This is the supplementary answer to that of drooze ( I think he finally hit the direct answer. )

As he said, according to this site( Japanese ), Nanshi records multiple quite unusual events occurred in Liang Dynasty ( English ).

Quote ( from the above Japanese source )

534年閏12月丙午、西南方で雷鳴が二度、響いた。

In the intercalary December, 534AD, we heard the lightening sound twice at South West. ( Nanshi 1.7.4.1 )

これは先にも引用した火山噴火への言及だが、恐らく梁の人々はこのようなことはすぐ忘れてしまっただろう。不可思議なことと言ってもやはり、庶民には何の関係もない･･･筈だった。しかしそれから異常なことが次々と起こった。翌535年の冬十月、雪のような黄塵が降った1。これが火山灰だったか気候の大異変に起因する季節はずれの砂嵐だったかは今となっては確かめる術もない。この黄塵は翌536年11月2、537年2月1日3、550年1月丁巳の日4にも観測された。

This would be the reference to the volcano explosion of the Krakatoa, in Indonesia, that occurred in 535 AD, though I assume people in Liang Dynasty would've forgotten such lightenings soon from their memories. So those, the unusual lightening sounds, seemed.., should have been nothing to do with the living of people. But parallels of extraordinary climate events occurred multiple time since the sound. In the next year, in October, yellow dusts amounted like snow ( Nanshi 1.7.4.1 ). We have no clue now to confirm that this was the dust of the result of the volcano explosion that happened in the previous year. But these dusts are recorded in Nanshi, observed in the next year, in November 536 ( Nanshi 1.7.4.2 ), on the first of February 537, ( Nanshi 1.7.4.3 ), on 4th of January in 550 ( Nanshi, 1.7.6.4 ).

何かがおかしい。梁の民もそう思い始めたことだろう。しかし時既に遅し、大異変の歯車は回り始めていた。537年の夏は異常な冷夏に見舞われ、6月、青州の胊山で霜害が発生し5、さらに秋7月、青州で雪が降り、穀物収穫に被害を及ぼした6。青州といえば、現在の山東半島の北緯37°の場点にあり、日本のいわき市、北米のカリフォルニア、中東のシリアなどと同緯度に当たる。茨城県で8月に雪が降るようなものである。

「There seems to be something wrong」, I assume Chinese people of Liang Dynasty must had begun to think. But the time was too late, the chains of the extravagant disasters already started. In the summer of the 537, Liang people suffered from the extraordinary cold summer, and in the same year, in June in Quingzhou, people suffered from the severe frost damage, ( Nanshi 1.7.4.3 ) and in the same year, in July, in the same Quingzhou snow fell thus it had enormous impact on the production of crops. ( Nanshi 1.7.4.3 ). If you account for Quingzhou province, it is situated at the same latitude of 37 degree in the northern hemisphere, same with Japanese Iwaki City, and the U.S's California, ans also with that of Syria. It would be equivalent with that snow falls in August at all these areas at the same time.

当然のようにこの後538年飢饉が発生し[7]、政府の当局では八月甲辰、南兗州など十二州に詔を下し、飢饉が発生した地域では、租税を滞納している者に特赦を与え、今年の三調の徴収を禁止[8]するほどの対応をとらなくてはならなかった。異常気象は続き、皇帝は541年11月、「『天の道を用いて、地の利を分かつ』とは古代の聖人の訓辞である。没収された耕作地や桑畑・住居について、皇室領となった土地を除いて、全て貧民に分け与えよう。彼らの労働力を調査し、耕作地を授けることとせよ。聞くところによると、近頃では有力者や富豪が多くの公田を占有し、高額の小作料を徴収して、貧民に与えるなどと、今日の行政に甚だしい損害を与えている。今より一切、公田を有力者に貸し与えることを禁ずる。すでに貸し与えられた分については特別に追及しないこととする。富豪が貧民に種籾を与え、ともに田地を経営するのであれば、この禁令の例外とする[9]」という詔を発するに至る。

Regardless of AlphaD's answer, who could potentially answer to the OP's question directly, but unfortunately as in my comment to him, I would like to continue. ( Or therefore ).

