {\rm{M}}{{\rm{M}}_{\rm{h}}}/({P_{\rm{s}}}/T).$$ (11)

    where Ps/T is the mean precipitation intensity/rate. The unit of RTh is the same as the unit of the study period T. That is, if the unit of T is day or h or second, the unit of RTh varies correspondingly.

    Similarly, the mean mass of water vapor (MMv) and renewal time of water vapor (RTv) are calculated by

    $$ \hspace{62pt} {\rm M{M_v}} = \frac{1}{N}\sum\limits_{i = 1}^{N} {{M_{\rm v}}_i},$$ (12)
    $$ \hspace{62pt} {\rm{R}}{{\rm{T}}_{\rm{v}}} = {\rm{M}}{{\rm{M}}_{\rm{v}}}/({P_{\rm{s}}}/T).$$ (13)

    Together with GMh, GMv, and GMw, the variables defined in this section represent the characteristics of the CWR in a specific region over a certain time period.

  • The CWR cannot be observed directly, but can be quantified through numerical simulations and observation-based diagnostic methods. The cycle and change of the atmospheric water substance is an overall balanced process, in which both atmospheric hydrometeors and water vapor participate. To quantify the CWR in a certain region and time period, it is necessary to consider the three balance equations [Eqs. (2)–(4)] of hydrometeors, water vapor, and atmospheric water substance mentioned above as a whole. On this basis, the state quantities/terms, the advection terms, the sources/sink terms, as well as GMh, GMv, GMw can be derived, and the CWR and its related characteristic variables [Eqs. (5)–(13)] can be quantitatively calculated according to their definitions and algorithms. The input (known) variables to these definitions and algorithms include wind field, water vapor content, cloud water content, cloud condensation and evaporation, surface evaporation, and surface precipitation, which can be obtained either from diagnostic analysis of available observations or from numerical model outputs.

    The diagnostic quantification of CWR based on observations (CWR-DQ) is as follows. We extract water vapor and wind fields from the reanalysis products (e.g., the NCEP/NCAR reanalysis data), and obtain precipitation directly from surface station and/or satellite observations. For the state quantities and advection terms, acquirement of three-dimensional cloud fields (cloud fraction and cloud water content) is difficult, as routine observations of three-dimensional, time-varying cloud fields are not available. We solve the problem as follows. First, satellite observations are used to establish cloud profiles based on atmospheric relative humidity and temperature. Second, NCEP/NCAR reanalysis data are then employed to produce three-dimensional cloud fields such as cloud detection (1 for existence of cloud and 0 for no cloud), cloud water content (i.e., hydrometeors content), as well as the integrated cloud water content (i.e., cloud water path, which is equivalent to the state quantity Mh). Third, the surface evaporation (Es) and the conversion between water vapor and hydrometeors (Cvh and Chv) are derived based on Eqs. (2)–(4). Finally, the CWR and related characteristic variables as well as GMh, GMv, GMw are calculated based on Eqs. (5)–(13).

    The numerical quantification of CWR is based on cloud resolving model outputs (CWR-NQ). There is an assumption that the cloud resolving model is able to describe the cloud microphysical processes completely and precisely, from which four-dimensional distributions of atmospheric water vapor, hydrometeors, and wind fields can be obtained. The data can then be used to quantify the CWR and related terms/quantities, as well as those characteristic variables in any area during the study pe-riod. The CWR-NQ method relies heavily on accurate description of cloud water distribution. It is also challenging to ensure that the model is stable after long-term integration, while the simulated wind, water vapor, cloud, and precipitation must be basically consistent with observations.

    By use of the CWR-DQ method or the CWR-NQ method, the basic balance equations of water substance in the atmosphere can be solved, and the items such as Mx, Qx, Cvh, Chv, and Es can be obtained. Furthermore, the variables including GMx and CWR, PEx and CEv, MMx and RTx, can also be quantitatively derived (x refers to hydrometeors, water vapor, or the total atmospheric water substance). Detailed introduction of the two sets of quantification methods for estimates of CWR and associated applications are presented in the companion paper (Cai et al., 2020).

