big, dramatic, huge, large, massive, sharp, strong, substantial
modest, slight, small
threefold, 80%, etc.
significant
alarming
the alarming rise in obesity in the US

abrupt, exponential, rapid, steep, sudden
gradual, slow
steady
continued, continuing
inexorable (esp. BrE)
the inexorable rise of oil prices

general, overall
global, worldwide
concomitant (formal), corresponding
the deterioration of our trade balance and the corresponding rise in protectionism

annual, monthly
temperature
sea-level
interest-rate, pay, price, tax, wage (all esp. BrE)
The union is demanding a pay rise of 5%.

on the rise (= rising)
Crime is on the rise.

rise in
a twofold rise in prices

rise on (BrE)
a rise on last year's levels

meteoric, quick, spectacular, swift
That is the quickest rise to power I have ever seen.

initial
the initial rise of a women's emancipation movement

rise from
his rise from the music halls into a beloved star

rise of
the rise of capitalism

rise to
His swift rise to the national team surprised everyone.

the rise and fall of sth
the rise and fall of the Roman Empire

sb's rise to fame, sb's rise to power, sb's rise to prominence
her meteoric rise to fame

majestically
the cliffs which rise majestically from the ocean

up
Lush green mountains rise up behind the airport.

from
Smoke rose from the chimney.

into
Tall chimneys rise into the air.

slowly
abruptly
Adam rose abruptly from the table.

stiffly
shakily, unsteadily
She rose unsteadily to her feet.

make to, try to
He made to rise but found his legs were not strong enough to support him.

manage to
Somehow he managed to rise to a sitting position.

be unable to

from
She rose slowly from her chair to greet us.

rise to your feet
She rose shakily to her feet and looked around.

rise to your full height
He rose to his full height and leaned across the table.

early, late
He rose early and went for a walk.

considerably, dramatically, markedly, sharply, significantly, steeply, substantially
House prices have risen sharply in recent months.

a little, slightly, etc.
further, higher
steadily
gradually
exponentially, fast, quickly, rapidly
The cost of health care is rising faster than ever.

be expected to, be likely to, be predicted to, be projected to, be set to
Entry standards into the profession are set to rise further.

be unlikely to
begin to, start to
continue to

above
Air pollution has risen above an acceptable level.

by
Unemployment has risen by 25 000 this month.

from, in
Gas rose in price.

in line with
Pensions will rise in line with inflation.

to
Inflation rose from 2% to 5% last year.

Rise is used with these nouns as the subject:
air, anger, barometer, blush, brow, bubble, chin, circulation, cliff, colour, concentration, confidence, consumption, cost, count, crime, currency, curtain, deficit, demand, density, dividend, dough, dust, employment, enrolment, excitement, expectation, expenditure, expense, export, eyebrow, fare, fee, flame, flush, fortune, funding, fury, hand, heat, hill, hope, humidity, import, income, index, inflation, investment, level, mist, moon, mountain, number, output, panic, parliament, peak, percentage, population, premium, pressure, price, production, productivity, profit, proportion, rate, rating, receipt, rent, reserve, revenue, river, salary, sale, sap, sea, share, sickness, skyscraper, slope, smoke, sob, spending, spirit, standing, stature, steam, stock, sun, support, takings, tax, temper, temperature, tension, tide, toll, total, turnover, unemployment, value, voice, volume, vote, wage, water, wave, wind, workforce, yield

Rise is used with these nouns as the object:
per cent, point