As expected normally, famine happened in 538 ( Nanshi 1.7.4.3 ), and the Imperial Court ( I would like not to use the word "government", since there was not a "government" in the modern sense. ) decided on the 30th of the January of the year, to implement an amnesty to the tax-cut to its' 12 southern provinces where famines were observed, especially to those who were unable to pay the tax. ( Nanshi 1.7.4.4 ). However, the extraordinarily strange climate continued, finally the Emperor declared on November 541, 「 「 Applying the Road Of Heaven in order to share the benefit of the earth 」 is the old proverb by sages. Except for the lands for the Imperial Household, let us give all the abandoned lands and mulberry fields and houses to the poor. We will look into the labor power of these poor, and in accordance with it, let's give them the appropriate size of arable lands. In accordance with our survey we heard, these riches and mighty people recently exploit our Imperial Houshold's lands, imposing heavy farm rents to the poor, so that damaging our administrative functions to the unparalleled degree. From now on, we will prohibit these mighty people from holding the Imperial Houses' lands, except for the already exploited. If the riches, in cooperation with the poor, try to cultivate the ( abandoned ) lands, this prohibition will be annulled. ( Nanshi 1.7.4.4 ).

I would like to skip the uprising part since the translation of the uprising which occurred at many areas at Liang Dynasty is too difficult with sorry.

Now, moving onto the Cannibalism which was observed in Liang Dynasty ( not in Wei's dynasty ( which is the difference between mine and Lars' ))

これらの乱は幸いにも鎮圧されるが、異常気象は止まることを知らない。545年9月に地震が起こった後、冬11月、大雪が降り、平地の積雪量は三尺[13]に及び、548年12月戊申、西北の空で天が裂けた。火のような閃光が走った。[14]これが何を示すのかは判らない。もしかすると550年に降った黄塵の原因となる別な火山噴火かも知れない。気候変動の上に地震までが重なり、飢餓が蔓延した。ついには549年7月、九江にわたって大飢饉が起き、人を食う者が現れ、死者は145人に及び[15]、550年には春から夏まで大旱になり、人々は人間を食った。首都近郊はとくにそれが甚しかった[16]という。南朝梁の経済は完全に崩壊し、本来なら簡単に鎮圧できたはずの侯景の叛乱であえなく崩壊して、陳王朝に交代する。

These uprisings ( which I skipped to translate ) were quenched happily, but the catastrophic climate didn't stop at all. In September 545, an earthquake happened, in November of the same year, huge snow fell and it amounted to about 99㎝, ( Nanshi 1.7.4.10 ). Nanshi writes, at 3 o'clock? in December in 548, people saw the sky was broken and saw the beam of the fire like a thunder. ( Nanshi 1.7.6.2 ). I don't know what this description by Nanshi would imply, but people in the Liang Dynasty might have seen another volcano explosion which became later the cause of the fall of the yellow dust in 550 ( which was previously mentioned ). Famine erupted elsewhere in the dynasty, so catastrophic it stretched to over 9 rivers? in the dynasty, there appeared the cannibalism, Nanshi reports the death toll of 145 people by it, ( Nanshi 1.8.0.3 ), in addition to it, from the spring to the summer of 550, a huge drought happened, people ate people everywhere. The famine was so devastating near the capitol, Nanshi reports ( Nanshi 1.8.1.1 ) The economics of the Liang Dynasty completely went out of control, which led to the collapse of the dynasty, replaced by the new Chen Dynasty, caused by Hou Jing.

In "my research" there is no description about the death toll of 70-80% by Nanshi. Either the blogger might have skipped to describe it intentionally or may be for another reason. )

I would like to lastly describe about the Beishi.

According to Beishi, the climate change was like this.

