Water Balance Models in Environmental Modeling

Water Balance Models in Environmental Modeling Khodayar Abdollahi, Alireza Bazargan, and Gordon McKay

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Environmental Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hydrological Regime and Water Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Water Balance Models and Their Classifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interrelationship Between Energy Balance and Water Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Water Balance Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selected Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . WetSpass Water Balance Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Surface Runoff . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evapotranspiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Recharge and Base-Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Since many complex environmental problems are linked to the hydrologic cycle, a better understanding of water balance can help us take more effective decisions K. Abdollahi Department of Engineering Measures for Nature Development, Faculty of Natural Resources and Earth Sciences, Shahrekord University, Shahrekord City, Iran e-mail: [email protected] A. Bazargan (*) Department of Civil Engineering, K.N. Toosi University of Technology, Tehran, Iran e-mail: [email protected] G. McKay Division of Sustainability, College of Science and Engineering, Hamad Bin Khalifa University, Doha, Qatar e-mail: [email protected] # Springer International Publishing AG 2018 C. M. Hussain (ed.), Handbook of Environmental Materials Management, https://doi.org/10.1007/978-3-319-58538-3_119-1

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for environmental challenges. A model is a tool that artfully combines available observations with our fundamental knowledge to describe the behavior of the system through implementation of scientific methods. Water balance models describe computational aspects of water movement through the water cycle. In environmental problems, our datasets are not complete, however recent advances in water balance modelling provides improved capabilities to conceptualize the hydrological system as an underlying infrastructure for environmental modeling. These developments have coincided with advances in geographic information system and further public availability of remotely sensed data. Recent freely available spatial datasets are considered a fortunate event for environmental modelers. This chapter and the sections herein are designed to outline the current modern view of water balance modelling. In addition to the general concepts about water balance modelling, this chapter explains how water balance models can be used for environmental modelling.

Introduction The hydrological cycle contributes to many environmental dynamic processes such as movement of nutrients, contamination, solute balance, and sediment transport. To study cycles, a system approach is typically used to evaluate the flow of water through the hydrologic system. “Water balance” generally describes tracking the balance between flowing input/output water of any hydrological system. Due to the high degree of complexity of our water systems, they are often broken down into seemingly independent components. As such, rainfall is generally considered as an input to this enclosed system while evapotranspiration is considered as an output component. However, on one hand, the hydrological components in the real world are interconnected; and on the other hand, the global system as a whole is considered as a closed system. Such an assumption typically improves our understanding about the movement of water at a certain space/time scale and assists with water accountability throughout the larger system. Water balance is a science and engineering principle that is applicable for assessing environmental impacts or improving environmental friendliness of a number of water projects including irrigation, municipal water supply, and wastewater systems. Water balance is a powerful tool to study the largest water system (hydrosphere) called the “global water balance” (Table 1). Drainage basins are topographically separated from these hydrological subsystems, which combine into the global system. Earth’s water balance cycle, the largest known closed water system with no starting point, describes the spatial distribution of water on the Earth’s surface and its subsurface. From UNESCO’s estimations, we know that about 96.5% of the global water is stored in oceans (Korzoun and Sokolov 1978). Only a small part of the total water remains as freshwater. Agricultural water use is responsible for over than 70% of the fresh water use, and depending on the country can be as high as 90% or even higher (Hoogeveen et al. 2015; Wisser et al. 2008). Study of the flow of water at global scale shows more than two billion people are living in highly waterstressed regions of the world (Oki and Kanae 2006). The great variability in water

Water Balance Models in Environmental Modeling

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Table 1 UNESCO’s estimation of the global water balance (Korzoun and Sokolov 1978) Item Oceans Fresh groundwater Salty groundwater Soil moisture Polar ice Other ice and snow Fresh lakes Salty lakes Marshes Rivers Biologic water Atmospheric water Total water Fresh water

