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Vishal K. Mehta Arghyam/Cornell University November 2006 A simple water balance model 2 The water balance 2 Key Features 3 Model Description 3 Notation 4 Equations 5 Model Input 6 Model output 6 The Hydrograph 6 Seasonal Soil Water status 7 Applications and Limitations 8 References 9 AUTHORS Vishal K. Mehta (Arghyam Trust/Cornell University) Dr. M. Todd walter (Cornell University) Dr. Stephen D. DeGloria (Cornell University) A simple water balance modelThe water balanceConstructing a water balance is one of the first tasks in understanding the water regime of a specific area. In simple terms, a water balance is a budgeting exercise that assesses the proportion of rainfall that becomes stream flow (or runoff), evapotranspiration, and drainage (or groundwater recharge). Figure 1 below represents a simple 'box' model representation of a water balance, which could be represented by Equation 1 (Thorntwaite et al, 1955;1957). Eq 1 P = ET + RO + dSW + D; where dSW is the change in soil water over the time step. Figure 1 A conceptual water balance Of these, rainfall and runoff (as stream flow) are directly measured, However to close the water balance, either drainage (or groundwater recharge) or Evapotranspiration (ET) also need to be estimated/measured. Both of these are nontrivial tasks. Water budgeting is frequently accomplished through water balance models, of which there are a vast number. The objectives of this document and following video tutorials are: 1. To introduce the reader to a simple water balance model, namely, the ThorntwaiteMather model, henceforth referred to as the TM model (Thorntwaite et al, 1955;1957; Steenhuis et al, 1986); 2. To provide the reader with the tools to construct a water balance for her/his own region of interest, with the help of video tutorials and a sample Excel spreadsheet that can be downloaded and modified. This document is intended for general instructive purposes for an audience that has some basic knowledge of water resources and associated terminology. No advanced expertise should be needed to understand and use this tutorial. Responsibility for conscientious and socially responsible use of this material rests solely with the reader. ThorntwaiteMather soil water balance model Key FeaturesThe TM model tracks the soil water status through time. It is a lumped model that tracks soil water through time. The entire watershed is treated as one unit (hence ‘lumped’). Is appropriate for modeling at daily, weekly or monthly time steps. A simple spreadsheet (e.g. Excel) model. No specialized software is required. Model DescriptionFigure 2 Conceptual Model Figure 2 above summarizes a simple water balance model. Water is stored in the soil reservoir until the soil water content (SW) exceeds the available water capacity (AWC), at which point the excess goes into storage (S). The monthly streamflow is a simple linear function of S. Determining the soil water budget requires keeping track of the accumulated potential water loss (APWL) and the amount of water in the soil (SW). Watershed Storage and River Discharge: All Excess water, i.e., water above the AWC, goes into watershed storage (S), which inturn, feeds river discharge (Q_{o}) from the watershed. Eq 2 Hydrologists commonly assume that discharge is a constant fraction of watershed storage, especially for groundwater discharge into rivers – this assumption is called the linear reservoir assumption. Eq 3 Where f is the reservoir coefficient and 0 < f < 1. If data are available, f can be empirically determined. NotationAWC = Available Water Capacity [depth] (field capacitywilting point)X(soil depth) SW = Available Soil Water (i.e., above wilting pt.) [depth] APWL = Accumulated Potential Water Loss (negative) [depth] P = Net Precipitation; P  PET [depth] P = Precipitation [depth] PET = Potential Evapotranspiration [depth] AET = Actual Evapotranspiration [depth] 
Situation in the Watershed  SW  APWL  Excess 
Soil is drying    = 0 
Soil is wetting but    = 0 
Soil is wetting above capacity but   = 0  
Soil Water Deficit (AET midNov to May in example 
Soil Water Recharge (from when P>AET until accumulated (AETP) is replenished) : May to August in example 
Soil Water Surplus : Sept to December in example 
Soil Water Utilization (when P 