3.   Features of the CWR in North China
  • Based on the quantification results of CWR conducted in North China for two typical months, i.e., April and August 2017 from Cai et al. (2020), the basic features of CWR is analyzed in this section. April is within the spring season when North China is prone to drought with a large demand of agricultural water storage. Spring is the main season for stratiform precipitation enhancement by cloud seeding. August is within the summer flood season when the largest precipitation in North China occurs. The study region for both methods covers 34°–44°N, 108°–121°E, the area size of which is about 1.34 × 1012 km2. The CWR-DQ method is applied over 13 × 10 grids with a horizontal resolution of 1°, while the CWR-NQ method is applied at a 3-km resolution.

  • The monthly quantification results of CWR and related variables over North China in April and August 2017 are listed in Table 1. For both numerical calculations and diagnostic calculations in the two months, the average state quantities and advection terms for hydrometeors are one order smaller in magnitude than the corresponding quantities of water vapor. The values of the four source/sink items, including Ps, are in the same order of magnitude. Therefore, GMh is also one order of magnitude lower than GMv. Except for Chv estimated by the diagnostic method, the value of each physical quantity in August 2017 is higher than that of April 2017. That is, in summer, the contents of cloud water and water vapor in the atmosphere in North China are higher, with more advection and more intense conversion of water vapor to hydrometeors, resulting in more abundant surface precipitation, compared with the situations in Spring.

    VariablesApril 2017 August 2017
    CWR-NQCWR-DQCWR-NQCWR-DQ
    MMh2.194.333.107.41
    MMv82.61150.46430.19478.34
    Qhi151.79220.44216.92253.83
    Qho126.16180.44231.46263.69
    Qvi3545.304403.109393.0910037.83
    Qvo3512.934362.069266.059933.74
    Cvh380.71362.112513.622164.60
    Chv178.1499.21703.4358.71
    Ps228.73301.301814.932094.30
    Es237.00335.541595.301760.78
    CWR304.83282.06944.66331.37
    GMh533.56583.362733.782425.67
    GMv4079.974907.0012107.4112425.41

    Table 1.  The CWR and related variables (unit: 1011 kg; equivalent to 0.77 mm for the study region) quantified by the CWR-NQ and CWR-DQ methods over North China (with an area size of 1.34 × 1012 km2) in April and August 2017

    According to Table 1, the importance of hydrometeors related quantities and water vapor related variables to the monthly regional CWR calculation can be seen. Take the numerical results as examples. The state quantity MMh is the smallest among the CWR contributors, with its values two orders of magnitude lower than others. The CWR in April and August are about 30.48 and 94.47 billion ton, respectively, equivalent to water depths of 22.7 and 70.5 mm in the study region. Only approximately 1% of CWR is from MMh. Among the source/sink terms, Cvh has the largest value, Ps is slightly smaller than Cvh, followed by Chv. For the advection terms, the values of Qhi and Qho are close, but both are smaller than Chv. To sum up, the contributions of the above five contributors to the CWR in descending order are as follows: Cvh, Ps, Chv, Qhi, and Qho. Their percentage contributions are 125.06%, 75.14%, 58.52%, 49.86%, and 41.44% in April, and the values are 266.19%, 192.13%, 74.46%, 22.96%, and 24.5% in August. As Ps is a negative term in Eq. (5) for calculation of CWR, the contributions of Cvh and Ps to CWR could be greater than 100%.

    For the diagnostic results, MMh is still the smallest quantity with less than 1% contribution to regional CWR. Among the other five contributors, Cvh is the largest, followed by Ps, and Qhi and Qho. These features are similar to the numerical quantification results. However, due to the underestimation of Chv by the diagnostic method, Chv contributes less to the CWR. The contributions of Cvh, Ps, Qhi, Qho, and Chv to CWR are descending in order. For example, their contributions to CWR in April 2017 are 128.2%, 106.45%, 77.96%, 63.81%, and 35.08%, respectively.