Area 106 km2 361.3 134.8

Volume 103 km2 1,338,000 10,530

% of total water amount 96.5 0.76

134.8

12,870

0.93

82 16 0.3

16.5 24,024 340.6

0.0012 1.7 0.025

0.05 68.6 1

1.2 0.8 2.7 148.8 510 510

91 85.4 11.5 2.1 1.1 12.9

0.007 0.006 0.0008 0.0002 0.0001 0.001

0.26

510 148.8

1,385,985 35,029

100 2.5

% of fresh water amount 30.1

0.03 0.006 0.003 0.04

100

balance of the land has established the basin as the basic land unit for water resource assessment. The Amazon basin by far is the greatest runoff generator among the major basins of the world (Fig. 1). This chapter covers a short overview of water balance in the atmosphere, surface, soil, and underground. In addition to the general concepts and principles of the water balance, this chapter explains how water balance models can be used for environmental modeling.

Environmental Water The term “environmental water” has developed diverse meanings under different scientific contexts. Among these, the term “ecological water consumption” (evapotranspiration) is the water not consumed by humans in order to keep ecosystems alive. This is a kind of allocated/stored water for environmental protection, conservation of living resources, or any ecological benefits (Sinclair Knight Merz 2006). Degradation of inland ecosystems and wetlands has been a concern for all waterrelated projects. For instance, assessments on Lake Urmia’s water balance in Iran over the past decades illustrate how man-made projects can lead to a great environmental problem (Fig. 2). Human activities, e.g., river diversions, dam construction, expansion of agricultural water usage in addition to climate factors, have had a great impact on the water balance for the lake. Zeinoddini et al. (2015) have warned of pronounced problems in the coming year, if the current situation continues (the

Average discharge(m3/s)

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K. Abdollahi et al. 250 200 150 100 50 0

Fig. 1 Long-term averaged daily discharge at the outlet of the world’s major river basins (Shiklomanov 1998)

good news is that after the issue has come to the forefront of environmental concerns in Iran, steps in the right direction have been taken in recent years). We have learnt from the Lake Urmia example that the water, which naturally flows through the lake, is either now becoming an evapotranspiration compartment or is being stored in man-made reservoirs. “Environmental water” implies that before making any change in water balance components, one should consider a share of water for riparian vegetation cover, wetlands, plants, wild animals, and other environmental assets. Smakhtin (2004) developed the Water Stress Indicator (WSI) that incorporates environmental water as a major parameter in freshwater availability: WSI ¼

Withdrawals Mean annual runoff þ environmental water requirements

(1)

Asheesh (2007) has introduced another water scarcity index (Wsci) that takes population growth impacts on water balance into account: 0

1

B C α C1 W sci ¼ B @ 100 A 100 β expðλΔtÞðε þ γ þ δÞ þhþb 100 P 100 K

(2)

Where α is fresh water availability; β is population; λ is population growth rate; ε, γ, and δ are annual per capita water demands for domestic, green areas, and irrigation applications, respectively; k is freshwater losses; h is annual evapotranspiration; b is environmental water requirements; and p is the industrial water demand.


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Fig. 2 Lake Urmia (Iran) is drying up due to the changes made by humans and impacts of climate change (Image sources: Landsat data visualized by Pengra 2012)

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Hydrological Regime and Water Balance In general, the term regime refers to any system of control. In water science, regime refers to a particular state where a physical phenomenon or boundary condition is significant, such as “the steady state regime.” In the case of basin scale modeling, most often we refer to a complex system in which the details of dominant processes are not completely known; however, the behavior of the system is largely controlled by these internal variations (Blöschl et al. 2007). In basin hydrology, regime refers to the temporal patterns of flow. Behavioral analysis of the system generally shows a clear seasonality or periodic variation in properties of the streamflow. There has been great interest in assessing the impacts of human activities and climate change on water balance and hydrological regime (Middelkoop et al. 2001; Porporato et al. 2004; Luu et al. 2010; Thompson et al. 2011). Botter et al. (2013) presented a measurable index for the resilience of streamflow regimes. They showed rivers with low mean discharges have erratic hydrological regimes while a reduced sensitivity to climate change is the typical regime for rivers with higher mean discharge. Adaptation may be the response of habitats to flow regime alteration in terms of timing, magnitude, frequency, and duration of flow that can appear in different modes including change in life history, morphological or behavioral changes (Lytle and Poff 2004). Flow regimes have a significant role in river water quality. Studies have shown that the concentration of a pollutant in large rivers will be lower during high flows conditions than during low flows (Murdoch and Shanley 2006). A rain river has a highly changeable flow regime controlled by the rainfall-runoff processes. Therefore, for a rain river, atmospheric events are more important than source rivers. It is recognized that transport processes are exerting the control on streams with high speeds, while under slow-moving currents biological and physico-chemical processes become predominant (Merritt and Wohl 2002).

