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Physical geography: follow a parcel through a threshold, not a slogan

“Air rises and cools” is a starting mechanism, not a complete mountain-temperature calculation. The path changes when a parcel becomes saturated, and the descent depends on what happened to condensed water. This route connects physical explanations to a piecewise model whose thresholds and limits can be checked.

Course topic: Physical Geography

Study route and exercise: University Reading List editorial project. How we curate · Sources checked:

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Scope and responsibility

For learners comfortable with temperature differences, kilometers and linear equations. The worksheet supplies idealized lapse rates and water-removal assumptions; it is not a weather forecast. The free introductory text provides accessible landform and atmosphere context, while the other books support broader systems comparisons.

Choose your starting point

I need a free physical-geography entry

Use Patrich’s selected Version 2 for the atmosphere, weather and landform context. Turn each process explanation into a diagram with inputs and changes.

I want an integrated systems survey

Use Geosystems to connect atmosphere, water, land and energy. Keep the assigned eleventh-edition print distinct from its later copyright label.

I want an explicit physical-systems framework

Use Smithson, Addison and Atkinson for energy, atmospheric moisture and linked environmental systems. Select physical principles rather than treating an older edition as a current climate-data source.

Compare the three books

Physical Geography

Jeremy Patrich · Edition: 2 · 2023

Free introductory context

Choose it when
You want an accessible physical-geography route with regional examples and process diagrams.
Use another route when
You need a quantitative meteorology course or assume every linked illustration has identical reuse terms.
Selected reading
Selected 2023 Version 2: atmospheric energy, moisture, weather and orographic/rain-shadow discussions, chosen by subject.
Limits and trade-offs
The authored text is free under CC BY 4.0 except where otherwise noted. The college catalogue and the specific 2023 text are distinguished from later folder contents.

Try before choosing

Draw an ascent/descent path and mark where expansion, cooling, saturation and water removal enter the model.

Check your work: Rising air expands as ambient pressure falls; do not describe cooling as contraction. Saturation is a threshold to calculate, not assume at the foot of every mountain.

Official free reading ↗

Book record and access options →

Geosystems: An Introduction to Physical Geography

Robert W. Christopherson; Ginger H. Birkeland · Edition: 11 · 2026

Integrated systems survey

Choose it when
You need a broad course spine connecting energy, water and landform processes.
Use another route when
You want every mountain explained by a single universal lapse rate or by a publisher date alone.
Selected reading
Eleventh edition: atmospheric moisture, weather and physical-system connections by topic.
Limits and trade-offs
The selected print ISBN 9780135485583 has a 2026 publication listing with ©2027 product labeling. Other digital products have different identifiers.

Try before choosing

Write a system boundary for the parcel and list the exchanges the worksheet excludes.

Check your work: A closed classroom path cannot silently import entrainment, radiation, precipitation quantities or observed regional weather.

Book record and access options →

Fundamentals of the Physical Environment

Peter Smithson; Ken Addison; Ken Atkinson · Edition: 4 · 2008

Process-oriented systems reference

Choose it when
You want to connect energy flows, moisture and environmental subsystems.
Use another route when
You need current observational climate statistics from a 2008 edition or a short first introduction without selection.
Selected reading
Fourth edition: energy and atmospheric heat, moisture and precipitation discussions; connect to regional systems afterward.
Limits and trade-offs
Its older publication does not invalidate basic physical reasoning, but dated examples and current observations require separate sources.

Try before choosing

Derive the temperature difference’s closing rate before solving the condensation height.

Check your work: Subtract the dew-point decline from the dry temperature decline; neither supplied rate alone determines the threshold.

Book record and access options →

Check your preparation

What is a lapse rate here?

A stipulated temperature change per kilometer along the parcel’s vertical path, not the surrounding atmosphere’s measured temperature profile.

When does the rule change?

At the first height where parcel temperature equals its dew point. Above that threshold this packet replaces the dry rule with the supplied moist rule.

What controls the return path?

All condensate is removed and no liquid remains available to evaporate during descent. The packet stipulates dry warming on descent; changing that water assumption could change the result.

A six-step study plan

These are your own study marks, not an assessment. They are not sent to this site.

  1. Draw the physical path

    Selected reading: Patrich atmospheric moisture and weather.

    What to do: Sketch sea level, summit and sea-level lee end, labeling heights and parcel state.

    Check your work: Do not confuse a moving parcel’s path with a measured environmental profile.

  2. Specify rates and units

    Selected reading: Selected heat/moisture reading.

