Conceptual Functional Equivalent (CFE) Model

CFE is a simplified (conceptual) model of the runoff scheme in the National Water Model. It was written by Fred Ogden, and this repository includes both the original author code and a version of CFE that has an implementation of the Basic Model Interface (BMI).

There are multiple ways to run CFE:

1. Through the BMI commands. There are script options, detailed below, for running the model in standalone mode and BMI allows the Next Generation Water Resources Modeling Framework to run CFE and couple it to surface routines. See Compiling and running CFE
2. As written by the original author. This includes a full program to read and process atmospheric forcing data, print the model output and check for mass balance closure. This code can be run from the original_author_code directory. This code does not have a BMI implementation.

Compiling and running CFE

There are three unique examples for running CFE as described below. They assume you have GCC on your machine.

1. ./make_and_run_bmi.sh: Have CFE read in its own forcing file
2. ./make_and_run_bmi_pass_forcings.sh: Use an external module to read in a forcing file and pass those data using BMI
3. ./make_and_run_bmi_pass_forcings_pet.sh: Use external modules to read in a forcing file and calculate potential evapotranspiration, and pass those data using BMI

Configuration File

A configs/ directory contains primiary configuration text files for three different catchments pertaining to each process identiified in The table below details information for catchment-87.

Variable	Datatype	Limits	Units	Role	Process	Description
forcing_file	char	256		filename		path to forcing inputs csv; set to BMI if passed via bmi.set_value*()
soil_params.depth	double		meters [m]	state		soil depth
soil_params.b	double			state		beta exponent on Clapp-Hornberger (1978) soil water relations
soil_params.satdk	double		meters/second [m s-1]	state		saturated hydraulic conductivity
soil_params.satpsi	double		meters [m]	state		saturated capillary head
soil_params.slop	double		meters/meters [m/m]	state		this factor (0-1) modifies the gradient of the hydraulic head at the soil bottom. 0=no-flow.
soil_params.smcmax	double		meters/meters [m/m]	state		saturated soil moisture content
soil_params.wltsmc	double		meters/meters [m/m]	state		wilting point soil moisture content
soil_params.expon	double			parameter_adjustable		optional; defaults to 1.0
soil_params.expon_secondary	double			parameter_adjustable		optional; defaults to 1.0
max_gw_storage	double		meters [m]	parameter_adjustable		maximum storage in the conceptual reservoir
Cgw	double		meters/hour [m h-1]	parameter_adjustable		the primary outlet coefficient
expon	double			parameter_adjustable		exponent parameter (1.0 for linear reservoir)
gw_storage	double		meters/meters [m/m]	parameter_adjustable		initial condition for groundwater reservoir - it is the ground water as a decimal fraction of the maximum groundwater storage (max_gw_storage) for the initial timestep
alpha_fc	double			parameter_adjustable		field capacity
soil_storage	double		meters/meters [m/m]	parameter_adjustable		initial condition for soil reservoir - it is the water in the soil as a decimal fraction of maximum soil water storage (smcmax * depth) for the initial timestep
K_nash	int			parameter_adjustable		number of Nash lf reservoirs (optional, defaults to 2, ignored if storage values present)
K_lf	double			parameter_adjustable		Nash Config param - primary reservoir
nash_storage	double			parameter_adjustable		Nash Config param - secondary reservoir
giuh_ordinates	double			parameter_adjustable		Giuh ordinates in dt time steps
num_timesteps	int			time_info		set to 1 if forcing_file=BMI
verbosity	int	0-3		option		prints various debug and bmi info
surface_partitioning_scheme	char	Xinanjiang or Schaake		parameter_adjustable	direct runoff
a_Xinanjiang_inflection_point_parameter	double			parameter_adjustable	direct runoff	when surface_partitioning_scheme=Xinanjiang
b_Xinanjiang_shape_parameter=1	double			parameter_adjustable	direct runoff	when surface_partitioning_scheme=Xinanjiang
x_Xinanjiang_shape_parameter=1	double			parameter_adjustable	direct runoff	when surface_partitioning_scheme=Xinanjiang

1. Read local forcing file

To compile and run CFE with locally read forcing data: ./make_and_run_bmi.sh

You can also build the model and run from the command line:

1. gcc -lm ./src/main.c ./src/cfe.c ./src/bmi_cfe.c -o run_bmi_cfe. This will generate an executable called run_cfe_bmi.
2. Then run the model with example forcing data: ./run_bmi_cfe ./configs/cat_58_bmi_config_cfe.txt

Or, you can use make to build CFE and run it by reading in a local forcing file:

1. cd src/
2. make clean; make
3. cd ..
4. ./run_cfe_bmi ./configs/cat_89_bmi_config_cfe.txt

2. CFE Model gets forcings passed from BMI

CFE was designed to read its own forcing file, but we have added an option to get forcings passed in through BMI using its set_value functionality. To demonstrate this functionality we have included the BMI-enabled AORC forcing read module. To compile and run CFE this way: ./make_and_run_bmi_pass_forcings.sh

You can also follow these steps:

1. gcc -lm ./src/main_pass_forcings.c ./src/cfe.c ./src/bmi_cfe.c ./forcing_code/src/aorc.c ./forcing_code/src/bmi_aorc.c -o run_cfe_bmi_pass_forcings. This generates an executable called run_cfe_bmi_pass_forcings.
2. To run this executable you must pass the path to the corresponding configuration files for BOTH CFE and AORC (in that order): ./run_cfe_bmi_pass_forcings ./configs/cat_89_bmi_config_cfe_pass.txt ./configs/cat_89_bmi_config_aorc.txt

3. CFE Model gets forcings AND potential evapotranspiration passed from BMI

CFE can remove mass from the modeled system through evapotranspiration (directly from precipitation and from the soil using the Budyko function). To compile and run CFE this way: ./make_and_run_bmi_pass_forcings_pet.sh.