Water Balance Models and Their Classifications A model is a tool that artfully combines available observations with our fundamental knowledge to describe the behavior of the system through implementation of scientific methods (Abdollahi 2015). In environmental problems, our datasets are not complete; however, recent advances in different aspects of modeling provide improved capabilities to conceptualize the hydrological system as an underlying infrastructure for environmental modeling. These developments have coincided with advances in geographic information systems and further public availability of remotely sensed data. Recent freely available spatial datasets are considered a fortunate event for environmental modelers. Water balance models describe computational aspects of water movement through the water cycle, thus can indeed be considered as a subgroup of hydrological models. A full water balance model is a conceptual representation of the hydrologic cycle typically used to apply water balance principles at atmospheric, surface, soil water media, and subsurface scales. Different points of view in understanding water


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Fig. 3 The practice of underlying principles for classification of water balance models as a subcategory of hydrological models (Chow et al. 1988)

balance and the complexity of their internal processes have led to the development of a large number of models (Wang and Pullar 2005) (Fig. 3). There exists no comprehensive model suitable for all applications. In some particular scenarios, modification or development of new water balance models would be inevitable. For example, if a model is designed for a special climate, it will be ill-suited elsewhere, unless possibly coupled with another model (Fig. 4).

Interrelationship Between Energy Balance and Water Balance Solar radiation provides energy (latent heat) supply for vaporization. If we neglect the effects of lateral advection, the equation for heat exchange between open water and the atmosphere (Fig. 5) can be written as: Rn ¼ H s þ m v þ G

(3)

Where Rn is incoming net radiation flux, Hs is sensible heat into the atmosphere, mv is vapor flow rate, and G is heat conducted to ground. Assuming a constant temperature in a control volume and relating exchanged heat to change in internal energy of evaporated water (E), we have: dH ¼ E K lv ρw A dt

(4)

Where dH dt is heat change over the time (Klvmv), ρw is water density, A is the cross-sectional area of the control volume. Combining Eqs. 3 and 4 gives: E¼

Rn Hs G K lv ρw A

(5)

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Fig. 4 A framework for application of water balance models from the developers’ versus users’ perspectives (Abdollahi 2015)

Fig. 5 The energy balance for a water body control volume

Hs

Rn

. mv = r w AE

ra

rw

E=–

dh dt

h

G The sum of evaporation and transpiration (evaporation through plants) is called evpotranspiration. Land surface characteristics and water availability significantly affects real evpotranspiration. Evapotranspiration (ET) accounts for the loss of water in several forms (Fig. 6), including interception (ETint), ET from bare soil (ETbSoil), ET from open water (ETow), transpiration (ETveg), ET from impervious areas (ETimp), ET from unsaturated zones (ETunst), and groundwater ET (ETgw): ET ¼ ET int þ ET bSoil þ ET ow þ ET veg þ ET imp þ ET unst þ ET gw

(6)

A wide range of methods have been used to estimate the ET. Interested readers are encouraged to refer to Szilagyi (2013) for more information about quantifying the ET component in water balance models.


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Fig. 6 The energy balance for a water body control volume

Water Balance Components Due to high complexity of hydrological systems, a single general-purpose water balance model, which involves all processes, does not exist (Table 2). Dividing the large hydrological system into a number of important constituent components facilitates the modeling process. In recent years, finding the most important components is becoming a new focus in water science (Kneis 2015). Another advantage of breaking down larger systems into smaller parts is gaining a better insight into the components. Base-flow separation is an example in which the total flow is divided into its various components (channel storage, runoff, interflow, and base-flow). Annual analysis of hydrographs may identify the type of streams in terms of being ephemeral, intermittent, or perennial (Balek 1989). An important point regarding component-based analysis in water balance models is the definition for each compartment. The base-flow component, for instance, in some modeling frameworks may be comprised of both inter-flow and base-flow. Sometimes this occurs as a result of structural simplifications, while other times it is just terminology. One modeler might consider interception as a part of evapotranspiration, another one might consider it as a separate water balance component (Abdollahi 2015). Description of the components of a distributed water balance is given in the next section.