    What to do: Write separate temperature and dew-point equations below saturation.

    Check your work: Every rate has units °C/km and every height is in km.

  3. Find the threshold

    Selected reading: Smithson and colleagues moisture discussion.

    What to do: Solve T(h)=Td(h) and check it lies below the summit.

    Check your work: A threshold outside the path cannot trigger the moist segment.

  4. Complete the high path

    Selected reading: The original worksheet.

    What to do: Calculate condensation level, summit and lee temperatures in order.

    Check your work: Use the moist rule only for ascent above the threshold.

  5. Lower the mountain

    Selected reading: The solved follow-up.

    What to do: Recompute for a 1 km summit and derive the piecewise lee-temperature function.

    Check your work: Continuity at 1.5 km is a useful check, not a reason to use the same slope everywhere.

  6. State the physical limits

    Selected reading: Geosystems linked-system reading.

    What to do: List what would be needed to infer rainfall amount, humidity or actual local weather.

    Check your work: Temperature rules alone do not supply a water-mass budget or a forecast.

Worked exercise

Original ideal parcel: a 3 km mountain crosses the saturation threshold

At sea level an invented air parcel has temperature T=24°C and dew point Td=12°C. It rises to a 3 km summit and returns to sea level on the lee side. Below saturation T falls 10°C/km and Td falls 2°C/km. Find the condensation height, summit temperature and final lee temperature.

Assumptions

Use these exact classroom rules: at T=Td saturation begins; subsequent ascent cools at 6°C/km with Td=T. All condensate is removed, no liquid remains for descent, and descent warms at 10°C/km. Exclude entrainment, radiation and other exchanges. These constants are supplied approximations, not universal moist rates.

  1. Before saturation T(h)=24−10 h and Td(h)=12−2 h, with h in km. Equality gives 12=8 h, so the condensation height is 1.5 km. T=Td=9°C there.
  2. The remaining ascent is 3−1.5=1.5 km at 6°C/km, cooling another 9°C. Summit temperature is 0°C.
  3. With all condensate removed and dry descent stipulated, 3 km descent warms 30°C. The lee temperature at sea level is 30°C.
  4. The parcel ends 6°C warmer than its initial 24°C. In this packet the unequal ascent/descent slopes above condensation explain that difference; no rainfall amount or final relative humidity follows from the given temperature rules alone.

Answer and interpretation

Condensation begins at 1.5 km and 9°C; the summit is 0°C; the sea-level lee end is 30°C, 6°C above the start.

Test the result

Check every segment’s height and units: −15−9+30=+6°C overall. A rain-shadow context does not authorize a rainfall estimate without additional moisture information.

Change an assumption

Changed summit: a lower mountain never reaches saturation

Change only the summit to 1 km, with the same initial state and path rules. Then express the final sea-level lee temperature as a function of summit height h for 0≤h≤3 km.

  1. At 1 km, T=24−10=14°C and Td=12−2=10°C. The parcel is unsaturated, so no moist-ascent segment occurs. Descent adds 10°C and returns T to 24°C.
  2. For 0≤h≤1.5 km, the dry ascent loses 10 h and dry descent gains 10 h, giving Tlee=24°C. At exactly 1.5 km there is no positive-length moist segment.
  3. For 1.5<h≤3 km, summit T=9−6(h−1.5)=18−6 h. Descent adds 10 h, so Tlee=18+4 h °C.
  4. The two branches agree at h=1.5: both give 24°C. At h=3 the second gives 30°C, reproducing the main case. The warming result depends on reaching saturation and on the stipulated removal/descent rules.

Answer and interpretation

At a 1 km summit, top T=14°C and Td=10°C, and final T=24°C. Piecewise: Tlee=24°C for h≤1.5; Tlee=18+4 h °C for 1.5<h≤3, with h in km.

Test the result

Check the threshold, continuity and both original endpoints. Changing liquid retention, mixing or rates requires a new path calculation; this is not a prediction for a real mountain.

Common mistakes

One slope everywhere

Dry and supplied moist ascent apply on different path segments.

Moist state assumed immediately

The initial temperature–dew-point gap must close before saturation.

Temperature result used as rainfall

The supplied model has no quantitative water-mass or precipitation calculation.

Before moving on

  • I can derive the threshold from two changing temperatures.
  • I can reproduce the segment ledger and continuous piecewise return function.
  • I can name the water and exchange assumptions limiting the result.

Sources and edition checks

Sources checked:

These are proposed study activities, not official course assignments or a claim that every book has been read cover to cover.

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