Add GEN_KW to heat equation and turn localization on

Makes it easier to write more realistic tests.

test-data/ert/heat_equation/config.ert

@@ -13,13 +13,19 @@ QUEUE_OPTION LOCAL MAX_RUNNING 100
 
 RANDOM_SEED 11223344
 
+ANALYSIS_SET_VAR STD_ENKF LOCALIZATION True
+ANALYSIS_SET_VAR STD_ENKF LOCALIZATION_CORRELATION_THRESHOLD 0.1
+
 NUM_REALIZATIONS 100
 GRID CASE.EGRID
 
 OBS_CONFIG observations
 
 FIELD COND PARAMETER cond.bgrdecl INIT_FILES:cond.bgrdecl FORWARD_INIT:True
 
+GEN_KW INIT_TEMP_SCALE init_temp_prior.txt
+GEN_KW CORR_LENGTH corr_length_prior.txt
+
 GEN_DATA MY_RESPONSE RESULT_FILE:gen_data_%d.out REPORT_STEPS:10,71,132,193,255,316,377,438 INPUT_FORMAT:ASCII
 
 INSTALL_JOB heat_equation HEAT_EQUATION

test-data/ert/heat_equation/config_forward_init_false.ert

@@ -20,6 +20,9 @@ OBS_CONFIG observations
 
 FIELD COND PARAMETER cond.bgrdecl INIT_FILES:cond_%d.bgrdecl FORWARD_INIT:False
 
+GEN_KW INIT_TEMP_SCALE init_temp_prior.txt
+GEN_KW CORR_LENGTH corr_length_prior.txt
+
 GEN_DATA MY_RESPONSE RESULT_FILE:gen_data_%d.out REPORT_STEPS:10,71,132,193,255,316,377,438 INPUT_FORMAT:ASCII
 
 INSTALL_JOB heat_equation HEAT_EQUATION

test-data/ert/heat_equation/corr_length_prior.txt

@@ -0,0 +1 @@
+x NORMAL 0.8 0.1

test-data/ert/heat_equation/heat_equation.py

@@ -1,6 +1,7 @@
 #!/usr/bin/env python3
 """Partial Differential Equations to use as forward models."""
 
+import json
 import sys
 
 import geostat
@@ -51,16 +52,28 @@ def heat_equation(
     return u_
 
 
-def sample_prior_conductivity(ensemble_size, nx, rng):
+def sample_prior_conductivity(ensemble_size, nx, rng, corr_length):
     mesh = np.meshgrid(np.linspace(0, 1, nx), np.linspace(0, 1, nx))
-    return np.exp(geostat.gaussian_fields(mesh, rng, ensemble_size, r=0.8))
+    return np.exp(geostat.gaussian_fields(mesh, rng, ensemble_size, r=corr_length))
+
+
+def load_parameters(filename):
+    with open(filename, encoding="utf-8") as f:
+        return json.load(f)
 
 
 if __name__ == "__main__":
     iens = int(sys.argv[1])
     iteration = int(sys.argv[2])
     rng = np.random.default_rng(iens)
-    cond = sample_prior_conductivity(ensemble_size=1, nx=nx, rng=rng).reshape(nx, nx)
+
+    parameters = load_parameters("parameters.json")
+    init_temp_scale = parameters["INIT_TEMP_SCALE"]
+    corr_length = parameters["CORR_LENGTH"]
+
+    cond = sample_prior_conductivity(
+        ensemble_size=1, nx=nx, rng=rng, corr_length=float(corr_length["x"])
+    ).reshape(nx, nx)
 
     if iteration == 0:
         resfo.write(
@@ -78,7 +91,9 @@ def sample_prior_conductivity(ensemble_size, nx, rng):
     # Note that this could be avoided if we used an implicit solver.
     dt = dx**2 / (4 * max(np.max(cond), np.max(cond)))
 
-    response = heat_equation(u_init, cond, dx, dt, k_start, k_end, rng)
+    scaled_u_init = u_init * float(init_temp_scale["x"])
+
+    response = heat_equation(scaled_u_init, cond, dx, dt, k_start, k_end, rng)
 
     index = sorted((obs.x, obs.y) for obs in obs_coordinates)
     for time_step in obs_times:

test-data/ert/heat_equation/init_temp_prior.txt

@@ -0,0 +1 @@
+x UNIFORM 0 1

tests/ert/ui_tests/cli/test_field_parameter.py

@@ -252,6 +252,8 @@ def test_field_param_update_using_heat_equation_zero_var_params_and_adaptive_loc
         experiment = storage.get_experiment_by_name("es-mda")
         prior = experiment.get_ensemble_by_name("default_0")
         cond = prior.load_parameters("COND")
+        init_temp_scale = prior.load_parameters("INIT_TEMP_SCALE")
+        corr_length = prior.load_parameters("CORR_LENGTH")
 
         new_experiment = storage.create_experiment(
             parameters=config.ensemble_config.parameter_configuration,
@@ -268,6 +270,8 @@ def test_field_param_update_using_heat_equation_zero_var_params_and_adaptive_loc
         cond["values"][:, :, :5, 0] = 1.0
         for real in range(prior.ensemble_size):
             new_prior.save_parameters("COND", real, cond)
+            new_prior.save_parameters("INIT_TEMP_SCALE", real, init_temp_scale)
+            new_prior.save_parameters("CORR_LENGTH", real, corr_length)
 
         # Copy responses from existing prior to new prior.
         # Note that we ideally should generate new responses by running the