    As for the quantities related to water vapor, the advection terms Qvi and Qvo have the largest values, one order of magnitude higher than the sink/source terms, among which Ps is between Cvh and Chv. The state quantity MMv, remains the smallest. Different from GMh and CWR, the advection terms make greater contribution to GMv. For instance, in April 2017, the numerical quantified Qvi and Qvo account for 91.18% and 89.75% of GMv, respectively.

  • Theoretically, since the integral dimensions of the CWR contributors are different, they cannot be accumulated temporally or spatially. The state quantities (Mx) are volume integrated. As the study period extends, only Mx2 changes, resulting in a decreasing importance of state quantities with extension of time. The advection terms (Qx) are integrals along the boundaries of the study region, which increase with time. However, as the study region expands, the advection within the area offset and only those along the boundaries reserve, leading to a decreasing importance with expansion of the area. The sink and source terms are accumulative, which increase with both time and space. In this section, we analyze the quantification results over different time periods and various areas in North China by the numerical and diagnostic methods to probe the impact of time and space scales on the CWR calculation.

  • Table 2 presents the numerical calculation results of the CWR and its contributors in various 10-day periods of April and August 2017. The state variables (Mh1 and Mh2) change with the chosen time period. For each 10-day period in April and August 2017, the values of the state terms at the initial and final time moments are different. Note that Mh2 of the first (second) period is actually the Mh1 of the second (third) period. When the quantification results of the first period are compared with the entire month, Mh1 remains unchanged and Mh2 becomes Mh at the end of the month. As a consequence, Mh cannot be accumulated with time.

    Quantification periodMh1Mh2QhiQhoCvhChvPsCWR
    April1–100.110.065.945.0212.118.674.3813.75
    11–200.060.055.934.9518.776.2113.5611.20
    21–300.050.013.322.657.192.934.945.59
    1–300.110.0115.1812.6238.0717.8122.8730.44
    August1–100.320.674.636.7583.9422.6659.4830.08
    11–200.671.324.474.1172.0521.3550.3226.78
    21–311.330.9812.5912.2995.3826.3371.6939.60
    1–310.320.9821.6923.15251.3670.34181.4994.47

    Table 2.  Results of numerically quantified CWR and its contributors (Unit: 1012 kg, i.e., billion ton) in different calculation periods

    Both the advection terms (Qhi and Qho) and the source/sink terms (Cvh, Chv, and Ps) can be accumulated over time; that is, the 10-day quantification result is the accumulation of daily quantification value during the 10-day period, and the monthly quantification result is the accumulation of all daily quantification in this month or all 10-day quantification during the month. Taking Chv as an example: it is 17.81 billion ton during 1–30 April, which is equal to the sum of quantification results of the three 10-day periods in April (8.67 + 6.21 + 2.93 = 17.81 billion ton).

    Since the state quantities cannot be accumulated with time, the CWR cannot be accumulated with time, either. The CWR in April is 30.44 billion ton, which is not equal to the sum of CWR of the three 10-day periods in April (30.55 billion ton). The difference between them is 0.11 billion ton. This is because when the results of indivi-dual 10-day periods are accumulated to calculate the monthly CWR, Mh2 of the first and second 10-day periods are repeatedly counted. As a result, the sum of 10-day CWR values in April is larger than the monthly CWR, and the difference between the two is equal to the sum of Mh2 of the first and second 10-day periods (0.06 + 0.05 = 0.11 billion ton). Similarly, the sum of 10-day CWR values in August is 96.46 billion ton, which is larger than the monthly CWR of August (94.47 billion ton) by 1.99 billion ton. The extra part is the sum of Mh2 in the first and second 10-day periods of August.

    Similarly, GMx (x refers to hydrometeors, water vapor, or atmospheric water substance) cannot be accumulated with time, neither PEx nor RTx can be accumulated with time either.

