Non-linear recharge models#
R.A. Collenteur, University of Graz
This notebook explains the use of the
RechargeModel stress model to simulate the combined effect of precipitation and potential evaporation on the groundwater levels. For the computation of the groundwater recharge, four recharge models are currently available:
Berendrecht(Berendrecht et al., 2006)
FlexModel(Collenteur et al., 2021)
Peterson(Peterson & Western, 2014)
The first model is a simple linear function of precipitation and potential evaporation while the latter two are simulate a non-linear response of recharge to precipitation using a soil-water balance concepts. Detailed descriptions of these models can be found in articles listed in the References at the end of this notebook.
import pandas as pd import pastas as ps import matplotlib.pyplot as plt ps.show_versions() ps.set_log_level("INFO")
Python version: 3.10.12 NumPy version: 1.23.5 Pandas version: 2.0.3 SciPy version: 1.11.1 Matplotlib version: 3.7.2 Numba version: 0.57.1 LMfit version: 1.2.2 Latexify version: Not Installed Pastas version: 1.1.0
Read Input data#
Input data handling is similar to other stressmodels. The only thing that is necessary to check is that the precipitation and evaporation are provided in mm/day. This is necessary because the parameters for the non-linear recharge models are defined in mm for the length unit and days for the time unit. It is possible to use other units, but this would require manually setting the initial values and parameter boundaries for the recharge models.
head = pd.read_csv( "data/B32C0639001.csv", parse_dates=["date"], index_col="date" ).squeeze() # Make this millimeters per day evap = pd.read_csv("data/evap_260.csv", index_col=0, parse_dates=).squeeze() rain = pd.read_csv("data/rain_260.csv", index_col=0, parse_dates=).squeeze() ps.plots.series( head, [evap, rain], figsize=(10, 6), labels=["Head [m]", "Evap [mm/d]", "Rain [mm/d]"], );
Make a basic model#
The normal workflow may be used to create and calibrate the model. 1. Create a Pastas
Model instance 2. Choose a recharge model. All recharge models can be accessed through the recharge subpackage (
ps.rch). 3. Create a
RechargeModel object and add it to the model 4. Solve and visualize the model
ml = ps.Model(head) # Select a recharge model rch = ps.rch.FlexModel(gw_uptake=True) # rch = ps.rch.Berendrecht() # rch = ps.rch.Linear() # rch = ps.rch.Peterson() rm = ps.RechargeModel(rain, evap, recharge=rch, rfunc=ps.Gamma(), name="rch") ml.add_stressmodel(rm) ml.solve(noise=True, tmin="1990", report="basic") ml.plots.results(figsize=(10, 6));
Fit report head Fit Statistics =================================================== nfev 46 EVP 90.32 nobs 351 R2 0.90 noise True RMSE 0.06 tmin 1990-01-01 00:00:00 AIC -2071.69 tmax 2005-10-14 00:00:00 BIC -2036.94 freq D Obj 0.46 warmup 3650 days 00:00:00 ___ solver LeastSquares Interp. No Parameters (9 optimized) =================================================== optimal stderr initial vary rch_A 0.408502 ±5.87% 0.438424 True rch_n 0.650443 ±3.07% 1.000000 True rch_a 328.564419 ±13.67% 10.000000 True rch_srmax 54.401860 ±5.82% 250.000000 True rch_lp 0.250000 ±nan 0.250000 False rch_ks 19.672814 ±10.91% 100.000000 True rch_gamma 4.064227 ±9.32% 2.000000 True rch_kv 1.000000 ±nan 1.000000 False rch_simax 2.000000 ±nan 2.000000 False rch_gf 0.236322 ±24.50% 1.000000 True constant_d 0.879642 ±3.66% 1.359779 True noise_alpha 31.275676 ±11.48% 15.000000 True
Analyze the estimated recharge flux#
After the parameter estimation we can take a look at the recharge flux computed by the model. The flux is easy to obtain using the
get_stress method of the model object, which automatically provides the optimal parameter values that were just estimated. After this, we can for example look at the yearly recharge flux estimated by the Pastas model.
recharge = ml.get_stress("rch").resample("A").sum() ax = recharge.plot.bar(figsize=(10, 3)) ax.set_xticklabels(recharge.index.year) plt.ylabel("Recharge [mm/year]");
A few things to keep in mind:#
Below are a few things to keep in mind while using the (non-linear) recharge models.
The use of an appropriate warmup period is necessary, so make sure the precipitation and evaporation are available some time (e.g., one year) before the calibration period.
Make sure that the units of the precipitation fluxes are in mm/day and that the DatetimeIndex matches exactly.
It may be possible to fix or vary certain parameters, dependent on the problem. Obtaining better initial parameters may be possible by solving without a noise model first (
ml.solve(noise=False)) and then solve it again using a noise model.
For relatively shallow groundwater levels (e.g., < 10 meters), it may be better to use the
Exponentialresponse function as the the non-linear models already cause a delayed response.
Berendrecht, W. L., Heemink, A. W., van Geer, F. C., and Gehrels, J. C. (2003), Decoupling of modeling and measuring interval in groundwater time series analysis based on response characteristics, Journal of Hydrology, 278, 1–16.
Berendrecht, W. L., Heemink, A. W., van Geer, F. C., and Gehrels, J. C. (2006), A non-linear state space approach to model groundwater fluctuations, Advances in Water Resources, 29, 959–973.
Collenteur, R. A., Bakker, M., Klammler, G., and Birk, S. (2021), Estimation of groundwater recharge from groundwater levels using nonlinear transfer function noise models and comparison to lysimeter data, Hydrol. Earth Syst. Sci., 25, 2931–2949.
Peterson, T.J., and A.W. Western (2014), Nonlinear time-series modeling of unconfined groundwater head, Water Resour. Res., 50, 8330-8355.
Von Asmuth, J.R., Maas, K., Bakker, M. and Petersen, J. (2008), Modeling Time Series of Ground Water Head Fluctuations Subjected to Multiple Stresses. Groundwater, 46: 30-40.
In this notebook we analysed a head time series near the town of De Bilt in the Netherlands. Data is obtained from the following resources: - The heads (
B32C0639001.csv) are downloaded from https://www.dinoloket.nl/ - The precipitation and evapotranspiration (
evap_260.csv) are downloaded from https://knmi.nl