AT the school gates on a Monday afternoon, I watch my 10-year-old son, Louis, pick up a discarded anonymous green jumper, and sniff it. “That's Ryan's,” he says. Louis has long had a particularly finely-tuned nose; since he started school he has been able to identify the clothing of class members by scent alone. “I can tell with even people from other classes,” he says. “If I know them well enough, I can tell.”

But when I ask him to describe more fully what particular items smell like he is often baffled by my request. “Max's trousers smell like Max,” he says. “School just smells like school.”

“Some of my friends' rooms,” he says now, venturing to be more specific, “smell quite sweet.” When I talk with my son about what his highly-tuned nose is identifying, he is often at a loss for words, despite being highly articulate on other subjects,

But, as Barney Shaw writes in The Smell Of Fresh Rain, an exploration of our olfactory sense, Louis is not alone in this. When it comes to scent, most of us resort to tautologies like “that bracken smells brackenish”.

“Smells are inarticulate,” observes Shaw. “We struggle to understand what they mean. We struggle to put them into words. It is common to experience what psychologists call a tip-of the-nose effect: we sniff something; we have a fleeting sensation that we almost recognise the smell: we cannot quite pin it down; and then we breathe in a new breath and a new smell.”

Shaw's book interests me, because I sometimes wonder if my children's experience of smell is very different from my own. A former civil servant, Shaw was triggered to write it when his 32-year-old, blind son asked: “What is the smell of three in the morning?”

His son, Nick, has severe learning difficulties but exceptional musical talent and an “unusual mind”, in his father's words . Shaw surmised that the smell Nick was talking about could be real, or could be a dream smell, or could even have something to do with his epilepsy. To try to find out, he took him on a 3am walk around London, and the answer he came back with was that, for Nick, 3am smelt of fox – the fox that breathed in his bad dreams.

Shaw's book is a welcome attempt to articulate a way of experiencing the world that is often not properly expressed.

Smell is strongly linked with memory and emotion. This is partly, as Shaw points out, because of the location of the brain's olfactory centre, situated “close to the emotional centres of the brain and its structures for laying down long-term memories”.

The olfactory bulb, the point in our brain where receptor nerves from the nose converge, is part of what's called “the limbic system”, a collection of structures which support emotions, behaviour motivation and long-term memory. “This very close connection," he writes, "probably explains the unusually evocative character of smells. It probably explains, too, why our immediate response to smells is to like or to be disgusted by them.”

This partly explains what has become known as “the madeleine effect”, named after a mesmerising passage in Marcel Proust's novel A La Recherche Du Temps Perdu. What Proust described was a moment in which the taste and smell of a small French cake, a madeleine, threw him back to his childhood in provincial France, and his visits to his Aunt Leonie, who, up in her bedroom, would offer him a madeleine that had been dipped in lime-flower herbal tea.

In the novel, Proust observes that “the smell and taste of things remained poised a long time, like souls, ready to remind us, waiting and hoping for their moment, amid the ruins of all the rest; and bear unfaltering, in the tiny and almost impalpable drop of their essence, the vast structure of recollection”.

Our heads, in other words, are filled with scents from our past, and, in particular, our childhood, linked to memories often otherwise buried. Shaw describes how on a summer afternoon a couple of years ago, a smell transported him 40 to 50 years back in time, “instantly and vividly at a single sniff”. “I stepped outside to the smell of fresh rain. A summer shower was falling. Fat rain drops landed on warm tarmac and earth. The gutters were running with water, in which unusually fat bubbles wobbled towards the drain ... The air smelled of rain on newly moistened earth and leaves, a smell which instantly transported me to my childhood.”

He was transported back to a suburban street where his parents had their house, and a similar scene in which the rain was causing unusually large bubbles to run down a gutter, and recalled “the sensation of being seven years old, close to the wavering bubbles, with bare knees and scratchy woollen clothes”.

As we age, Shaw writes, “the smell memories endure. By the end of our lives, our heads are full of extinct smells. My head is full of the extinct smells of my childhood, and the heads of the next generation will be full of smells from their childhoods that in their turn will have disappeared from ordinary life, and will be preserved only in memory”.

It's this next generation, my children, Louis, 10, and Max, eight, I find myself particularly interested in. For it's right now that they are laying down probably their most potent smell-linked memories, drawing them out of the air of the city that surrounds them.

Because their world looks and smells very different from that of my own childhood, it's likely that when they grow up, their madeleine moments will be very different from mine. I grew up on a farm in the countryside; they breathe the air of the city. In fact, the smells that already dominate their lives tell a great deal about how the world has changed, and how different their childhoods are from my own. Daily walks take them past the spicy hum of the Indian restaurant, the heady whiff of sometimes over-filled rubbish bins, a pavement pizza of splattered vomit, the fruity whiff of the pub, front gardens full of rosemary bushes and geraniums.

I suspect their smell memories are also destined to be more multi-cultural. No doubt they will include the scents of their Sikh childminder's home, in which they have spent many hours over the years. “I really like that smell, the curry smell,” says Max. “Makes me really want a chapati.”

It's a far cry from my childhood. The odours that coloured the first 13 years of my life were primarily agricultural. Damp wool, the breath of cows and ponies, the whiffs of chicken coop and old hay, the stench of a dead sheep and rusting machinery, the sweet reek of cow pats. These are smells that don't often drift around the city, though occasionally I am hit by a blast of one of them. A rotten potato in a supermarket bag can cast me back to the stink of my childhood job of tattie-sorting, and I'm there again in that big barn, wearing over-sized muddied gloves, sifting out the putrefied tubers from the good ones.