    For CWR quantification in a short period (such as daily), the percentage of CWR accounted for by the state quantity (Mh) increases significantly, while that accounted for by advection items (Qhi and Qho) decreases. The sink/source terms (Cvh, Chv, and Ps) still contribute the most to CWR. Taking April as an example (Fig. 1), it is found that during the 30 days of April, the contributions to CWR of Cvh, Ps, Chv, Qho, and Mh2 are within the ranges of 5.19%–278.88% (with an average value of 77.64%), 0.11%–240.23% (46.93%), 9.2%–77.81% (40.58%), 1.49%–78.07% (33.11%), and 0.8%–34.88% (16.7%), respectively. Among the CWR contributors, Cvh in rainy days is generally larger than the others.

    Figure 1.  Daily variations of numerical quantification results of the CWR contributing terms (unit: 1012 kg, i.e., billion ton) in North China in April 2017. (a) Mh1, Cvh, and Qhi, and (b) Mh2, Chv, Ps, and Qho.

    For the daily CWR quantification, the contribution of the state items cannot be ignored. With the extension of the calculation period, the importance of the state terms gradually decreases, while that of advection and source/sink terms gradually increases. Similar features can be found for water vapor and atmospheric water substance. However, for the quantification of a large area, despite the varying calculation period, the value of Cvh remains higher than that of other CWR contributors, i.e., Cvh makes the most important contribution to CWR. Therefore, the CWR in a large area mainly depend on cloud physical processes, followed by advection along the boundary.

  • Figure 2 presents the diagnostic results on the 1° x 1°grids in North China in April 2017. Comparing the grid results with the overall regional quantification results, the impact of spatial scale on CWR can be revealed. To facilitate comparison, the calculation results have been converted into the equivalent water depth per unit area (unit: mm).

    Figure 2.  Spatial distributions of (a) MMh, (b) Qhi, (c) Cvh, (d) Ps, (e) GMh, and (f) CWR in North China for April 2017 (unit: mm). The thick black curves denote the provincial boundaries and the red curve denotes the Yellow River.

    For the quantification results on 1° grids, Mh is the smallest contributor to CWR, with a value below 0.45 mm. The magnitude and spatial distribution of Cvh are consistent with those of Ps, with the maximum value of about 65 mm. Qhi has the largest value, three times higher than the source/sink terms, and can exceed 210 mm. Therefore, the grid values of GMh and CWR are mainly affected by Qhi, and their spatial distributions are also similar to Qhi. This feature is quite different from the quantification results of the whole region, which is characterized by more contribution to CWR of Cvh than Qhi.

    For the calculation results of North China, Cvh, and Ps are spatially accumulative, being equal to the sum of gridded value within the region. The advection terms (Qhi and Qho) are integrals along the boundary of the study region, those at interior grid points have been completely cancelled out. Consequently, advection terms of large region have a much smaller value than the sum of gridded values. For instance, regional Qhi (22.04 billion ton) through the boundary of North China in April are much smaller than the sum of Qhi (229.76 billion ton) at all grid points inside the area. Therefore, when the evaluation area is larger, the effect of Qhi is weakened. Furthermore, CWR cannot be simply spatially accumulated, either. The regional CWR is much smaller than the sum of CWR at all grids as well, and the difference between them should be equal to the sum of gridded Qho within the area. Similarly, GMx cannot be accumulated with expanded area; consequently, neither PEx nor RTx can accumulate or average with the area.

    In summary, the CWR and its contributors have unique spatial and temporal characteristics, and cannot be simply accumulated with time or area.

  • Precipitation is formed by cloud physical processes. Therefore, Ps should be closely related to cloud physical parameters such as Cvh. According to Fig. 1, there occurred several precipitation processes in April 2017, on 4, 6–8, 13–16, 18–20, and 24–25 April, respectively. For each precipitation event, Qhi increased before the occurrence of precipitation, and Cvh increased accordingly. When Ps reached its maximum, Cvh also reached the maximum, well correlated to Ps. Once the precipitation ended, Cvh decreased rapidly, evaporation prevailed in the atmosphere, leading to smaller Cvh than Chv. Among the CWR contributors, Ps and Cvh have a very good consistency, with a similar evolution curve over time. In this section, we use the daily quantification results to further analyze the relationship between each of the CWR contributors and the precipitation.

