DIRINT

This function implements the modified DISC model known as “DIRINT” to predict DNI from measured Global Horizontal Irradiance (GHI).

DIRINT calculates DNI using time-series GHI data and solar zenith angles. It can optionally incorporate dew point temperature for improved accuracy. The stability index is utilized by default to adjust DNI in response to dynamics in the time series.

Excel Usage

=DIRINT(ghi, solar_zenith, times, pressure, use_delta_kt_prime, temp_dew, min_cos_zenith, max_zenith)
  • ghi (list[list], required): Global horizontal irradiance (W/m^2).
  • solar_zenith (list[list], required): Solar zenith angles (degrees).
  • times (list[list], required): Timestamps corresponding to the observations in ISO8601 format.
  • pressure (float, optional, default: 101325): Site air pressure (Pa).
  • use_delta_kt_prime (bool, optional, default: true): Include stability index delta_kt_prime in the model.
  • temp_dew (list[list], optional, default: null): Optional dew point temperature time series (°C) aligned to ghi observations.
  • min_cos_zenith (float, optional, default: 0.065): Minimum value of cos(zenith) when calculating clearness index.
  • max_zenith (float, optional, default: 87): Maximum value of zenith to allow in DNI calculation (degrees).

Returns (list[list]): 2D list of estimated DNI values (W/m^2), or an error string.

Example 1: Calculate DNI from GHI with default parameters

Inputs:

ghi solar_zenith times pressure use_delta_kt_prime
800 40 2024-01-01T12:00:00Z 101325 true
800 40 2024-01-01T13:00:00Z
800 40 2024-01-01T14:00:00Z
800 40 2024-01-01T15:00:00Z

Excel formula:

=DIRINT({800;800;800;800}, {40;40;40;40}, {"2024-01-01T12:00:00Z";"2024-01-01T13:00:00Z";"2024-01-01T14:00:00Z";"2024-01-01T15:00:00Z"}, 101325, TRUE)

Expected output:

Result
857.709
857.709
857.709
857.709
Example 2: DIRINT using dew point corrections

Inputs:

ghi solar_zenith times temp_dew pressure use_delta_kt_prime
500 65 2024-06-21T08:00:00Z 12 100500 true
700 45 2024-06-21T10:00:00Z 14
850 25 2024-06-21T12:00:00Z 16
600 50 2024-06-21T14:00:00Z 15

Excel formula:

=DIRINT({500;700;850;600}, {65;45;25;50}, {"2024-06-21T08:00:00Z";"2024-06-21T10:00:00Z";"2024-06-21T12:00:00Z";"2024-06-21T14:00:00Z"}, {12;14;16;15}, 100500, TRUE)

Expected output:

Result
534.527
776.165
578.504
750.125
Example 3: DIRINT without stability index adjustment

Inputs:

ghi solar_zenith times use_delta_kt_prime min_cos_zenith
300 70 2024-09-22T07:00:00Z false 0.08
550 55 2024-09-22T09:00:00Z
780 35 2024-09-22T11:00:00Z
520 60 2024-09-22T13:00:00Z

Excel formula:

=DIRINT({300;550;780;520}, {70;55;35;60}, {"2024-09-22T07:00:00Z";"2024-09-22T09:00:00Z";"2024-09-22T11:00:00Z";"2024-09-22T13:00:00Z"}, FALSE, 0.08)

Expected output:

Result
702.838
780.042
653.316
889.943
Example 4: DIRINT with tighter zenith cutoff

Inputs:

ghi solar_zenith times max_zenith pressure
200 80 2024-03-21T06:30:00Z 80 95000
450 68 2024-03-21T08:30:00Z
650 52 2024-03-21T10:30:00Z
400 78 2024-03-21T16:30:00Z

Excel formula:

=DIRINT({200;450;650;400}, {80;68;52;78}, {"2024-03-21T06:30:00Z";"2024-03-21T08:30:00Z";"2024-03-21T10:30:00Z";"2024-03-21T16:30:00Z"}, 80, 95000)

Expected output:

Result
630.356
745.445
761.993
420.681

Python Code

Show Code 
import pandas as pd
import numpy as np
from pvlib.irradiance import dirint as result_func

def dirint(ghi, solar_zenith, times, pressure=101325, use_delta_kt_prime=True, temp_dew=None, min_cos_zenith=0.065, max_zenith=87):
    """
    Estimate Direct Normal Irradiance (DNI) from GHI using the DIRINT model.

    See: https://pvlib-python.readthedocs.io/en/stable/reference/generated/pvlib.irradiance.dirint.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        ghi (list[list]): Global horizontal irradiance (W/m^2).
        solar_zenith (list[list]): Solar zenith angles (degrees).
        times (list[list]): Timestamps corresponding to the observations in ISO8601 format.
        pressure (float, optional): Site air pressure (Pa). Default is 101325.
        use_delta_kt_prime (bool, optional): Include stability index delta_kt_prime in the model. Default is True.
        temp_dew (list[list], optional): Optional dew point temperature time series (°C) aligned to ghi observations. Default is None.
        min_cos_zenith (float, optional): Minimum value of cos(zenith) when calculating clearness index. Default is 0.065.
        max_zenith (float, optional): Maximum value of zenith to allow in DNI calculation (degrees). Default is 87.

    Returns:
        list[list]: 2D list of estimated DNI values (W/m^2), or an error string.
    """
    try:
        def flatten_num(data):
            if not isinstance(data, list): return [float(data)]
            flat = []
            for row in data:
                row = row if isinstance(row, list) else [row]
                for val in row:
                    if val == "": flat.append(float('nan'))
                    else: flat.append(float(val))
            return flat

        def flatten_str(data):
            if not isinstance(data, list): return [str(data)]
            return [str(val) for row in data for val in (row if isinstance(row, list) else [row]) if val != ""]

        ghi_list = flatten_num(ghi)
        zen_list = flatten_num(solar_zenith)
        time_list = flatten_str(times)
        temp_dew_list = None
        if temp_dew is not None and temp_dew != "":
            td = flatten_num(temp_dew)
            if len(td) != len(ghi_list):
                return "Error: temp_dew must match the length of ghi"
            temp_dew_list = pd.Series(td, index=pd.DatetimeIndex(time_list))

        n = len(ghi_list)
        if n == 0 or len(zen_list) != n or len(time_list) != n:
            return "Error: All input arrays must have the same non-zero length"

        idx = pd.DatetimeIndex(time_list)
        ghi_s = pd.Series(ghi_list, index=idx)
        zen_s = pd.Series(zen_list, index=idx)

        p = float(pressure) if pressure is not None else 101325.0
        use_kt = bool(use_delta_kt_prime) if use_delta_kt_prime is not None else True
        min_cz = float(min_cos_zenith) if min_cos_zenith is not None else 0.065
        max_z = float(max_zenith) if max_zenith is not None else 87.0

        # dirint requires pandas Series if use_delta_kt_prime is True
        dni = result_func(ghi_s, zen_s, idx, pressure=p, use_delta_kt_prime=use_kt, temp_dew=temp_dew_list, min_cos_zenith=min_cz, max_zenith=max_z)

        return [[float(v) if not pd.isna(v) else ""] for v in dni]
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Global horizontal irradiance (W/m^2).
Solar zenith angles (degrees).
Timestamps corresponding to the observations in ISO8601 format.
Site air pressure (Pa).
Include stability index delta_kt_prime in the model.
Optional dew point temperature time series (°C) aligned to ghi observations.
Minimum value of cos(zenith) when calculating clearness index.
Maximum value of zenith to allow in DNI calculation (degrees).