Selected Model Several water balance models have been developed in response to the given problems (e.g.,SWAT (Arnold et al. 2000), DREAM (Manfreda et al. 2005), WetSpa (Wang et al. 1996), etc.). One of them is the WetSpass model. Since WetSpass-M is a distributed model, the basin is divided into a grid of cells. Based on land cover heterogeneity, each cell itself is composed of four fractions comprising the

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Table 2 Common processes involving different types of water balance models Type of model process Precipitation Interception ET Runoff Infiltration Soil moisture Run-on Inter-flow Base-flow Recharge GW head Sewer Water uptake Storage Snowmelt Water vapor

Atmospheric water balance + +

Surface water balance + + + + +

Soil water balance + + + + + +

Groundwater balance + + + + +

vegetated, bare soil, open-water, and impervious areas. The total water balance of a given cell is calculated as the summation of the water balance of each fraction (Fig. 7).

WetSpass Water Balance Components WetSpass (Water and Energy Transfer between Soil, Plants and Atmosphere under quasi-Steady State) is a distributed model that performs the water balance computation at a raster cell level. The previous version of this GIS based model had the ability to simulate spatially distributed recharge, surface runoff, and evapotranspiration for seasonally averaged input (Batelaan et al. 1996). The set of validated parameters has been used successfully for water balance simulation for temperate regions of Europe. It has been used to estimate recharge for arid regions such as Ethiopia as well. Abdollahi et al. (2017) presented a modified methodology to downscale the model (WetSpass-M) from a seasonal temporal resolution to a monthly scale by modifying the water balance components to be on a monthly scale. In several ways, the new methodology is an attempt to extend the scope of the model for a wider application. New features like base-flow, snowmelt, and dynamic leaf area index have been included in this development.


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Fig. 7 Water balance formulation in a single cell with nonhomogenous land-cover (Batelaan and De Smedt 2001, 2007; Ampe et al. 2012)

Interception WetSpass-M applies a LAI-based monthly interception equation (Table 3) to estimate the monthly interception ratio (IR) (De Groen and Savenije 2006). Interception WetSpass-M limits the available water for surface runoff. The model assumes a threshold value ID as the minimum daily threshold so that if the rainfall is less than this amount, the entire rainfall becomes interception (De Groen 2002).

Surface Runoff To compute monthly surface runoff SRm in [mm/month], the WetSpass-M model applies a rational method with two runoff coefficients (Table 4). The first coefficient (Csr) is an actual runoff coefficient and the second one (Ch) is a coefficient representing soil moisture conditions.

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Table 3 Functions for the calculation of interception Function

Notation LAI: Leaf area index Im: Interception [mm/month] a model parameter Pm is monthly precipitation [mm/month] dp the number of rainy days per month

IR ¼ 1 exp IPDmdp (7) ID ¼ a LAI 1 Pm ½1exp1ð0:463 LAIÞ (8) 1þ

a LAI

Im = PmIR (9) Table 4 Equations for calculating monthly runoff Function Cwp P24 Csr ¼ C P RCDC (11) wp 24 wp þRCD AImp AImp Cwp ¼ 1 100 Cper þ 100 CImp

Cper ¼ w1

0:02 n

þ w2

θW 1θW

(12) S þ w3 10þS

(13) w1 + w2 + w3 = 1 (14) Pm Ch ¼ if ET m > Pm (15) α α 1 LPðPm þET m Þα

Ch ¼ 1 if ET m Pm Q(t) = xQ(t 1) + 0.001(1 x) A SRm (16)

