DWBmodelUN

The R package Modelling aims to implement Dynamic Water Balance model
proposed by Zhang et al. (2008) in a monthly time step. It is a tool for
hydrologic modelling using the Budyko Framework and the Dynamic Water
Balance Model, with DDS Tolson and Shoemaker (2007) algorithm to
calibrate the model and analyze the outputs.

Installation

Installing the latest stable version from CRAN:

install.packages("DWBmodelUN")

Or, you can install the version under development from
Github, using these commands:

install.packages("devtools")
devtools::install_github("dazamora/DWBmodelUN")

Concepts behind DWBmodelUN

Two physical laws are taken into account in Dynamic Water Balance model
(DWB), mass balance and energy balance. To represent the mass
conservation, DWB is based on the equilibrium of water balance shown in
equation (1).

Where (S_{c}) is the total stored water in the basin, P is the
precipitation, ET is actual evapotranspiration, R corresponds to
surface runoff and Q to aquifers recharge. To evaluate the water
balance of a basin is necessary to know several kind information like
climatic variables, basin physical characteristics and further
uniqueness relationships of each study. In the case of water balance
models, some information can be replaced by equations and mathematical
relations physically based, which makes the models much simpler but
functional.

To represent energy conservation the model includes a conceptualization
made by Budyko (1961) where the energy availability influences over the
atmospheric water demand which is represented by potential
evapotranspiration (PET). The conceptualization also states that the
dominant control of the water balance is atmospheric demand and water
availability (P), which impose a limit to how much water can be
evapotranspirated. Zhang et al. (2008) worked on the mathematical
assumption presented by Baw-Puh (1981) (equation 2) that is a
continuation of Budyko framework.

Where (\alpha) is a model parameter with an interval of [0-1]. Zhang
et al. (2008) detailed the influence of α parameter on the hydrological
response in their model DWB. DWB is a lumped conceptual hydrological
model developed for annual and monthly time step. The model inputs are
precipitation, potential evapotranspiration and streamflow. In general
terms, DWB calculates the streamflow using two tanks and doing the
following processes:

1. Precipitation is partitioned to basin water consumption and basin
   water yield. When it rains the soil is replenished and part of the
   rainfall is returned to the atmosphere, this process corresponds to
   basin water consumption, by the other hand, the remaining rainfall
   is the basin water yield.
2. Total water available for evapotranspiration is divided into water
   remaining in the soil storage and actual evapotranspiration.
3. The basin water yield is divided into surface runoff and water that
   supplies the groundwater store.
4. The base flow is the result of groundwater storage drainage.
5. The total monthly flow is the result of adding base flow and surface
   runoff.

All these processes are done under the Top Down approach consider only
four parameters are added to the model structure: (\alpha_{1}),
precipitation catchment efficiency; (\alpha), evapotranspiration
efficiency; d, groundwater store time constant; (S_{max}), maximum
water holding capacity of soil store (Zhang et al. (2008)).

DWBmodelUN functions

DWBmodelUN package contains 12 functions, most of them have a practical
example about their usage. The functions are:

• BuildGRUmaps: This function builds raster maps for each parameter
  based on a raster file where the location of the Grouped Response
  Units (GRUs) are defined.
• cellBasins: This function identifies the cells that are within a
  basin.
• Coord_comparison: This function compares three characteristics
  from two rasters:coordinates, resolution, and number of layers
• dds: This function allows the user to calibrate the DWB or other
  models with the Dynamical Dimension Search (DDS) algorithm (Tolson
  and Shoemaker (2007)).
• DWBCalculator: The function performs the distributed DWB
  hydrological model calculations in the defined domain and time
  period.
• funFU: Fu’s function for relationship between precipitation and
  potential evapotranspiration.
• graphDWB: This function dynamically graphs the inputs and results
  of the Modelling. It has four types of graphs.
• init_state: This function uploads or creates the initial
  conditions of the two-state variables present in the DWB model, in
  raster format.
• printVar: This function that allows to print some of the variables
  simulated by the DWB model.
• readSetup: This function reads the setup features of the model.
  These include the dates that define the simulated time period, and
  also the variables that will be printed in individual directories
• upForcing: This function loads the precipitation and
  evapotranspiration estimates that will be used to run or force the
  DWB model
• varBasins: This function retrieves the value of a variable in each
  of the cells that are within a basin boundary. It also returns the
  time series average value of the variable.

Datasets

DWBmodelUN also contains 11 data that allow to run the practical
examples (Duque (2018)):

• basins: The polygons of the 23 subbasins across the Sogamoso
  Basin.
• cells: Coordinates (Latitud and Longitud) and ID number of cells
  in Sogamoso River Basin.
• dwb_results: Results from DWB in Sogamoso River Basin.
• EscSogObs: Flow rates observed in Sogamoso River Basin at 32
  gauges from January 2001 to December 2016.
• GRU: Raster data of Group Response Units in Sogamoso River Basin
• param: Values to four parameters alpha_{1}, alpha_{2} d,
  S_{max} of DWB model in each GRU.
• PET_sogamoso: Distributed monthly potential evapotranspiration in
  Sogamoso River Basin from January 2001 to December 2016.
• setup_data: Data.frame with the initial configuration of the model
  run.
• simDWB.sogamoso: Simulated runoff by the DWBmodelUN in the same
  stations where there were observed data from the Sogamoso basin.
• sogamoso: Sogamoso River Basin data.
• P_sogamoso: Distributed monthly precipitation in Sogamoso River
  Basin from January 2001 to December 2016.
• r.cells: Data.frame with the initial configuration of the model
  run.

Disclaimer

DWBmodelUN is a public R library that is made freely available by the
voluntary work of the researchers/authors of the Grupo de Investigación
en Recursos Hídricos (GIREH) at the Universidad Nacional de Colombia
(UNAL), hereafter call as creators, so as to promote the environmental
modelling of the water cycle.

The representations of the physical world within the software are widely
known. The codification and use of them are offered through this R
library as a public service and are no cause of action against the
creators. The user of this software/information is responsible for
verifying the suitability, accuracy, completeness and quality for the
particular use of it and hence the user asumes all liability and waives
any claims or actions against the creators. Creators do not make any
claim, guarantee or warranty the, expressed or implied, suitability,
accuracy, completeness and quality for the particular use of the
library. The creators disclaim any and all liability for any claims or
damages that may result from the application of the information/software
contained in the library. The information/software is provided as a
guide.

Regarding other information contained in the library. The links or
information that are accessed through external sites, which are not
maintained by the creators, do not make the creators responsible for
that content or the any claims or damages that may result from the use
of these external sites. Information within this library is considered
to be accurate with the considerations of uncertainties associated with
hydrological modelling.

References