一方北の魏でも『北史』によると異常気象が始まり、535年5月辛未、旱の故に勅令が下された。曰く「京邑及びに全州以下郡におよぶまで死体は埋葬すべし」[17]。しかし旱魃は更に続き、同年夏五月，大変な旱が起こった。（当局は長安の）市門や（宮殿の）門、そして官庁の門の所で水を配ることにし[18]、さらに翌8月、並、肆、涿、建の四州で霰が降り、大飢饉が発生した[19]ことから冬十一月戊申，河北流（黄河北辺）を彷徨いている饑人の様子を調査するため、巡檢使を派遣した[20]。旱からうってかわって538年夏、今度は山東地方で洪水が発生し、蛙は樹上で鳴いていた[21]ともはや想像さえつかないような異変が続いた。

On the other hand, according to Beishi, in northern Wei too, abnormal climate started so that at 15-17 o'clock? on Saturday? in May 535, an Imperial decree was issued due to the drought. It orders, 「　From Luoyang ( 洛陽 ) to Chang'an ( 長安 ) and to the all provinces including all the counties, one should bury the corpses. 」( Beishi 1.5.4.1.2 ). However the drought could not be stopped and continued, even for 5 months in the summer of the same year, a dramatic drought occurred. The imperial court ordered that water be provided to all the people at the gate of Chang'an and that of the Imperial palace, as well as the at the gates of all the imperial offices, ( Beishi 1.5.4.1.2 ). Furthermore, what worsened the situation was, in 4 provinces, 並、肆、涿、建 ( untranslatable ), there was a frost in August, which caused the pandemic of the great famine, ( Beishi 1.5.4.1.3 ), therefore on the day of 戊申 ( unknown ), in November in the winter, Court decided to dispatch the imperial monitors to observe those who were damaged by the famine around The Yellow River. ( Beishi 1.5.4.1.3 ). The pandemic reached to the unimaginable level, Beishi records frogs croaking on the branch of the tree, mass flood occurred in Shandong province, in exchange for the drought which happened previously, in the summer of 538.

This line coincidentally speaks the same devastating events that occurred in Northern Wei described in Lars' answer.

Conclusion

I think drooze made a direct answer to all of the OP's question completely.

I would like to conglomerate some of the supposed events here, as given from the primary historical sources from 《北史》 (History of the Northern Dynasties) and 《南史》 (History of the Southern Dynasties).

The date conversions given in the footnotes are based on the website 兩千年中西曆轉換. All translations given are my own.

《北史》 (History of the Northern Dynasties)

• 卷05 (Volume 5)

  • 大統......二年......是歲關中大饑人相食死者十七八

    Second year¹...of the Dàtǒng era²...this year, Guānzhōng³ suffered a great famine, and cannibalism ensued. Seven to eight out of every ten people died.

《南史》 (History of the Southern Dynasties)

• 卷07 (Volume 7):

  • 大同......三年春正月......壬寅雨灰黃色

    In Spring, on the first month of the third year⁴...of the Dàtóng era⁵...on the rényín day, yellow-coloured dust/ash rained.

  • 六月青州朐山隕霜

    On the sixth month⁶, the counties of Qīngzhōu and Qúshān suffered frosts.

  • 秋七月青州雪害苗稼

    In autumn, on the seventh month⁷, Qīngzhōu suffered snowfall, harming the crops.

  • 冬十月丙辰都下地震是歲饑

    In winter, on the tenth month and bǐngchén day⁸, an earthquake occurred at the capital city. There is a famine this year.

Footnotes:

1. The second year of the Dàtǒng era is dated CE 536 February 8^th to 537 January 26^th.

2. Dàtǒng (大統) is an era name of Emperor Wén of the Western Wèi dynasty.

3. Guānzhōng (關中) does literally translate to within the passes as given by @LarsBosteen's quote, but I think it is rather inappropriate to translate proper nouns literally, regardless of the proper noun's etymology.