Above all, though, it is the smell of animals that gets me. When, recently, after years of prevaricating about whether to get a cat, we finally got a kitten, it was her scent that floored me. I had forgotten that warm cakeiness and all I wanted to do was keep sticking my nose into her soft, black fur and taking it in, revelling in the memory rush of cats from my own childhood.

Our cat, in fact, forms an odorous link between my childhood and that of my children. When I ask them what their favourite smells are, they both mention her. Max sinks back into his bed, smiling, and says: “Cats ... but not the cat food or the cat poo. Yeuuurk.”

What does she smell of? I ask. “Uncle Thomas and sweeties,” says my youngest son, Max.

“Uncle Thomas?” I say, trying to imagine what the link might be between my brother, who does not own a cat, and my kitten. “Well, she doesn't smell that much of him now, but she used to.”

“She's smelly,” says Louis. “But nice smelly. Kind of sweet.”

But this particular aromatic appreciation is not the only one we share. My sons also rave over a favourite scent of mine, the smell of books. “I like new book smell,” says Louis.

“I like the old ones,” considers Max, “that are like 1950s or something. The ones that are all dusty and stuff. The really dusty ones.”

“You mean including Dad's really, really, really ripped old dictionary?”

I know what they mean. The smell of old books is a madeleine-like trigger for me, one that has me crouched in the corner of Grandmother's living room, where a small glass-fronted cabinet stood, which I would wedge open and sit against, pulling out old leathery Walter Scott novels and Alistair MacLean paperbacks.

It also takes me to Paris, aged 19, to Shakespeare And Company, the bookshop I worked and lived in for a summer, whose dank, forgotten, aromatic shelves I think of every time I enter a secondhand bookstore, and which summon up memories of cockroaches and pancakes and a bespectacled American boy I had a fling with.

When my children describe such pleasures, I can't help but wonder if some of the smells they are enjoying will still be commonplace when they are older. Will books be rare objects, only occasionally encountered? Will the phony strawberry shampoo smell my son Max likes to sniff, fall out of fashion, be perceived as too fake?

Shaw, in his book, lists some already extinct smells. “The harsh aroma of French and Balkan cigarettes; the sad stink of boiled cabbage in grim lodgings, the eggy stench of fluid for cleaning silver and of ladies' hair remover; fishy smells of bad electrical wiring, given off by an ancient plastic called Bakelite.”

“The old smells,” he writes, “of dentists are now extinct – a clove scent to disguise the foul stink of the dentists' drill (that smelled like burned hair).”

I can't help but wonder too, if a smell already disappearing from our public spaces, but still present in my own family, will join the list of those extinct. For many of my generation, a distinctive scent of childhood was cigarette smoke. Yet a massive cultural shift has seen it start to disappear – though not from our home, where it lurks in the yard, a spot where the children's father goes to “check the barometric pressure”. For my kids, no doubt, the smell will carry memories, though for many, even of their age, the key smell may well be a particular scent of vape.

Meanwhile, there are other smells that I've no doubt will have meaning for my children in a way they will never have for me. I ask what, for them, is the worst smell. “Seafield,” Max says. “Awwrgg ... urrghh.” He is referring to the odour that periodically comes off the local sewage treatment centre, a smell whose rubbery, faecal, eye-watering tones, are so offensive that one friend told me she cried when she took her children to school and smelt it.

“Here's another thing I don't like,” he says, wincing. “The car. It smells like rotten dust.”

A further source of howling disgust, is certain school dinners. “The chicken wrap smell is just horrible,” says Louis, grimacing.

“And the school curry,” says Max, “ Yeuurgh chicken wrap.”

Their reactions to such odours are extreme, often accompanied by scrunched up faces and contorted retching poses. They remind me of an observation, by Professor Thomas Hummel of the Taste and Smell Clinic of the University of Dresden, of how emotional our responses to smell are. “As soon as we perceive an odour, we like or we dislike it," he said. "It always has an emotional quality. We see a house on a hill or we hear a dog barking in the dark – much of the time we perceive these things without emotion. But we smell rotten eggs and everyone has an immediate emotional reaction.”

Barney Shaw reflects upon this: “Smell is more emotional and more evocative than our other senses. Not only is it more emotional, but the emotions that it stirs up are a peculiar lot.”

I can't help but wonder how my children's sense of smell may change. My own has undoubtedly altered over my lifetime, intensifying during pregnancy, blossoming when my children were babies, so that, in a diary letter I wrote to my youngest, I wrote swooningly of the smell of his cradle cap and declared of his nappies: “You are a kitchen of sweet delights. Your confections are often like a liquid caramel, warm from the pan. There even seems a whiff of burnt sugar in the air when you poo.”

Smell has often been belittled. German philosopher Immanuel Kant, for instance, viewed it as the “least rewarding” and “most dispensable” of the senses. Sigmund Freud, Shaw points out, “asserted that the more civilised a society, the less attention is paid to smell”. Sometimes it seems as if this sense is further withering in importance as we enter the digital era. Nowadays what's prized is the directness and immediacy of the image, or of words, preferably delivered in no more than 140 characters, with a punchy message.

Yet even as smell seems to be fading in value, a brave new synthetic world of odours is developing, in which real smells are masked by fake concoctions, of vanilla, spice, freshly baked bread, and other comforts.

“Ambient scenting” via fragrance diffusers, as Shaw observes, is now in vogue whether in the retail world or at events like weddings and film previews.

We ought not to lose our connection with the real smells that tell us about the true nature of our environment. For, as Shaw contends, smell is a key, revealing and intimate sense. “The molecules that convey smell come from the inner substance of the things that smell. It's a closer contact with the substance of things than our other senses afford”.

In a world where we worry that too much is fake – it can be an honest connection not just with our present environment, but with our elusive, personal pasts.

The Smell Of Fresh Rain by Barney Shaw is published by Icon Books