You can also follow these steps:

1. gcc -lm ./src/main_cfe_aorc_pet.c ./forcing_code/src/pet.c ./forcing_code/src/bmi_pet.c ./src/cfe.c ./src/bmi_cfe.c ./forcing_code/src/aorc.c ./forcing_code/src/bmi_aorc.c -o run_cfe_aorc_et_bmi. This generates an executable called run_cfe_aorc_et_bmi.
2. To run this executable you must pass the path to the corresponding configuration files for CFE, PET and AORC (in that order): ./run_cfe_aorc_et_bmi ./configs/cat_89_bmi_config_cfe_pass.txt ./configs/cat_89_bmi_config_aorc.txt ./configs/cat_89_bmi_config_pet_pass.txt

Direct Runoff

In CFE the user has the option to pick a particular direct runoff (aka surface partitioning) method:

1. Schaake function (configuration: surface_partitioning_scheme=Schaake)
2. XinanJiang function (configuration: surface_partitioning_scheme=Xinanjiang).

If XinanJiang is choosen these parameters need to be included in the configuration file: a_Xinanjiang_inflection_point_parameter b_Xinanjiang_shape_parameter x_Xinanjiang_shape_parameter

The CFE was based on the t-shirt approximation of the National Water Model

Development here was based off the t-shirt approximation of the hydrologic routing functionality of the National Water Model v 1.2, 2.0, and 2.1 This code was developed to test the hypothesis that the National Water Model runoff generation, vadose zone dynamics, and conceptual groundwater model can be greatly simplified by acknowledging that it is truly a conceptual model. The hypothesis is supported by a number of observations made during a 2017-2018 deep dive into the NWM code. These are:

• Rainfall/throughfall/melt partitioning in the NWM is based on a simple curve-number like approach that was developed by Schaake et al. (1996) and which is very similar to the Probability Distributed Moisture (PDM) function by Moore, 1985. The Schaake function is a single valued function of soil moisture deficit, predicts 100% runoff when the soil is saturated, like the curve-number method, and is fundamentally simple.
• Run-on infiltration is strictly not calculated. Overland flow routing applies the Schaake function repeatedly to predict this phenomenon, which violates the underlying assumption of the PDM method that only rainfall inputs affect soil moisture.
• The water-content based Richards' equation, applied using a coarse-discretization, can be replaced with a simple conceptual reservoir because it never allows saturation or infiltration-excess runoff unless deactivated by assuming no-flow lower boundary condition. Since this form of Richards' equation cannot simulate heterogeneous soil layers, it can be replaced with a conceptual reservoir.
• The lateral flow routing function in the NWM is purely conceptual. It is activated whenever the soil water content in one or more of the four Richards-equation discretizations reaches the wilting point water content. This activation threshold is physically unrealistic, because in most soils lateral subsurface flow is not active until pore water pressures become positive at some point in the soil profile. Furthermore, the lateral flow hydraulic conductivity is assumed to be the vertical hydraulic conductivity multiplied by a calibration factor "LKSATFAC" which is allowed to vary between 10 and 10,000 during calibration, resulting in an anisotropy ratio that varies over the same range, without correlation with physiographic characteristics or other support.

This code implements these assumptions using pure conceptualizations. The formulation consists of the following:

• Rainfall is partitioned into direct runoff and soil moisture using the Schaake function.
• Rainfall that becomes direct runoff is routed to the catchment outlet using a geomorphological instantaneous unit hydrograph (GIUH) approach, eliminating the 250 m NWM routing grid, and the incorrect use of the Schaake function to simulate run-on infiltration.
• Water partitioned by the Schaake function to be soil moisture is placed into a conceptual linear reservoir that consists of two outlets that apply a minimum storage activation threshold. This activation threshold is identical for both outlets, and is based on an integral solution of the storage in the soil assuming Clapp-Hornberger parameters equal to those used in the NWM to determine that storage corresponding to a soil water content 0.5 m above the soil column bottom that produces a soil suction head equal to -1/3 atm, which is a commonly applied assumption used to estimate the field capacity water content. The first outlet calculates vertical percolation of water to deep groundwater using the saturated hydraulic conductivity of the soil multiplied by the NWM "slope" parameter, which when 1.0 indicates free drainage and when 0.0 indicates a no-flow lower boundary condition. The second outlet is used to calculate the flux to the soil lateral flow path, using a conceptual LKSATFAC-like calibration parameter.
• The lateral flow is routed to the catchment outlet using a Nash-cascade of reservoirs to produce a mass-conserving delayed response, and eliminates the need for the 250 m lateral flow routing grid.
• The groundwater contribution to base flow is modeled using either (a) an exponential nonlinear reservoir identical to the one in the NWM formulation, or (b) a nonlinear reservoir forumulation, which can also be made linear by assuming an exponent value equal to 1.0.

This code was written entirely by Fred L. Ogden, May 22-24, 2020, in the service of the NOAA-NWS Office of Water Prediction, in Tuscaloosa, Alabama.