4. The rényín day of the first month of the third year of the Dàtóng era is dated CE 537 February 1^st.

5. Dàtóng (大同) is an era name of Emperor Wǔ of the Southern Liáng dynasty. Do not get Dàtóng (大同) mixed up with Dàtǒng (大統).

6. The sixth month of the third year of the Dàtóng era is dated CE 537 June 24^th to 537 July 22^nd.

7. The seventh month of the third year of the Dàtóng era is dated CE 537 July 23^rd to 537 August 21^st.

8. The bǐngchén day of the tenth month of the third year of the Dàtóng era is dated CE 537 December 12^th.

The main descriptions of the abnormal weather is found as mentioned in the other answers from the 北史/南史 beishi/nanshi which mentions snow in September and August respectively.

As for the highlighted quote I've managed to track it down to a passage in the 资治通鉴第一百五十七卷 Zizhi Tongjian 157th Juan (13th chapter in the Liang Dynasty sections). The original texts has the following:

是岁，魏关中大饥，人相食，死者什七八。

which translates roughly to:

AD536, Large famine in Wei, Cannibalism reported, death seven to eight in ten.

The chronicles Beishi 北史 "History of the North" and Nanshi 南史 "History of the South" have at least some of what you are looking for.

The Nanshi chronicle mentions frost and snow. This is cited in Catastrophe: An Investigation into the Origins of the Modern World by David Keys:

In July 537 China was hit by frost, while in August it snowed. The History of the Southern Dynasties recorded that “in July in Qingzhou and [another province] there was a fall of frost” and that “in August in Qingzhou there was snow,” which “ruined the crops.”

The Nanshi chronicle is also cited in the The Palgrave Handbook of Climate History:

the early seventh-century Nanshi chronicle refers to “yellow dust” that “fell like snow” in 536 and 537. In the latter year, it “filled scoops when picked up.” The dust was almost certainly Gobi sand (not volcanic ash), but this signals that 536 and 537 were unusually dry.

Keys also has the following paragraph which cites the Beishi:

“Because of drought, there was an imperial edict which ordered that in the capital [Ch’ang-an], in all provinces, commanderies and districts, one should bury the corpses,” says the Bei shi for late April to early May 535.1 “[There was] great drought. [The government] had to provide water at the city gates [of Ch’ang-an] and the hall gates [of the palace] as well as the gates of the government offices,” says the entry for late June and early July of the same year. Then in September 536, in the north Chinese “provinces of Bian, Si, Zhuo and Jian, hail fell” and there was “a great famine.” By December the situation had deteriorated to such an extent that the government had to send special inspectors “to investigate [the conditions of] the famished refugees who were roaming around north of the Yellow River.”

The next paragraph then adds:

And in Shaanxi province, “the land within the Passes,” The Annals of the Western Wei in the Bei shi state that there was “a great famine,” and that “the people practiced cannibalism and 70 to 80 percent of the population died.”

Notes on the original sources:

Beishi 北史 "History of the North" is a one-book parallel to the the official dynastic histories ( 正史) of the Northern Wei dynasty 北魏 (386-534; Weishu 魏書), its two short-lived successor dynasties of the Northern Qi 北齊 (550-577; Beiqishu 北齊書) and (Northern) Zhou 北周 (557-581; Zhoushu 周書), and the Sui dynasty 隋 (581-618; Suishu 隋書).

Nanshi 南史 "History of the South" is a one-book parallel to the the official dynastic histories (zhengshi 正史) of the Southern Dynasties 南朝 (420-589): the Liu-Song 劉宋 (420-479; Songshu 宋書), Southern Qi 南齊 (479-502; Nanqishu 南齊書), Liang 梁 (502-557; Liangshu 梁書), and Chen 陳 (557-589; Chenshu 陳書).

Note on the secondary source (David Keys)

David Keys' book is somewhat controversial and received mixed reviews. However, he does at least cite sources, but this does not mean his overall thesis (and the way he used those sources) is validated.