    Table 3 lists the correlation coefficient (R) of daily precipitation with CWR contributors in North China from the two methods. The results indicate that Cvh and Cvh Chv produced by cloud microphysics processes have the best correlation with Ps, showing an obvious positive correlation. The correlation coefficient (R) exceeds 0.9 in both months. Mh also has a certain correlation with Ps, and the R between them is higher in August than in April. The correlation between Qhi and Ps are not as obvious as Ps with Cvh or Mh. The reason might be that the state terms and the advection terms change very little in the hydrometeors budget equation, and Ps is mainly determined by Cvh.

    MMhQhiCvhCvh ChvMMvQviQvi Qvo
    AprilRNQ0.620.550.950.970.320.140.14
    RDQ0.370.460.990.990.460.540.13
    AugustRNQ0.710.440.900.900.330.590.54
    RDQ0.630.530.990.990.300.750.69

    Table 3.  Correlation coefficients (R) of daily Ps with the CWR contributors in April and August 2017 for numerical (NQ) and diagnostic (DQ) quantification results

    Table 3 also lists the correlation coefficients between Ps and water vapor related variables commonly used by other studies. For short-term (such as daily) precipitation, the correlation of Mv with Ps is relatively low. The surface precipitation in April is weak, and the correlation between water vapor convergence (Qvi Qvi) with Ps is poor from both quantification methods although the R between the diagnostic Qvi and Ps is 0.54. As the precipitation increases in August, the correlation between the advection terms and precipitation is significantly enhanced, with R of Qvi and Qvi Qvi with Ps exceeding 0.5.

  • Figure 3 displays scatter plots and fitting curves of gridded daily Ps versus Cvh (unit: mm) in the study area for April and August 2017 from diagnostic quantification results. Ps is highly correlated with Cvh with R of 0.98 (April) and 0.99 (August), respectively. The values of Ps and Cvh demonstrate consistent variation characteristics, i.e., the larger the Cvh, the larger the Ps is.

    Figure 3.  Scatter plots and fitting curves of observed daily Ps versus Cvh (unit: mm) at each grid in North China for (a) April and (b) August 2017.

    The correlations between the 1° × 1° gridded Ps and other diagnostic contributors to CWR during different periods such as 1-, 5-, 10-day, and 1-month are further analyzed and the results are listed in Table 4. In general, among the CWR contributors, Cvh has the best correlation with Ps. Regardless the length of the period for quantification, R of Cvh with Ps always exceeds 0.98. The correlations of Ps with the advection terms Qhi and Qvi increase with the extension of the study period. For the one-month quantification, R of the advection terms with Ps is close to 0.7. The state quantities MMh and MMv are poorly correlated to Ps, compared with the other variables.

    PeriodMMhQhiCvhMMvQvi
    April1-day0.280.390.980.360.35
    5-day0.300.530.980.460.57
    10-day0.220.580.980.520.69
    1-month0.220.580.980.520.69
    August1-day0.490.510.990.280.41
    5-day0.460.490.990.300.48
    10-day0.510.520.990.390.54
    1-month0.530.640.990.540.62

    Table 4.  Correlation coefficients (R) of diagnosed CWR contributors over each 1° grid with Ps in April and August 2017

    The above results indicate that during the processes of water substance variation and precipitation formation in the atmosphere, the relationship between hydrometeors and precipitation is quite close. Compared with state quantities and advection transport, the condensation process from water vapor to hydrometeors has more important impacts on the distribution and magnitude of precipitation. Despite the varying size of the study area and varying length of calculation, Ps keeps strongly and positively correlated with Cvh. Consequently, it is not sufficient to study the CWR and precipitation by only investigating on the state quantities and/or advection terms, as the hydrometeors converted from water vapor have played a more significant role.