Notation Csr: actual runoff coefficient, Cwp: weighted potential runoff coefficient, RCD: regional consecutive dryness level, AImp: percentage of impervious surface per grid cell, Cper: runoff coefficient for permeable areas, CImp: runoff coefficient of the impervious area, n: Manning’s roughness coefficient, θW: volumetric soil water content, S: land surface slope in percentage, w1, w2, and w3: weights, Ch: coefficient representing soil moisture, α:parameter, Pm:rainfall [mm/month], Q(t): volumetric runoff[m3/month], x: delay factor, Q(t 1) volumetric runoff of previous month[m3/month]:, A:, AImp:, P24 : average daily rainfall in rainy days, ETm: potential evapotranspiration [mm/month], LP: parameter

SRm ¼ Csr Ch ðPm I m Þ

(10)

To perform calculations, the model divides each grid cell into impervious and permeable surfaces fractions. Next, it will obtain a weighted potential runoff coefficient out of their combination. Then, the effect of the depth of rainfall will be taken into account to convert potential runoff to the actual runoff coefficient.

Evapotranspiration To compute grid cell evapotranspiration, WetSpass adds up actual evapotranspiration obtained from impervious surface (ETi), open water (ETO), bare soil (ETs), and the vegetated (ETV) fractions. Actual evapotranspiration is calculated using monthly potential evaporation and vegetation coefficients. To calculate the reference transpiration from the potential evapotranspiration (ETP), a vegetation coefficient is needed: γ 1þ Δ c¼ γ rc 1þ 1þ Δ ra

(17)


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where γ is the psychrometric constant [kPa/ C], rc (bulk) surface resistance [s m1], and ra aerodynamic resistance [s m1] 2 1 Za Zd ra ¼ ln 0:168 U a Za Z0

(18)

where the constant 0.168 is the square of von Karman coefficient (0.41), Ua [m/s] is the wind velocity at elevation Za[m] and Z0 is the aerodynamic roughness height [m], and Zd is zero displacement elevation [m]. Transpiration Trv is calculated as T rv ¼ c ET p

(19)

For vegetated regions where the root zone is above the ground water level, the modified Trv is: T v ¼ 1 a1 w=T rv T rv

(20)

where a1 is a calibrated parameter and w is the available water for transpiration: w ¼ Pm þ θfc θpwp Rd

(21)

where θfcθpwp is the plant available water content per time step and Rd is the rooting depth. The total actual evapotranspiration (ETm [mm/month]) in this model is calculated by: ET m ¼ av ET V þ as ET s þ aO ET O þ ai ET i

(22)

Where aV is the vegetated area fraction; ETV is the evapotranspiration for vegetated area. The bare soil and its evapotranspiration are expressed as aS and ETS, respectively; the open water is referred to with aO and the evapotranspiration for that area is ETO; and ai is the impervious surface and ETi is the evapotranspiration from the impervious surface (Batelaan and De Smedt 2001, 2007).

Recharge and Base-Flow The primary purpose of developing the WetSpass methodology was to simulate long-term average spatial patterns of recharge (Batelaan and De Smedt 2001). In WetSpass-M, monthly recharge (Rm [mm/month]) is calculated as the residual term of the water balance: Rm ¼ Pm SRm ET m The storage parameter (β) relates the previous base-flow (Qb(t base-flow (Qb(t)):

(23) 1))

and current

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QbðtÞ ¼ βQbðt1Þ þ 0:001 N m ð1 βÞ∅Rm

(24)

Where Nm is the number of days per month and ∅ [m2/day] is the contribution parameter to base-flow.

Applications WetSpass has been applied for numerous applications. For example, to analyze the relation between a number of hydrological processes such as distributed land use change for the Grote Nete basin, Belgium (Batelaan et al. 2002, 2003). Applications have also focused on past, present, and future climate scenarios (Mogheir and Ajjur 2013); recharge estimation (Batelaan and De Smedt 2007; Al Kuisi and El-Naga 2013; Melki et al. 2017; Mustafa et al. 2017); or other components of the water balance (Abu-Saleem et al. 2010; Gebreyohannes et al. 2013; Abdollahi et al. 2017).

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