Streamflow Analysis: Upper Colorado Basin

Introduction

This notebook demonstrates basic streamflow analysis using hypothetical gauge data modeled after USGS monitoring sites in the Upper Colorado River basin. The synthetic record simulates a water year (Oct 2023 – Sep 2024) for a snowmelt-driven system — characterised by low winter baseflow and a sharp spring peak as mountain snowpack melts.

Setup

import pandas as pd
import matplotlib.pyplot as plt
import matplotlib.dates as mdates
import numpy as np

np.random.seed(42)
plt.rcParams["figure.dpi"] = 120

Synthetic Streamflow Record

Daily mean discharge is constructed from three components: a Gaussian snowmelt pulse peaking in late May, a low-amplitude seasonal baseflow cycle, and random measurement noise.

dates = pd.date_range("2023-10-01", "2024-09-30", freq="D")
n = len(dates)

day_of_year = np.array([d.timetuple().tm_yday for d in dates])

# Snowmelt pulse centered on day 145 (~late May)
snowmelt  = 800 * np.exp(-((day_of_year - 145) ** 2) / (2 * 28 ** 2))
baseflow  = 120 + 30 * np.sin(2 * np.pi * day_of_year / 365)
noise     = np.random.normal(0, 18, n)

discharge = np.clip(snowmelt + baseflow + noise, 45, None).round(1)

df = pd.DataFrame({"date": dates, "discharge_cfs": discharge})
print(f"Water year: {df['date'].min().date()} → {df['date'].max().date()}")
print(f"Peak discharge: {df['discharge_cfs'].max():.0f} cfs on "
      f"{df.loc[df['discharge_cfs'].idxmax(), 'date'].date()}")
print(f"Min  discharge: {df['discharge_cfs'].min():.0f} cfs")

Water year: 2023-10-01 → 2024-09-30
Peak discharge: 975 cfs on 2024-05-22
Min  discharge: 56 cfs

Hydrograph

fig, ax = plt.subplots(figsize=(10, 4))

ax.fill_between(df["date"], df["discharge_cfs"],
                alpha=0.25, color="#3b82f6")
ax.plot(df["date"], df["discharge_cfs"],
        color="#3b82f6", linewidth=1.4, label="Daily mean discharge")

ax.axhline(df["discharge_cfs"].mean(), color="#f59e0b",
           linewidth=1, linestyle="--", label=f"Annual mean ({df['discharge_cfs'].mean():.0f} cfs)")

ax.set_ylabel("Discharge (cfs)")
ax.set_title("Daily Mean Streamflow — Upper Colorado Basin (WY 2024)")
ax.xaxis.set_major_formatter(mdates.DateFormatter("%b '%y"))
ax.xaxis.set_major_locator(mdates.MonthLocator())
plt.xticks(rotation=30, ha="right")
ax.grid(True, alpha=0.25)
ax.legend(fontsize=9)
fig.tight_layout()
plt.show()

Monthly Summary Statistics

month_order = [
    "October", "November", "December", "January", "February",
    "March", "April", "May", "June", "July", "August", "September",
]

summary = (
    df.assign(month=df["date"].dt.month_name())
    .groupby("month")["discharge_cfs"]
    .agg(
        Mean="mean",
        Median="median",
        Min="min",
        Max="max",
    )
    .round(1)
    .reindex(month_order)
)

summary

	Mean	Median	Min	Max
month
October	87.7	85.9	56.3	118.6
November	97.0	97.0	60.7	127.6
December	113.6	114.9	64.2	142.0
January	127.9	127.8	95.1	175.5
February	141.3	141.0	110.7	176.3
March	200.8	193.4	142.5	299.7
April	475.3	458.7	288.6	718.8
May	874.0	901.6	727.5	975.4
June	694.7	715.9	454.6	894.3
July	263.7	234.3	146.5	430.8
August	116.0	115.7	80.0	162.2
September	89.9	88.4	65.8	117.7

Flow Duration Curve

A flow duration curve shows what fraction of the time streamflow equals or exceeds a given discharge — a standard tool for characterising a basin’s hydrologic regime.

sorted_q = np.sort(df["discharge_cfs"])[::-1]
exceedance = np.linspace(0, 100, len(sorted_q))

fig, ax = plt.subplots(figsize=(8, 4))
ax.semilogy(exceedance, sorted_q, color="#3b82f6", linewidth=1.5)
ax.set_xlabel("Exceedance probability (%)")
ax.set_ylabel("Discharge (cfs) — log scale")
ax.set_title("Flow Duration Curve — WY 2024")
ax.grid(True, which="both", alpha=0.2)
fig.tight_layout()
plt.show()