  • Figure 4 shows the daily evolution of CWR, Ps, GMh, and PEh in April 2017 obtained from the CWR-NQ method. In general, GMh and CWR accumulate prior to rainfall, and decrease after rainfall occurs. The CWR on days without rainfall is generally smaller than that on rainy days. GMh reaches its peak on 16 April, and is larger than that during 7–8 April. However, Ps is also the largest on 16 April, which is significantly larger than that during 7–8 April. Therefore, the CWR during 7–8 April is only a bit larger than that on 16 April. Abundant CWR appears when GMh is very high and PEh (the efficiency of cloud microphysical processes in transforming hydrometeors in the atmosphere into surface precipitation) is low, such as that during 3–10 April (see the two peaks before 12 April 2017). When both GMh and PEh are high, Ps is large and CWR is low, as indicated by the three peaks of the curves in Fig. 4 after 12 April 2017.

    Figure 4.  Daily variations of CWR, Ps, and GMh (unit: 1012 kg, i.e., billion ton), as well as PEh (unit: %) in North China in April 2017.

    The above results indicate that precipitation is mainly produced by the cloud physical process. It is the hydrometeors that are the truly source of Ps. Compared with water vapor, it is more reasonable to use CWR and Cvh formed through cloud microphysical processes to investigate precipitation and its variations. When GMh is large but PEh is small (that is, precipitation formation through natural cloud microphysical processes is not efficient), abundant CWR will remain in the atmosphere. Such understandings are important for improving not only the accuracy of precipitation forecast, but also the effects of weather modification and CWR exploitation.

  • The quantification results in North China show that PEh is much higher than PEv. Taking the numerical quantification result as an example, PEh values in April and August 2017 are 42.87% and 51.65%, while PEv values are only 5.61% and 14.99% respectively. Based on MM5 simulations, Zhou et al. (2010) estimated the PE in a stratiform cloud system that occurred in Henan Province of central China. They found that PEh was about 69.7% and PEv was about 31.1%. Tao et al. (2015) used the CAMS (Chinese Academy of Meteorological Sciences) mesoscale cloud-resolving model to calculate the PE in a stratocumulus precipitation process in Beijing. According to their study, PEh and PEv were about 44.9% and 5.6%, respectively. The previous results are in good agreement with those obtained from the monthly results by the CWR-NQ method in this study. Similar features can also be derived from the monthly diagnostic results, where PEh of North China are 51.65% (April) and 86.34% (August), while PEv are 6.14% (April) and 16.85% (August), respectively.

    It is found that RTh is significantly shorter than RTv. With regard to the diagnostic quantification results, RTh in April and August are 10.34 and 2.56 h, while RTv are 14.98 and 6.92 days respectively. According to Encyclopedia of China (China Encyclopedia General Committee, 1987), RTv is about 8 days, while RTh is about 2 h (Zhang, 2002). Results of the present study are of the same magnitude as those of previous studies.

4.   Discussion
  • According to the definition of CWR, from the perspective of local exploitation (such as through weather modification), if Mh1 and Qhi are uncontrollable, it is necessary to either increase Cvh or reduce Chv, Qhi, and Mh2 to enhance precipitation. At present, weather modification is conducted by seeding catalysts into clouds to promote cloud–precipitation conversion, improve precipitation efficiency, reduce cloud evaporation and hydrometeors outflow, and hence reduce the amount of CWR retained in the atmosphere and increase precipitation eventually. Meanwhile, increased latent heat release from the condensation process would affect dynamic processes in the atmosphere, which may lead to more cloud condensation and eventually realize the better utilization of the CWR.

  • The utilization of CWR should consider the local socioeconomic needs. CWR often exists for a short time period in limited areas. Exploitation of CWR has positive effects such as alleviating agricultural drought, modulating water storage in reservoirs, helping ecological restoration, assisting fire prevention and extinguishment, improving air quality and replenishing groundwater, etc., and thus has great social and economic benefits. On the contrary, inappropriate exploitation of CWR would have negative effects, such as causing geological disasters, especially during flood seasons and heavy rainfall periods. For practical applications, comprehensive investigations on the utilization of CWR and terrestrial water resources should be combined with advanced surveys of the various local socioeconomic needs. The exploitation of CWR should also be closely incorporated with studies of terrestrial hydrology, ecological environment, and disaster prevention and mitigation.

    At present, the technology for CWR exploitation is mainly to spread catalysts into clouds. In order to make the exploitation more effective, cloud seeding must be conducted at the right time in the right place. The technology of cold-cloud seeding is relatively mature and the amount of seeding material is small. Warm cloud has certain potential to be exploited, but the current seeding technique needs to be further developed, especially under the conditions of heavy pollution. Other methods and technologies, such as sound waves and laser, also need further developments.

5.   Conclusions
  • Based on the budget/balance equations of atmosphe-ric water substance (i.e., water vapor and hydrometeors), this study proposes basic concepts and calculation algorithms for the CWR, its contributors, and related characteristic variables. Through analyses of the CWR quantification results for typical months in North China in 2017, the physical characteristics of the CWR are revealed. Main findings and results are summarized as follows.

    (1) The water in the atmosphere is composed of water vapor and hydrometeors (cloud water). Precipitation mainly comes from hydrometeors instead of directly from water vapor. The condensation process in clouds converts water vapor into hydrometeors (Cvh), which has a significant positive correlation with surface precipitation (Ps). The ratio of total surface precipitation to the gross mass of hydrometeors (PEh) is in general several times larger than the ratio of total surface precipitation to the gross mass of water vapor (PEv). With regard to the variations of water substance in the atmosphere, investigations on the hydrometeors and the CWR are more imperative and should be strengthened.

    (2) CWR is defined as those hydrometeors that have participated in the change of water substance in the atmosphere, remain in the air, and have not formed surface precipitation in a specific area over a certain period of time. CWR is composed of state variables (Mh1 and Mh2), advection terms (Qhi and Qho), and the sink/source terms (Cvh, Chv, and Ps), among which Cvh makes the greatest contribution to CWR. For daily CWR quantification, the role of state variables cannot be ignored. As the quantification period expands, the importance of state variables deceases gradually, with their contribution to CWR less than 1% for quantification on the monthly scale. For monthly 1° grid quantification, the advection terms are the largest; however, their importance diminishes as the quantified area expands. For larger-area quantification, the contribution of advection terms to CWR turns smaller than that of sink/source terms. Therefore, the CWR and its contributors and characteristic variables have unique temporal and spatial characteristics.

    (3) During the variations of the water substance in the atmosphere, characteristics of hydrometeors and CWR are significantly different from those of water vapor. The state quantities and the advection items of hydrometeors are one order of magnitude lower than those of water vapor. CWR and Ps are of the same magnitude, and both are one order of magnitude lower than the gross mass of atmospheric water vapor (GMv). The hydrometeors have a much higher precipitation efficiency and much shorter renewal time than those of water vapor. Cvh makes the greatest contribution to the gross mass of atmospheric hydrometeors (GMh) and CWR, while Qvi and Qvh makes larger contribution to GMv.

    In summary, from the perspective of artificial precipitation enhancement, CWR is a more suitable characteris-tic quantity. Since CWR is a climatic variable, the long-term quantification of CWR over China and the world in certain climatic periods needs to be conducted in the future. The temporal and spatial characteristics of CWR will be studied further, as well as its changing trends and impact factors under the global climate change.

    Different from previous studies concentrated on water vapor, this paper emphasizes the role of atmospheric hydrometeors. The results of the present study are important not only to adaptation and mitigation of global climate change and improvement of precipitation forecast, but also to more effective exploitation of the CWR for the purpose of alleviating the increasingly serious water shortage around the world. These results may have broad application potentials in disaster prevention and mitigation, and in studies of terrestrial hydrology, water resources, and ecological environment.

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